AN INDIVIDUAL LIFE HISTORY MODEL FOR HEART DISEASE, …andrewc/actuarial/chatterjee_thesis.pdf · DISEASE, STROKE AND DEATH: STRUCTURE, PARAMETERISATION AND APPLICATIONS. By Tushar

AN INDIVIDUAL LIFE HISTORY MODEL FOR HEART

DISEASE, STROKE AND DEATH: STRUCTURE,

PARAMETERISATION AND APPLICATIONS.

By

Tushar Chatterjee

Submitted for the Degree of

Doctor of Philosophy

at Heriot-Watt University

on Completion of Research in the

School of Mathematical and Computer Sciences

January 2008.

This copy of the thesis has been supplied on the condition that anyone who consults

it is understood to recognise that the copyright rests with its author and that no quo-

tation from the thesis and no information derived from it may be published without

the prior written consent of the author or the university (as may be appropriate).

I hereby declare that the work presented in this the-

sis was carried out by myself at Heriot-Watt University,

Edinburgh, except where due acknowledgement is made,

and has not been submitted for any other degree.

Tushar Chatterjee (Candidate)

Professor Howard R. Waters (Supervisor)

Professor Angus S. Macdonald (Supervisor)

Date

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Contents

Abstract xiv

Acknowledgements xv

Introduction 1

1 Background 3

2 Cardiovascular diseases, their risk factors and mortality 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 The disease process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Some forms of cardiovascular diseases . . . . . . . . . . . . . . 82.2.2 Factors affecting cardiovascular diseases . . . . . . . . . . . . 9

2.3 Risk factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Insulin resistance syndrome . . . . . . . . . . . . . . . . . . . 132.3.2 Hypercholesterolaemia . . . . . . . . . . . . . . . . . . . . . . 132.3.3 Hypertension . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.4 Diabetes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.5 Body mass index . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Data 223.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Data requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Different sources of data . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.1 Cohort study data . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Framingham Cohort Data . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.1 Availability and classification of data . . . . . . . . . . . . . . 313.4.2 Treatment of missing data . . . . . . . . . . . . . . . . . . . . 40

3.5 Estimation of transition intensities . . . . . . . . . . . . . . . . . . . 413.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4 The Model 514.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2 Structure of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Parameterisation of the model . . . . . . . . . . . . . . . . . . . . . . 55

4.3.1 Generalised Linear Models . . . . . . . . . . . . . . . . . . . . 57

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4.3.2 Smoothed transition intensities . . . . . . . . . . . . . . . . . 624.3.3 Modelling second and subsequent MI and HS . . . . . . . . . 704.3.4 Modelling sudden death . . . . . . . . . . . . . . . . . . . . . 73

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5 Occupancy Probabilities 785.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Calculation of occupancy probabilities . . . . . . . . . . . . . . . . . 79

5.2.1 Kolmogorov Forward Equations . . . . . . . . . . . . . . . . . 795.2.2 Solutions to the Kolmogorov Forward Equations . . . . . . . . 80

5.3 A model consistent with English prevalence . . . . . . . . . . . . . . 815.3.1 Health Survey for England . . . . . . . . . . . . . . . . . . . . 815.3.2 Adjustments to the model . . . . . . . . . . . . . . . . . . . . 825.3.3 Futher adjustments . . . . . . . . . . . . . . . . . . . . . . . . 1015.3.4 Patterns in English Prevalence . . . . . . . . . . . . . . . . . . 102

5.4 Accuracy in obtaining transition intensities . . . . . . . . . . . . . . . 1025.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Treatments 1126.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.2 Treatment for conditions . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.2.1 Cholesterol-lowering drugs . . . . . . . . . . . . . . . . . . . . 1136.2.2 Blood pressure lowering drugs . . . . . . . . . . . . . . . . . . 1146.2.3 Other drugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.3 Statins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.3.1 Classes of statins . . . . . . . . . . . . . . . . . . . . . . . . . 1156.3.2 Effect on cholesterol . . . . . . . . . . . . . . . . . . . . . . . 1156.3.3 Effect on cardiovascular diseases . . . . . . . . . . . . . . . . . 1166.3.4 Adverse effects of statins . . . . . . . . . . . . . . . . . . . . . 118

6.4 Treatment recommendations . . . . . . . . . . . . . . . . . . . . . . . 1186.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186.4.2 Incorporating the recommendations in our model . . . . . . . 1216.4.3 Proportion of population treated . . . . . . . . . . . . . . . . 121

6.5 Model for treatment effects . . . . . . . . . . . . . . . . . . . . . . . . 1236.5.1 Model for treatment recommendations based on risk . . . . . . 1246.5.2 Model for treatment recommendations based on age . . . . . . 1256.5.3 Uncertainty in treatment effects . . . . . . . . . . . . . . . . . 132

6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7 Modelling and forecasting Body Mass Index 1377.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1377.2 Increasing prevalence of obesity . . . . . . . . . . . . . . . . . . . . . 1377.3 Models for BMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.3.1 Models with calendar time effect . . . . . . . . . . . . . . . . 1397.3.2 Comments on the models . . . . . . . . . . . . . . . . . . . . . 144

7.4 Applications of these models . . . . . . . . . . . . . . . . . . . . . . . 1457.4.1 Comparison with other studies . . . . . . . . . . . . . . . . . . 154

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7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

8 Effect of changes in smoking behaviour 1568.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1568.2 Effect of smoking ban in public places . . . . . . . . . . . . . . . . . . 157

8.2.1 Smoking ban . . . . . . . . . . . . . . . . . . . . . . . . . . . 1578.3 Effect of giving up smoking . . . . . . . . . . . . . . . . . . . . . . . 159

8.3.1 Risk factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1598.3.2 Cardiovascular diseases . . . . . . . . . . . . . . . . . . . . . . 1598.3.3 Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

8.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1638.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

9 Conclusions and further research 1719.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1719.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1729.3 Further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

A Table numbers describing the parameters for the model 175

B Distribution of the English population in 1994 and 2003 176

C Expected values and variance-covariance matrices for the parame-ters estimated from the Framingham cohort data. 179

References 208

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List of Tables

3.1 Summary statistics for the Framingham data sets. . . . . . . . . . . . 29

3.2 Number of individuals at each examination. . . . . . . . . . . . . . . 32

3.3 Categories of body mass index. . . . . . . . . . . . . . . . . . . . . . 35

3.4 Categories of hypercholesterolaemia. . . . . . . . . . . . . . . . . . . 36

3.5 Categories of hypertension. . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6 Categories of diabetes status. . . . . . . . . . . . . . . . . . . . . . . 38

3.7 Categories of smoking status. . . . . . . . . . . . . . . . . . . . . . . 38

3.8 Relationship between significant events. . . . . . . . . . . . . . . . . . 39

3.9 Summary of the data available in the Framingham data sets. . . . . . 49

3.10 Code representing the risk profile . . . . . . . . . . . . . . . . . . . . 50

3.11 Risk profile of individual 1 in the OS data . . . . . . . . . . . . . . . 50

4.12 Modifiable risk factors. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.13 Results from the first step of the GLM process for transition fromcategory 2 to category 3 of hypertension. . . . . . . . . . . . . . . . . 61

4.14 Results from the last step of the GLM process for transition fromcategory 2 to category 3 of hypertension. . . . . . . . . . . . . . . . . 61

4.15 ANOVA of the accepted model for transition from category 2 to cat-egory 3 of hypertension. . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.16 Parameters for the models for body mass index. . . . . . . . . . . . . 65

4.17 Parameters for the model for hypertension. . . . . . . . . . . . . . . . 66

4.18 Parameters for the models for hypercholesterolaemia. . . . . . . . . . 67

4.19 Parameters for the models for diabetes. . . . . . . . . . . . . . . . . . 67

4.20 Parameters for the models for the first diagnosis of IHD or stroke. . . 69

4.21 Parameters for the model for mortality. . . . . . . . . . . . . . . . . . 75

4.22 Parameters for the models for the second and subsequent Events. . . 76

4.23 Probability of sudden death following MI and HS consistent with theEnglish population. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.24 Significant risk factors. . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.25 Parameters consistent with the English population for the models forbody mass index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.26 Parameters consistent with the English population for the model forhypertension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.27 Parameters consistent with the English population for the models forhypercholesterolaemia. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.28 Parameters consistent with the English population for the models fordiabetes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

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5.29 Parameters consistent with the English population for the models forthe first diagnosis of IHD or stroke. . . . . . . . . . . . . . . . . . . . 108

5.30 Parameters consistent with the English population for the models forthe second and subsequent events. . . . . . . . . . . . . . . . . . . . . 109

5.31 Probability of sudden death following MI and HS consistent with theEnglish population. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.32 Parameters consistent with the English population for the model formortality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.33 Results of calculations using simulated parameters. . . . . . . . . . . 1116.34 Standard dosage for different statins. . . . . . . . . . . . . . . . . . . 1166.35 Percentage reduction in risk of fatal and non-fatal MI by duration of

treatment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.36 NCEP guidelines regarding levels at which to consider treatment. . . 1196.37 Proportion treated at each age based on different treatment recom-

mendations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.38 Percentage treated at each age based on their risk profile starting at

age 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.39 Effect of treatment with statins based on risk profile on expected

future lifetime and expected future “Event Free” lifetime. . . . . . . . 1256.40 Effect of treatment with statins on expected future lifetime and ex-

pected future “Event Free” lifetime from age 20 by age of treatment. 1266.41 Effect of treatment with statins on expected future lifetime and ex-

pected future “Event Free” lifetime for different categories of the En-glish population. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.42 Effect of treatment with statins on expected future lifetime and ex-pected future “Event Free” lifetime for different categories of BMI. . . 130

6.43 Effect of treatment with statins on expected future lifetime and ex-pected future “Event Free” lifetime for individuals with different riskprofiles from age 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.44 Percentage reduction in risk by duration of treatment–non standarddose scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.45 Effect of treatment with statins on expected future lifetime and ex-pected future “Event Free” lifetime for individuals with different riskprofiles from age 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6.46 Effect of treatment from age 20 using fixed parameters estimatedfrom the data and simulated parameters sampled from the adjustedasymptotic distribution of the corresponding estimates. . . . . . . . 135

6.47 Effect of treatment from age 50 using fixed parameters estimatedfrom the data and simulated parameters sampled from the adjustedasymptotic distribution of the corresponding estimates. . . . . . . . . 136

7.48 The changing prevalence of BMI in England between 1994 and 2003. 1437.49 Actual and modelled prevalence of obesity. . . . . . . . . . . . . . . . 1477.50 Forecasts of obesity in England in 2010. . . . . . . . . . . . . . . . . 1487.51 Expected future lifetime and prevalence of diabetes, hypertension and

IHD/stroke – males. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.52 Expected future lifetime and prevalence of diabetes, hypertension and

IHD/stroke – females. . . . . . . . . . . . . . . . . . . . . . . . . . . 150

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7.53 Expected future lifetime and prevalence of diabetes, hypertension andIHD/stroke, starting at age 20 with given BMI for never–smoked.Figures in brackets are the corresponding values when BMI does notchange over lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

7.54 Expected future lifetime and prevalence of diabetes, hypertension andIHD/stroke, starting at age 20 with given BMI for current smokers.Figures in brackets are the corresponding values when BMI does notchange over lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

8.55 Prevalence of smoking (%) in Great Britain. Source: Rickards et al.(2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

8.56 Percentages of smokers and ex-smokers in 2003 in Great Britain,classified by age at which they started smoking regularly. Source:Rickards et al. (2004). . . . . . . . . . . . . . . . . . . . . . . . . . . 158

8.57 Revised parameters for the models consistent with the English pop-ulation for the first diagnosis of IHD or stroke. . . . . . . . . . . . . . 165

8.58 Relative risk of mortality for different smoking profiles. Source:Kawachi et al. (1993) . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.59 Revised parameters consistent with the English population for themodel for mortality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

8.60 Effect on lifetime on giving up smoking at different ages. . . . . . . . 168

8.61 Effect on prevalence on giving up smoking at different ages. . . . . . . 169

A.62 Summary of tables describing the transition intensities. . . . . . . . . 175

B.63 Dynamic risk factor profile (percentages) in England in 1994. . . . . . 177

B.64 Dynamic risk factor profile (percentages) in England in 2003. . . . . . 178

C.65 Notation used in tables describing the expected values and variance-covariance between parameters. . . . . . . . . . . . . . . . . . . . . . 180

C.66 Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of BMI. . . . . . . . . . . . . 181

C.67 Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 2 of BMI for smoking: Current–ex.181

C.68 Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 2 of BMI for smoking: Base caseand ex–current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

C.69 Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 3 of BMI for smoking: Current–ex.181

C.70 Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 3 of BMI for smoking: Base caseand ex–current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182




C.74 Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 1 of BMI for smoking: Ex–current.182

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C.75 Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 1 of BMI for smoking: Base caseand current–ex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183


C.77 Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of hypertension. . . . . . . . . 184






C.83 Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of hypercholesterolaemia. . . . 189






C.89 Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of diabetes. . . . . . . . . . . 193

C.90 Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 0 of diabetes. . . . . . . . . . . 193

C.91 Expected values and variance–covariances for parameters of transitionintensity to MI as the first event. . . . . . . . . . . . . . . . . . . . . 194

C.92 Expected values and variance–covariances for parameters of transitionintensity to MI as the first event (contd.). . . . . . . . . . . . . . . . . 195

C.93 Expected values and variance–covariances for parameters of transitionintensity to AP as the first event. . . . . . . . . . . . . . . . . . . . . 196

C.94 Expected values and variance–covariances for parameters of transitionintensity to CI as the first event. . . . . . . . . . . . . . . . . . . . . . 197

C.95 Expected values and variance–covariances for parameters of transitionintensity to TIA as the first event. . . . . . . . . . . . . . . . . . . . . 198

C.96 Expected values and variance–covariances for parameters of transitionintensity to HS as the first event. . . . . . . . . . . . . . . . . . . . . 199

C.97 Expected values and variance–covariances for parameters of transitionintensity to HS following a MI. . . . . . . . . . . . . . . . . . . . . . 199

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C.98 Expected values and variance–covariances for parameters of transitionintensity to MI following an AP. . . . . . . . . . . . . . . . . . . . . . 199

C.99 Expected values and variance–covariances for parameters of transitionintensity to HS following an AP. . . . . . . . . . . . . . . . . . . . . . 200

C.100Expected values and variance–covariances for parameters of transitionintensity to MI following a CI. . . . . . . . . . . . . . . . . . . . . . . 200

C.101Expected values and variance–covariances for parameters of transitionintensity to MI following a TIA. . . . . . . . . . . . . . . . . . . . . . 200

C.102 Expected values and variance–covariances for parameters of transi-tion intensity to HS following a TIA. . . . . . . . . . . . . . . . . . . 200

C.103 Expected values and variance–covariances for parameters of transi-tion intensity to MI following a HS. . . . . . . . . . . . . . . . . . . . 200

C.104 Expected values and variance–covariances for parameters of proba-bility of sudden death following an MI. . . . . . . . . . . . . . . . . . 201

C.105 Expected values and variance–covariances for parameters of proba-bility of sudden death following an HS. . . . . . . . . . . . . . . . . . 201

C.106 Expected values and variance–covariances for parameters of long–term mortality transition intensity. . . . . . . . . . . . . . . . . . . . 202

C.107 Expected values and variance–covariances for parameters of long–term mortality transition intensity (contd.). . . . . . . . . . . . . . . 203





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List of Figures

3.1 Life history of individual 1 in the OS data. . . . . . . . . . . . . . . . 45

3.2 Transition intensities calculated from Framingham cohorts of tran-sition from hypercholesterolaemia category 1 to category 2 for indi-viduals who have never smoked, have lowest categories of diabetes,hypertenstion, are lightweight and have not been diagnosed with anysignificant event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3 Transition intensities calculated from Framingham cohorts of transi-tion from hypertension category 2 to category 1 for individuals whohave never smoked, have lowest categories of diabetes, hypercholes-terolaemia, are lightweight and have not been diagnosed with anysignificant event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4 Transition intensities calculated from Framingham cohorts of tran-sition from diabetes category 0 to category 1 for females, who havenever smoked, have category 1 of hypercholesterolaemia, category 1of hypertenstion and have not been diagnosed with any significantevent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 Individual life history model terminating in death. . . . . . . . . . . . 56

4.6 Relative risks of mortality for selected ages and each category of BMI. 71

5.7 Prevalence rates of male individuals with lightweight, from HSE(2003) and those calculated from the model for different smokingprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.8 Prevalence rates of male overweight individuals, from HSE (2003) andthose calculated from the model for different smoking profiles. . . . . 86

5.9 Prevalence rates of male obese individuals, from HSE (2003) and thosecalculated from the model for different smoking profiles. . . . . . . . 87

5.10 Prevalence rates of female individuals with lightweight, from HSE(2003) and those calculated from the model for different smokingprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.11 Prevalence rates of female overweight individuals, from HSE (2003)and those calculated from the model for different smoking profiles. . 88

5.12 Prevalence rates of female obese individuals, from HSE (2003) andthose calculated from the model for different smoking profiles. . . . . 88

5.13 Prevalence rates of blood pressure for males, from HSE (2003) (SBP≥140 mmHg and DBP ≥90 mmHg) and those calculated from themodel (SBP ≥140 mmHg and DBP ≥90 mmHg) for different smokingprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

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5.14 Prevalence rates of blood pressure for males, from HSE (2003) (SBP≥160 mmHg and DBP ≥95 mmHg) and those calculated from themodel (SBP ≥160 mmHg and DBP ≥100 mmHg) for different smok-ing profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.15 Prevalence rates of blood pressure for females, from HSE (2003) (SBP≥140 mmHg and DBP ≥90 mmHg) and those calculated from themodel (SBP ≥140 mmHg and DBP ≥90 mmHg) for different smokingprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.16 Prevalence rates of blood pressure for females, from HSE (2003) (SBP≥160 mmHg and DBP ≥95 mmHg) and those calculated from themodel (SBP ≥160 mmHg and DBP ≥100 mmHg) for different smok-ing profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.17 Prevalence rates of cholesterol level for males, from HSE (2003) (totalcholesterol ≥5 mmol/l) and those calculated from the model (totalcholesterol ≥5.17 mmol/l) for different smoking profiles. . . . . . . . . 93

5.18 Prevalence rates of cholesterol level for males, from HSE (2003) (totalcholesterol ≥6.5 mmol/l) and those calculated from the model (totalcholesterol ≥6.66 mmol/l) for different smoking profiles. . . . . . . . . 93

5.19 Prevalence rates of cholesterol level for females, from HSE (2003)(total cholesterol ≥5 mmol/l) and those calculated from the model(total cholesterol ≥5.17 mmol/l) for different smoking profiles. . . . . 94

5.20 Prevalence rates of cholesterol level for females, from HSE (2003)(total cholesterol ≥6.5 mmol/l) and those calculated from the model(total cholesterol ≥6.66 mmol/l) for different smoking profiles. . . . . 94

5.21 Prevalence rates of diabetic males, from HSE (2003) and those calcu-lated from the model for different smoking profiles. . . . . . . . . . . 95

5.22 Prevalence rates of diabetic females, from HSE (2003) and those cal-culated from the model for different smoking profiles. . . . . . . . . . 96

5.23 Prevalence rates of IHD among males, from HSE (2003) and thosecalculated from the model for different smoking profiles. . . . . . . . 98

5.24 Prevalence rates of IHD among females, from HSE (2003) and thosecalculated from the model for different smoking profiles. . . . . . . . 98

5.25 Prevalence rates of stroke among males, from HSE (2003) and thosecalculated from the model for different smoking profiles. . . . . . . . 99

5.26 Prevalence rates of stroke among females, from HSE (2003) and thosecalculated from the model for different smoking profiles. . . . . . . . 99

5.27 Probability of death for males, from ELT15 and those calculated fromthe model for different smoking profiles. . . . . . . . . . . . . . . . . 100

5.28 Probability of death for females, from ELT15 and those calculatedfrom the model for different smoking profiles. . . . . . . . . . . . . . 101

7.29 Prevalence of obesity for males in England. . . . . . . . . . . . . . . 138

7.30 Prevalence of obesity for females in England. . . . . . . . . . . . . . 139

7.31 Prevalence of obesity for males in the Framingham Heart Study, Off-spring & Spouses data. . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.32 Prevalence of obesity for females in the Framingham Heart Study,Offspring & Spouses data. . . . . . . . . . . . . . . . . . . . . . . . . 141

xii

8.33 Prevalence rates of smokers in Ireland. Source: Office of TobaccoControl, Republic of Ireland. . . . . . . . . . . . . . . . . . . . . . . 159

8.34 Risk of mortality relative to never–smoked for different durations ofgiving up smoking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

xiii

Abstract

We have developed a multiple - state stochastic Markov model incorporating the fac-

tors hypertension, hypercholesterolaemia, diabetes, body mass index and the events

ischaemic heart disease, stroke and death. Smoking is treated deterministically in

our model. The model is specified by transition intensities obtained from Fram-

ingham Heart Study data and adjusted using Health Survey for England data to

produce results that are consistent with the English population.

We can calculate the expected future lifetime for an individual using the model.

In terms of the expected future lifetime we have estimated the effect of treatment

with a statin, a cholesterol lowering drug that reduces the intensity of having my-

ocardial infarction and stroke. Statins can increase expected future lifetime by more

than a year for certain classes of individuals. Also current smokers have a substan-

tially reduced lifetime compared to those who never smoke and expected lifetime

increases on giving up smoking.

We have used the model to project future levels of obesity which can increase to

very high levels if present trends continue, but this is unlikely to have a substantial

effect on expected future lifetime.

Due to unavailability of suitable longitudinal data from the UK, the model was

parameterised using data from USA and adjusted to obtain results for the English

population. As a result we have been unable to measure the uncertainty in the

results for the English population directly. We have used parameter simulation to

quantify the uncertainty in the results obtained.

The results obtained in this thesis are based on the Framingham data sets and

some of the results may be affected by characteristics specific to this population.

xiv

Acknowledgements

I would like to thank my supervisors Professor Howard Waters and Professor Angus

Macdonald for their guidance and support in completing this work. They have

encouraged me for the duration of the project and have found time to discuss the

various aspects of this work. Their inputs and criticisms in this work were very

valuable.

This work was carried out while I was employed as a Research Associate at

Heriot-Watt University and funded by the Engineering and Physical Sciences Re-

search Council (EPSRC). I would also like to thank the UK Actuarial Profession for

their support and the guidance given by the Actuaries Panel on Medical Advances

(APMA). My colleagues Pradip Tapadar, Tunde Akodu, Alex Cook and Lu Li were

very helpful and a pleasure to work with.

The thesis uses data supplied by the National Heart, Lung and Blood Institute

(NHLBI) from the Framingham Heart Study. The Framingham Heart Study –

Offspring Study is conducted and supported by the NHLBI in collaboration with

the Framingham Heart Study – Offspring Study Investigators. This thesis was

not prepared in collaboration with investigators of the Framingham Heart Study

– Offspring Study and does not necessarily reflect the opinions or views of the

Framingham Heart Study – Offspring Study or the NHLBI.

I would like to thank my wife, Debarchana, for her patience, support, encourage-

ment and love which helped me in the difficult times. I dedicate this thesis to my

parents who have always encouraged me in my studies and helped me in building a

strong foundation which made this work possible.

xv

Introduction

Human life expectancy has increased in the last 20 years in the UK (see Gallop

and Baker (2006)). Among the possible medical reasons are awareness of different

diseases, medicines for their prevention and medicines for their cure. Other reasons

may be individuals’ emphasis on fitness and better quality of living. There are

factors which have been detrimental to our health, for example, sedentary lifestyle

which has increased obesity levels.

Overall the benefits to life expectancy are higher and have resulted in the in-

creased life expectancy. Advances in medical sciences and specifically in drugs for

different conditions have contributed to the improvements in life expectancy. There

are drugs to prevent and treat conditions like diabetes, hypercholesterolaemia and

hypertension which are risk factors for other conditions like heart attack, stroke,

renal diseases and eventually death.

At different points in their lifetime individuals will have different levels of glucose

or cholesterol in their blood or have different levels of blood pressure. These levels

can go down as well as up over time. In general, higher levels of these factors are

detrimental. In this thesis we will propose a model for an individual’s changes in

the levels of the different risk factors and we will also model the onset of some

cardiovascular diseases for such an individual.

We will discuss the disease process leading to the cardiovascular diseases, is-

chaemic heart disease and stroke, in Chapter 2. We describe the role played by

the different risk factors, age, sex, smoking, hypertension, hyperchoelsterolaemia,

diabetes and body mass index in the development and occurrence of these diseases.

These diseases can be fatal and we will describe the effects of these diseases and the

risk factors on mortality.

1

In Chapter 3, we describe the data used to parameterise the individual life history

model. Most of the data for the factors are recorded as continuous variables and we

describe the categorisation of the data for these factors into different groups. We

categorise the risk factors based on the categorisation described in the literature and

sometimes on the thresholds used to prescribe medication or lifestyle changes.

Chapters 4 and 5 describe the parameterisation of the multiple - state Markov

model and compare the population estimates obtained from our model for different

conditions with the population estimates for England published by the Department

of Health in the UK. We have obtained a model described by parameters estimated

from data. We check the accuracy of these estimates in Chapter 5.

In Chapter 6 we describe the changes to the model to measure the effects of

statins, a drug to lower cholesterol. We calculate the expected future lifetime and

the expected future lifetime before ischaemic heart disease, stroke or death and

compare these with the untreated model to measure the beneficial effect of treating

individuals with statins. We will measure the uncertainty in the effect of treatments

with a statin.

Chapter 7 investigates the effect of body mass index on other risk factors, car-

diovascular diseases and mortality. We develop models that are consistent with

the progression of obesity over time in England and use the models to project the

prevalence of obesity in England in the future.

Chapter 8 investigates the effect of giving up smoking on the onset of cardiovas-

cular diseases and mortality.

2

Chapter 1

Background

In this thesis we will discuss an individual life history model incorporating the

following risk factors for ischaemic heart disease and stroke – age, sex, hypertension,

hypercholesterolaemia, diabetes, smoking and body mass index.

Our model is a long-term model, and it will be helpful in determining the long-

term effects of having a particular risk profile or, specifically, having a particular

level of a risk factor at a certain age.

Medical studies have determined the effects of one risk factor on another and also

the effect of risk factors on events like myocardial infarction, stroke and mortality.

Although some of the results obtained in these studies will be comparable to the

results obtained from our model, the majority of our results are obtained using

an approach different from the ones used in these studies. The major differences

between models used in medical studies and our model are:

(i) The models used in medical studies are generally short–term. These models are

based on data from studies with 10-20 years follow-up. Studies based on the

effect of medicines are even shorter in duration.

(ii) Generally medical studies will concentrate on only one primary outcome.

(iii) Medical studies will not model the dynamics of risk factors over time, and most

of their results on the effect of some factor will be based on the baseline values

of that factor.

(iv) Medical studies do not aim to model the life history of an individual and as a

result are unable to measure long-term impacts on life expectancy.

3

Our model can be applied for a variety of purposes. We will measure the impact

of interventions using medicines assuming that the short-term effects continue over

a long term. We will also measure the long-term effects of changes in the prevalence

of risk factors on life expectancy and on the prevalence of other risk factors.

A similar model was proposed in Macdonald et al. (2005a) and Macdonald et al.

(2005b). Our model is different in several aspects:

(i) The models have different objectives. The earlier model was developed with

insurance, particularly Critical Illness insurance, applications in mind. The

current model has been designed to quantify the long term effects of treatments

and changes in lifestyle.

(ii) The earlier model used only the Original Cohort data set from the Framingham

study. The current model uses both the Original Cohort and the Offspring and

Spouses cohort data sets.

(iii) The current model allows for backward transitions between categories of the

risk factors; the earlier model did not.

(iv) For the current model, transition intensities depend on the current category of

each significant risk factor, rather than the highest ever level, as was the case

for the earlier model.

(v) Body mass index is a dynamic risk factor for the current model. It was a static

risk factor for the earlier model.

(vi) Smoking is a dynamic, though deterministic, risk factor for the current model.

It was a static risk factor for the earlier model.

(vii) The current model has a wider definition of heart disease (ischaemic heart

disease = coronary insufficiency + angina pectoris + myocardial infarction)

and stroke (stroke = transient ischaemic attack + hard stroke). The earlier

model incorporated only myocardial infarction and hard stroke.

(viii) The current model allows for multiple myocardial infarctions and hard strokes.

(ix) The current model includes mortality after ischaemic heart disease and/or

stroke.

(x) The categories for some risk factors have been updated and/or the number of

categories increased for the current model. For example, body mass index is

4

now divided into five categories rather than three.

5

Chapter 2

Cardiovascular diseases, their risk

factors and mortality

2.1 Introduction

Cardiovascular diseases are a major cause of death in the UK (see

Office of National Statistics (2006)) and throughout the world (see Mathers and

Loncar (2005)). Cardiovascular diseases are the diseases of the circulatory system,

which is made up of the organs and vessels that carry and control the blood flow to

different parts of the body. The diseases are caused by either blockage or rupture

of these vessels. We will look at the disease process in Section 2.2. We will look

at some specific cardiovascular diseases, namely ischaemic heart disease and cere-

brovascular diseases in Section 2.2.1. These diseases are multi-factorial in nature

and are affected by a variety of factors which help and accelerate the disease process.

We will look at these factors and the mechanism by which they affect the disease

process in Section 2.2.2.

In Section 2.3, we look at the individual risk factors and how they are influenced

by changes in the other risk factors. Insulin resistance syndrome is associated with

accumulation of risk factors and we investigate its effect on the risk factors in Section

2.3.1.

Finally in Section 2.4, we investigate how ischaemic heart disease, stroke and

their risk factors affect mortality.

6

2.2 The disease process

The disease process known as atherosclerosis develops over a long period of time in

various stages. Atherosclerosis can develop in our body for decades before resulting

in any significant event.

A high level of low-density-lipoprotein (LDL) is one of the most significant factors

for atherosclerosis. LDL is present in the circulating blood and consists of cholesterol

and some other proteins. Some small dense LDL molecules can move through the

endothelium, which is the protective layer present in many organs, and the arterial

walls. The endothelium in the arteries can also be viewed as a barrier between the

components of the circulating blood and the walls of the arteries. The endothelium

releases nitrous oxide, which helps in reducing the aggregation of platelets to form

blood clots and adhesion to the endothelium. Platelets are a form of blood cells

involved in blood clotting. Inside the endothelium the LDL molecules are prone

to oxidation. The oxidised LDL damages the endothelium increasing its adhesion

properties and enhances the problem by attracting more scavenger cells known as

macrophages to the area. On oxidation the LDL molecules generally get attached to

the macrophages and transform them into large foam cells. Macrophage cells also

contribute to plaque inflammation. The lipid rich foam cells die by a mechanism

known as apoptosis, which is uncontrolled cell death, depositing the lipids into the

core of the forming plaques.

The plaques can be seen at the start as small spots on the arterial walls and

they eventually develop into streaks. Arterial walls also calcify making them harder

and less elastic. The plaques protrude (outward remodelling) and obstruct blood

flow. Smooth muscle cells migrate to the endothelial cells and secrete some proteins

forming a fibrous cap over the plaques. These caps prevent the inner lipid core from

coming into contact with circulating blood. As long as the plaques are stable, they

may obstruct blood flow, but do not cause acute damage.

Macrophages secrete metalloproteinases, a group of enzymes responsible for mak-

ing and breaking body tissues and removing dead tissues, which are responsible for

weakening these fibrous caps. Some of the fibrous caps can become unstable and

prone to rupture. The plaques that are at greater risk of rupture are generally large,

7

have large lipid cores, have inflammatory cells like foam cells, exhibit outward re-

modelling and have thin caps. On rupture, the circulating blood comes into contact

with the lipid core and coagulates forming a blood clot. This is enhanced by the fact

that endothelial cells at the site are not functioning properly and cannot reduce the

platelet aggregation, which causes the clot to form. These clots can obstruct blood

flow at the site or can be dislodged and carried to a different part of the circulatory

system obstructing blood flow at a different site. The obstruction of blood flow at

different parts of the body causes different forms of cardiovascular diseases. More

details about the disease process can be found in Khachigian (2005) and Stanner

(2005).

2.2.1 Some forms of cardiovascular diseases

In the previous section we have seen how the disease process progresses over time

resulting in cardiovascular diseases. Now we look at some of the clinical manifesta-

tions of this disease process. The events of particular interest to us are ischaemic

heart disease (IHD) and cerebrovascular disease. IHD is also known as coronary

heart disease (CHD) or coronary artery disease (CAD).

There are different forms of IHD (I20-I25 of the International Classification of

Diseases, Version 10) which include stable angina, unstable angina and myocardial

infarction (MI). The extent of blockage and the lack of blood supply to the heart

results in the different forms of IHD. The deficiency in the blood supply can cause

chest pains or breathlessness on exertion. This can happen without the death of

any heart muscle and is known as angina pectoris. Angina with stability in the

frequency and duration of these chest pains is referred to as stable angina. But

it is possible to have acute chest pain over a prolonged period even in the resting

state, and this is known as unstable angina. Myocardial infarction is the death of

some portion of heart muscle due to lack of blood supply. In the extreme case of

myocardial infarction, sudden death can occur due to heart failure. The condition

“unstable angina” is sometimes referred to as “coronary insufficiency”, for example,

in the Framingham Study.

There are different forms of cerebrovascular diseases which include hard stroke

8

(I60-I69 of the International Classification of Diseases, Version 10) and transient

ischaemic attack (G45 of the International Classification of Diseases, Version 10).

Blood clots are a stage in the disease process mentioned above. Sometimes these

blood clots can dislodge themselves from where they have formed and can move

with the circulating blood and lodge themselves in the arteries in the brain. This

significantly reduces blood flow to the brain and can impair brain function. This

form of hard stroke is known as ischaemic stroke. When the arteries supplying blood

to the brain rupture, the result is haemorrhagic stroke. The impaired brain function

in a hard stroke lasts for more than 24 hours or until sudden death, if earlier. If the

brain impairment lasts for less than 24 hours due to insufficient supply of blood to the

brain, it is classified as transient ischaemic attack. We will refer to cerebrovascular

disease as stroke in this thesis.

2.2.2 Factors affecting cardiovascular diseases

There are several conventional risk factors (see Table 1.1 in Stanner (2005)) and

emerging risk factors (see Table 1.2 in Stanner (2005)) that are associated with

atherosclerosis and cardiovascular diseases. Details of the effect of these risk factors

on cardiovascular diseases can be found in Stanner (2005). We will consider some

of these risk factors.

Hypercholesterolaemia

Hypercholesterolaemia is a condition defined by high concentrations of cholesterol

in the blood. Total serum cholesterol can be divided into three components,

HDL (high-density-lipoprotein), LDL(low-density-lipoprotein) and VLDL(very-low-

density-lipoprotein). We have seen earlier that LDL cholesterol that carries choles-

terol from the liver to the different parts of the body has a significant effect in

atherosclerosis. HDL on the other hand is the good cholesterol, which is responsible

for excretion of cholesterol from our body. Thus, low levels of HDL are a risk factor

for cardiovascular diseases. Details can be found in Stanner (2005).

9

Hypertension

Another major risk factor for cardiovascular diseases is hypertension, which is having

high blood pressure. When the blood flows with a higher force, it can cause physical

damage to the endothelial cells. It is also associated with decreased endothelial

function like reduced production of nitric oxide by the endothelial cells. Details can

be found in Stanner (2005).

Diabetes

The endothelium of the arteries does not function properly in individuals diagnosed

with diabetes. Diabetes can make the arterial walls less elastic. Diabetes also

contributes to atherosclerosis through insulin resistance syndrome by changing the

lipid characteristics. Details can be found in Stanner (2005).

Smoking

Smoking can also affect the endothelial cells by changing their structure and pro-

ducing chemicals that are harmful to the endothelium. Nicotine increases the in-

flammatory cells and helps in the oxidation process. Cigarette smoke contains large

amounts of nitrogen dioxide, which produces a highly oxidising environment to which

the LDL is exposed and eventually undergoes oxidation in the presence of catalysts

like copper and iron ions.

For the harmful effects of smoking on cardiovascular diseases we refer to

Humphries et al. (2001):

(a) Smoking damages the arterial walls directly and promotes the disease process

by helping the accumulation of certain molescules to the arterial walls.

(b) Smoking increases insulin resistance and lipid intolerance and helps in the pro-

duction of small dense LDL-cholesterol.

(c) Lung damage caused due to smoking can lead to increased risk of thrombosis.

(d) Smokers have less antioxidants in their blood and can favour oxidation of LDL.

The literature contains the following, not wholly consistent, points in relation to

the effect of smoking on IHD and stroke:

10

(i) The effects of smoking are both long and short term. Giving up smoking reduces

the short-term effects immediately, but the long-term effect due to atheroscle-

rotic damage continues even after quitting. See Negri et al. (1994) and Light-

wood and Glantz (1997).

(ii) The odds ratio of acute myocardial infarction for current smokers relative to

non-smokers is 3.4. See Negri et al. (1994).

(iii) The odds ratios for myocardial infarction or coronary death for current smokers

was 2.71 for men and 4.70 for women, compared to individuals who have never

smoked. See Dobson et al. (1991).

(iv) Cook et al. (1986) state that “ ... there was no trend in risk of IHD or stroke

with the number of cigarettes smoked per day”. This view is consistent with

Lightwood and Glantz (1997), who modelled the effect of smoking, and of quit-

ting, without taking account of the number of cigarettes smoked. However,

Negri et al. (1994) found that the risk estimates for former smokers are higher

at younger ages and directly related to the number of cigarettes smoked, but

not to the duration of smoking.

(v) Men who have given up smoking for less than 5 years have a risk of IHD virtually

identical to current smokers. The risk goes down to about twice that of never–

smokers for men who have given up smoking for more than 5 years. But this

risk does not go down further even after quitting smoking for 20 years. See

Cook et al. (1986).

(vi) The odds ratios of MI or coronary death for ex-smokers was similar to those of

current smokers for the first year of giving up smoking and then they decreased.

After about 3 years the risk was not significantly higher that for never–smokers.

See Dobson et al. (1991).

(vii) The odds ratio of acute MI for ex-smokers relative to never–smokers is 1.4 for

those who have given up smoking for one year, 1.5 for two to five years and

1.1 for over six years. The relative risk tends to decrease with the time since

quitting and to become close to that of never–smokers after 10 years without

smoking. See Negri et al. (1994).

11

Obesity

Obesity promotes the atherosclerosis due to its contribution to insulin resistance

syndrome. Obesity is a measure of adipose tissue in the body and adipose tissue

can affect the lipids by changing their characteristics. Mostly obesity affects cardio-

vascular diseases indirectly through its effect on other risk factors like hypertension

and diabetes. Details are given in Stanner (2005).

Age

Age is a non-modifiable risk factor that increases in a deterministic manner. The

effect of all the risk factors for cardiovascular diseases generally increases with age

and age is a significant predictor of cardiovascular diseases.

Sex

Sex is also a non-modifiable risk factor. The risk of cardiovascular diseases is likely

to be significantly higher in men than in women before the age of 50. After age

50, the cardiovascular risk in women increases significantly due to development of

abdominal fat after menopause.

Prior cardiovascular event

According to Caro et al. (2005), an increased risk of myocardial infarction is associ-

ated with prior myocardial infarction (1.53 times that of an invidual without a heart

attack) and prior stroke (1.26 times that of an individual without a prior stroke).

An increased risk of stroke is associated with prior stroke (2.23 times that of an

individual without a prior stroke).

2.3 Risk factors

In Section 2.2.2, we saw that atherosclerosis is affected by various risk factors.

Among these risk factors, sex is fixed and does not change in a lifetime and age

increases in a deterministic manner over time. Smoking status is not a deterministic

12

risk factor, but is influenced by human choice. The other factors like hypercholes-

terolaemia, hypertension, diabetes and body mass index change over time and to a

large extent are out of our control. We will call these dynamic factors. How they

develop over time is also determined by other factors. Generally these dynamic risk

factors tend to appear together in an individual and can sometimes be attributed to

insulin resistance syndrome, which we describe in Section 2.3.1. In Sections 2.3.2 to

2.3.5 we look at the development of dynamic risk factors and the factors that affect

their development.

2.3.1 Insulin resistance syndrome

Insulin is a hormone produced in the pancreas and is present in the circulating

blood. One of its main functions is to carry glucose to different cells in our body.

Insulin resistance syndrome occurs when there is a resistance to the insulin working

normally. Abnormal function of insulin can affect various organs in the body and

thus affect the other risk factors. Increased uptake of glucose can result in diabetes

and increased retention of sodium in the kidneys can cause hypertension. It can

affect the fat cells, causing obesity, and affect the functioning of the liver and cause

hypercholesterolaemia. Details can be found in Stanner (2005). As a result, we

may see that higher levels of one factor are associated with higher levels of another

factor, but they may not have a causal relationship and the effect can be due to

insulin resistance.

2.3.2 Hypercholesterolaemia

Cholesterol is essential for the body. It is not water soluble and is stored in the

body as a source of energy. It is also responsible for repairing cell membranes and

production of certain vitamins and hormones. Despite its beneficial effects, it is

harmful in higher concentrations.

The body accumulates some of the cholesterol from the food we eat, especially

animal fat, but also a lot of cholesterol is produced in the liver. Although cholesterol

is dependant on the food we eat, its relationship with obesity is not well established.

The cholesterol levels in women are generally different when compared to men and

13

the relative levels change as age increases. Cholesterol levels generally increase with

age.

Another factor that contributes to unhealthy levels of cholesterol is hyperthy-

roidism. It is also affected by certain diseases like polycystic ovarian syndrome in

women and kidney diseases. There are also genetic factors responsible for an in-

dividual’s cholesterol levels. More details are available in Well-Connected Reports

(2007b).

2.3.3 Hypertension

Hypertension occurs when the circulating blood puts higher pressure on the walls of

the arteries. This can happen due to narrowing of the arteries due to atherosclerosis

or if the heart pumps blood with greater than normal force. As we have seen before,

such pressure can injure the walls of the arteries.

Insulin resistence is one of the causes of hypertension. Obesity can damage

the kidneys and result in abnormal handling of sodium in the body leading to

hypertension. Obesity can also affect hypertension by affecting the system of

blood flow in the arteries. Smoking is another risk factor that leads to hyperten-

sion. Hypertension also increases with age and can be significantly higher in older

women. Details of the mechanism and risk factors for hypertension can be found in

Well-Connected Reports (2007a).

2.3.4 Diabetes

Insulin resistance can inhibit insulin from working properly in the body with the

result that insulin cannot transport blood glucose to places in the body where it can

be used up. Consequently, the glucose in the blood increases. This is also enhanced

by the fact that over time the pancreas reduces insulin production and the blood

glucose in the circulating blood can rise significantly after a meal. Eventually the

pancreas can stop insulin production resulting in diabetes. Diabetes is a condition

when the glucose in the blood is higher than normal.

Obesity and higher concentration of fat in the abdominal area and the upper part

of the body is significantly associated with insulin resistence. Obesity therefore, is

14

a significant risk factor for diabetes. There are genetic causes of diabetes, but they

are not in the scope of this research. Usually diabetes is diagnosed in individuals

over the age of 40. Details of the mechanism and risk factors for development of

diabetes can be found in Well-Connected Reports (2006).

2.3.5 Body mass index

The difference between the calories consumed and calories used is stored in the body

as a reservoir of fat cells. The fat cells can accumulate if balance is not maintained

between calories consumed and used, leading to weight gain. Some genetic factors

and hormones in our body contribute to weight gain as well as effects of underlying

diseases and medications.

Lifestyle patterns like sedentary habits and binge eating contribute to increasing

obesity. Also, quitting cigarette smoking is associated with weight gain in individ-

uals. More details can be obtained from Well-Connected Reports (2007c).

2.4 Mortality

The cardiovascular diseases and their risk factors are risk factors for increased mor-

tality from all causes. Some of these risk factors may increase the risk of death

directly, through another risk factor or through certain diseases. In this section, we

will discuss the effect of the risk factors and cardiovascular diseases on mortality.

Body Mass Index

The effects of body mass index (BMI) on mortality are not well established and

different studies have reported conflicting results. Body mass index is defined in

Chapter 3. Some of the results reported in various studies are discussed below:

(a) “The standardised mortality ratios increase with BMI, but within each BMI

group, they decrease with age”. See Bender et al. (1999).

(b) Increased mortality risk has a J or U shaped association with BMI. See Solomon

and Manson (1997) , Hart et al. (1999) and Jee et al. (2006).

15

(c) The risk of death is increased for most obese people, but is not significantly dif-

ferent for normal, overweight or Class I obese (defined in Chapter 3) individuals.

See Rogers et al. (2003).

(d) The increased risk of death from any cause was highest for BMI greater than

35Kg/m2 and for BMI less than 21Kg/m2 in both men and women at all ages

and all racial and social classes. See Adams et al. (2006).

(e) “... the lowest rates of death from all causes were found at BMI between 23.5 and

24.9 in men and 22.0 and 23.4 in women; relative risks were not significantly

elevated for the range of BMI between 22.0 and 26.4 in men and 20.5 and 24.9

in women. Death rates increased throughout the range of moderate and severe

overweight for both men and women in all age groups for all causes ...”. See

Calle et al. (1999).

(f) Flegal et al. (2007), in a study based on data from the USA, report

that:. . . underweight was associated with increased mortality . . . overweight was

associated with significantly decreased mortality . . . (obesity) was associated with

increased mortality . . .

According to Solomon and Manson (1997) “... there are several possible expla-

nations for discrepant findings in the relation between body weight and mortality”.

(a) “Possibly, there is some adverse effect of leanness or beneficial effect of excess

body weight on overall survival”.

(b) “ ... weight or BMI may be inadequate surrogates for adiposity”. The adverse

effects of obesity appear to be closely related to the distribution of body fat.

(c) “Leanness may be associated with underlying disease, with cigarette smoking or

with both, both may independently shorten survival”.

According to Calle et al. (1999), the risk of death from respiratory causes was

higher among subjects with a lower BMI and the risk of death from atherosclerotic

cardiovascular disease or cancer was higher among subjects with a higher BMI.


The relationship between cholesterol and mortality is not established and different

studies have reported conflicting results. Some of the results reported in various

16

studies are discussed below;

(a) There is a significant, positive, continuous graded relationship of serum choles-

terol level to long-term mortality from all causes. See Stamler et al. (2000).

(b) All-cause mortality was higher among low-cholesterol men during the early part

of the follow-up period but was higher among high-cholesterol men during the

later part of the follow-up period. According to the findings in the study, it

can take up to 10 years before the positive association of cholesterol with coro-

nary heart disease mortality overcomes the negative association with early non-

coronary heart disease mortality. See Pekkanen et al. (1992).

(c) “Coronary heart disease mortality increased with increasing cholesterol concen-

tration ... Only for lung cancer was there a consistent inverse trend with choles-

terol level ...”. The inverse associations between certain causes of death and

cholesterol levels could be because the participants with low cholesterol levels

possess other characteristics that place them at an elevated risk of death. See

Smith et al. (1992).

(d) In a study to measure the effects of atorvastatin, a drug used to lower cholesterol

in patients, the overall mortality rate was similar in the treated group and the

untreated group, with 216 deaths in the atorvastatin group and 211 deaths in

the placebo group. This indicates that cholesterol reduction does not necessarily

reduce mortality. See The SPARCL Investigators (2006).

(e) “... there was no relationship between cholesterol and stroke mortality in men

and women. The highest rate was seen for men and women in the lowest quintile

of cholesterol and a U-shaped relationship was observed”. See Hart et al. (1999).

Hypertension

Hypertension is associated with increased mortality mainly due to stroke and other

cardiovascular diseases. Both systolic and diastolic blood pressures are associated

with stroke mortality. More details can be found in Hart et al. (1999). In a study

by Van Den Hoogen et al. (2000) over a 25 year period, the relative risk of all cause

mortality for hypertensive patients (defined as a systolic blood pressure of 160 mm

Hg or greater, a diastolic blood pressure of 95 mm Hg or greater, or both) was 2.13.

17

Diabetes

Diabetes is also associated with excess deaths, mostly from cardiovascular diseases.

Mortality from stroke in diabetics is 3 times the mortality from stroke in non-

diabetics. See Hart et al. (1999).

In 1996, the relative risk of mortality from all causes for diabetics was 1.15 in

males and 1.35 in females when compared to non-diabetics (Morgan et al. (2000)).

The resulting reduction in life expectancy was 7 years for men and 7.5 years for

women. Similar results were published by Gu et al. (1998), who found a decrease in

life expectancy of 8 years for those diagnosed with diabetes between the ages 55-64

and 4 years for diagnosis between the ages 65-74.

It has also been suggested that for diabetics the increased risk of all-cause mor-

tality was highest among young patients and the risk declined with increasing age.

See Berger et al. (1999).

Smoking

A study by Doll et al. (2004) found that men born between 1900 and 1930 in the

UK, who continued smoking, died about 10 years younger than individuals who

never smoked. They also found that quitting smoking at ages 60, 50, 40 or 30 years

increased life expectancy by about 3, 6, 9 or 10 years respectively.

In a study in New Zealand, Hunt et al. (2005) found that the relative risk for all-

cause mortality was 2.05 for men and 2.01 for women in the period 1996-1999. This

had increased from 1.59 for males and 1.49 for females in the period 1981-1984. A

similar study in Hong Kong by Lam et al. (2001) found the relative risk for all-cause

mortality was 1.92 for males and 1.62 for females.

In a Finnish study, Qiao et al. (2000) found that “adjusted ratios for 35-year

all cause mortality were 1.62 in current smokers and 1.13 in former smokers com-

pared with non–smokers ... the risk of 10 year mortality was stronger than the 35

year mortality among both former and current smokers, given the same number of

cigarettes consumed”. The increased 10-year mortality was observed in all smokers

including smokers with minimum tobacco consumption. Prescott et al. (2002) also

found that smoking small amounts of tobacco or not inhaling can increase the risk

18

of all-cause mortality they emphasise that harmful effects of smoking are not limited

only to individuals consuming large amounts of tobacco.

Critchley and Capewell (2003) found a 36% reduction in risk of mortality for ex-

smokers compared to current smokers. According to them, there is a possibility that

this risk reduction is quick and can happen as early as within 2 years and as a result

greater risk reductions over time (a period of of up to 7 years) are not observed. A

study by Godtfredsen et al. (2002) suggests that smoking cessation and not smoking

reduction is associated with a decrease in mortality from tobacco-related diseases.

From the above studies we can conclude that there is an excess risk of mortality

associated with smoking and this risk decreases on giving up smoking. The ex-

cess deaths associated with smoking are mostly due to respiratory or cardiovascular

diseases. Reduction in the amount of tobacco consumption does not reduce the

risk significantly and even consumption in small amounts has significant effects on

mortality.

IHD or stroke

In the study by Capewell et al. (2000), “overall case fatality following admission with

acute myocardial infarction was 22.2%, 31.4%, 51.1% and 64.0% at 1 month and

1, 5 and 10 years respectively”. For the 30-day case fatality from acute myocardial

infarction, age had a strong impact and the other factors were diabetes, respira-

tory disease, peripheral vascular disease, cancer and heart failure. For longer-term

mortality significant factors were age, diabetes and cerebrovascular diseases.

According to Hart et al. (1999), “men and women with preexisting CHD had a

higher rate of stroke mortality than men and women without preexisting CHD”.

A study by Lee et al. (2003) found that survival at 28 days was lowest for haemor-

rhagic stroke. Following the first month after admission, survival after haemorrhagic

stroke was similar to that after ischaemic stroke. Among all patients significant

predictors of death were age, atrial fibrillation, other cardiac conditions, sex and di-

abetes. Among 28-day survivors of ischaemic stroke, additional predictors of death

included sex and diabetes.

Hart et al. (2000) demonstrated that in their study cohort, risk factors for stroke

19

had a similar effect on stroke incidence as on stroke mortality. They also found that

a high level of glucose in non-diabetic subjects was significantly related to stroke

incidence and mortality in women but not in men. They also mention that the Oslo

study failed to find significant relationships between glucose and stroke incidence

or stroke mortality. Body mass index was not clearly related to stroke incidence or

mortality in their study. Rastenyte et al. (1996) also failed to show that cholesterol

level, impaired glucose tolerance or BMI are related to the risk of death from stroke.

According to Hardie et al. (2005), the crude risk of death was greatest in the first

year after stroke (36% in 1989-90 and 37% in 1995-96) and particularly in the first

30 days after onset (22% in 1989-90 and 23% in 1995-96). The results were based on

outcomes from follow-up of two cohorts in Perth, Australia. They also found that

the 1989-90 cohort had a relative mortality risk of 3.8 compared with individuals of

the same sex and age in the general population of Western Australia.

The crude death rates in Caro et al. (2005) suggest a significantly higher death

rate within 30 days of a myocardial infarction (≈ 17%) or stroke (≈ 10%), than the

mortality following 30 day survival from these events (≈ 40% in the first 5 years

after MI and ≈ 49% in the first 5 years after stroke). They also found that the

increased risk of death following 30 day survival after the event was associated with

prior heart attack (2.06 times that of an invidual without a heart attack) and prior

stroke (1.53 times that of an individual without a prior stroke).

2.5 Summary

We have seen in this chapter that the disease process for atherosclerosis progresses

over a long duration and is a complex mechanism involving risk factors like hy-

perchoelsterolaemia, hypertension, diabetes, smoking, obesity, age and sex. Mostly

these cardiovascular diseases are a result of the blockage of arteries supplying blood

to different organs and sometimes due to the rupture of these arteries.

The disease process and the risk factors affecting this process are complex and

can produce conflicting evidence based on the data used and aims of the study. The

evidence we present in this chapter gives a summary and provides a justification for

20

some of the assumptions used in this thesis. The medical evidence presented here

was reviewed by the Actuaries Panel on Medical Advances which is a subcommittee

of the Social Policy Board of the UK Actuarial Profession and included doctors and

actuaries.

21

Chapter 3

Data

3.1 Introduction

In Chapter 2 we have seen how cardiovascular diseases develop and the effect of risk

factors on these diseases. We also saw how these risk factors and the cardiovascular

diseases themselves lead to death. The risk factors affect the disease processes

at different stages and to different extents. Our aim is to quantify these effects

numerically, i.e. to determine the rates at which individuals develop these risk

factors or the rates at which individuals are diagnosed with cardiovascular diseases

and ultimately the rates at which individuals die. These rates will eventually allow

us to calculate the probabilities of individuals with certain sets of risk factors being

diagnosed with cardiovascular diseases or dying in a given time frame.

To quantify numerically the effects of risk factors on diseases and on death we

need data. We need to determine the data requirements and these are detailed in

Section 3.2. We will then look at potential sources of data in Section 3.3 and we

will discuss the characteristics of the data we have used in Section 3.4.

3.2 Data requirement

The scope of this study includes cardiovascular diseases, their risk factors and mor-

tality. We want to model the development of the risk factors for an individual over

time (specifically with increasing age), along with the diagnosis of cardiovascular

22

diseases and eventual death. To parameterise such a model, we would like to have

data that has the following characteristics:

(a) The data will need to record observations specific to an individual, repeatedly.

This will enable us to determine the rate at which factors develop in an indi-

vidual.

(b) The results will be more precise if these observations are recorded frequently,

ideally every 1 or 2 years. If the duration between two subsequent observations

is small, we will be able to observe intermediate steps for larger transitions, say

from very low levels to very high levels of a particular risk factor.

(c) We will also need the recordings over a long period, so that we can monitor the

development of risk factors before a significant event (IHD, stroke or death) is

diagnosed.

(d) We will ideally need the exact dates of transitions from one level of a factor

to another. We understand that this is not practical for some factors that are

measured on a continuous scale and regular observations will enable us to make

better estimates about the dates of these transitions. But we will need to have

exact dates of diagnoses of significant events.

(e) Sex needs to be recorded for each individual and the data needs to have a good

mix of males and females in it.

(f) Age of the individual will be required at each observation and on event dates.

This can also be calculated if age at the start is available and exact dates of

first and subsequent observations are recorded.

(g) Smoking status needs to be recorded at each examination. Some form of in-

formation, related to intermediate smoking behaviour between two consecutive

observations is also helpful.

(h) The data will need to record data on different risk factors. For body mass

index it will need to record height and weight, for hypercholesterolaemia it will

need to record total cholesterol, HDL cholesterol and LDL cholesterol, for blood

pressure it will need to record systolic as well as diastolic blood pressure and

for diabetes it will need to record blood glucose levels.

(i) The data should have the date of diagnosis and form of significant events. There

23

is a likelihood of more than one significant event being diagnosed in an individ-

ual’s lifetime and the data will need to record the dates and forms of each of

these events.

(j) An ideal data set will have individuals spread over a wide range of age groups,

both for males and females, with enough individuals in each age group to obtain

credible estimates. We understand that at the boundaries of the age range of

the data there may be very little data and we will be exposed to high variability

in our estimates at these ages as well as ages outside the range of the data.

3.3 Different sources of data

We considered different sources of data to parameterise our model. The potential

sources of data were cohort studies, drug trials, national or international surveys or

medical studies (for example, studies to monitor changing obesity patterns or the

effect of smoking on obesity). We look at these sources of data and investigate if

they are suitable for parameterising our model.

Drug trials

Data from drug trials are not suitable for parameterising our model for the following

reasons:

(a) Drug trials are very specific to a particular disease.

(b) They are unlikely to have observations on all the risk factors that we would like

to model.

(c) When data from a drug trial has all the risk factors needed, the observations

are generally not repeated and are available only at the outset. This does not

allow us to model movements in the different levels of the risk factors.

(d) Sometimes the diseases develop at older ages and the individuals recruited for

these trials are older, which does not give us any information about the factors

at younger ages.

24

Medical studies

Data from medical studies are not suitable for parameterising our model for the

following reasons:

(a) Medical studies may not have any data on significant events.

(b) Medical studies are unlikely to have data on all risk factors.

“MONICA” is one such medical study. It is a large medical study, set up with the

objective of studying the trends in cardiovascular diseases. A feature of data from the

MONICA study is the unavailability of data for the risk factors, which are recorded

only for a sample population rather than the whole study population and the samples

are usually different at different examinations. Although the data is adequate to

measure the trends in cardiovascular diseases, it is unsuitable for measuring the

effects of risk factors on these diseases. More details about the MONICA study can

be obtained from its website http://www.ktl.fi/monica/index.html.

National and international surveys

Data from surveys are not suitable for parameterising our model for the following

reasons:

(a) Surveys are generally based on questionnaires and only a few surveys supplement

the data with measurements based on blood or urine samples. As a result we

may not have data on all the risk factors. Where results are available on the risk

factors, a significant amount of data are based on self-reporting and is exposed

to bias and errors.

(b) The surveys are generally not repeated on the same group of individuals. Thus,

the data are not suitable for parameterising an individual lifetime model.

Cohort studies

Data from cohort studies are likely to be the most suitable data for parameterising

our model for the following reasons:

(a) Cohort studies follow a group of individuals over a significant amount of time.

(b) Records are collected at regular intervals.

25

(c) Some cohort studies, but not all, will record all the risk factors that we need.

(d) Some cohort studies, but not all, will have a broad range of ages for both males

and females.

Although cohort studies provide us with the best possible data sets for parame-

terising our model, there are some limitations of this type of data.

(a) The cohorts age as time increases. The effect of age obtained from these data

can mask the effect of progression through calender time.

(b) The observations are recorded at regular intervals, which can be far apart. Also,

individuals may not turn up for all observations and we will need to make

suitable assumptions about the data in the intermediate time period.

(c) The variables recorded at each observation may not be the same. We will

need to use the variables available to make inferences about some other related

variables.

(d) Results are specific to the cohort and may not be suitable for a different mix of

individuals.

Multiple sources of data

Cohort data are the best suited data for our model, but they may not be sufficient

to parameterise a model applicable to the reference population, for example the

population of the UK.

Our approach will be to use some cohort data to parameterise our model and use

data or results from drug trials or medical studies to parameterise specific portions of

the model, where the cohort data is not suitable for use. Finally we adjust the model,

so that it produces summary statistics that are consistent with the summary statis-

tics obtained from the surveys conducted within the reference population. In our

example, we can adjust our model so that it produces summary statistics consistent

with the summary statistics published in the surveys based on the UK population.

26

3.3.1 Cohort study data

In this section we look at some of the cohort data available, their features and their

suitability for parameterising the model.

The 1946 National Birth Cohort

Wadsworth et al. (2006) published the cohort profile for the 1946 British National

Birth Cohort. According to them, the 1946 British National Birth Cohort study

was set up to address two important health and social policy questions:

(a) Why has the national fertility rate been falling consistently since the middle of

the 19th century?

(b) What was the national distribution and use of obstetric medical and midwifery

services, and how far do they prevent premature and infant death, and promote

the health of mothers and infants?

The target was to collect data for all the births that took place during 3rd March

1946 to 9th March 1946 throughout England, Wales and Scotland. Subsequent data

collection was from a sample of all single births to married women using some selec-

tion criteria. The data collection was frequent in infancy and school years because

of the pace of development and growth, but in adulthood the periods between col-

lections lengthened as biological and cognitive function slowed. The original sample

was of size 16695 and there were 5362 individuals in the follow-up sample. The

aim of the study has changed as the population aged and it is presently looking at

mortality and morbidity related issues.

Table 3 in Wadsworth et al. (2006) provides details of the number of data col-

lections conducted between different age ranges and the characteristics that have

been recorded in the data. We note from the table that cardiovascular risk factors

like blood pressure and smoking were recorded only after 32 years and there are

only 3 recordings of these data. We also note that in 1999 the cohort was aged 53

years and is too young for significant recordings of cardiovascular diseases or death.

These observations lead us to conclude that this cohort did not have sufficient data

to parameterise our model.

27

There were other data relating to Birth Cohorts from later years, but they will

be younger than the 1946 cohort and hence will be unsuitable for our purpose.

The Framingham Heart Study Cohorts

The Framingham Heart Study recorded the data from a population of a small town

called Framingham near Boston, Massachusetts in the USA. Details can be found in

Dawber et al. (1951). This resulted in a wide range for age and a good mix of males

and females. The collection of the data was organised by the National Heart, Lung

and Blood Institute (NHLBI) and the data was collected from regular check-ups of

individuals over time.

The collection of Framingham data started with the Original Cohort (OC) in

1948, where individuals were recruited over a period of two years and the individuals

went through a physical examination and answered lifestyle questionnaires. They

were invited back for regular examinations approximately every two years.

In 1971 another set of individuals was recruited for a study with the same ob-

jective as the OC, from the offspring and spouses of original cohort members. We

will call this cohort the Offspring and Spouses Cohort (OS). The examinations for

this cohort were less frequent, with subsequent examinations being 6 years apart on

average.

We look at some of the characteristics of these cohorts in Table 3.1.

Data from Framingham cohorts are suitable for parameterising a major portion

of our model due to the following advantages:

(a) We can use both the OC and OS data in conjunction with each other. This can

be done because both the cohorts were recruited with the same objectives and

hence have records of the same variables recorded in the same way using the

same instruments. There are very slight differences in the way a few variables

are recorded (like weight), but these differences do not affect our modelling. We

also have some additional data in OS that was not available in OC. For example,

in OC we only had records of total cholesterol, but in OS we have the records of

the components of total cholesterol, i.e., HDL cholesterol and LDL cholesterol

(we will see how to use this extra information later in this section).

28

Table 3.1: Summary statistics for the Framingham data sets.

Sex Original Cohort Offspring & SpousesPeriod of examination 1948 – 1986 1971 – 1997

No. of examinations 20 6

No. of individuals M 2336 2483F 2873 2641

Total exposure (years) M 57,911 42,779F 77,545 45,449

Age range at first M 28 – 62 13 – 62examination F 29 – 62 13 – 62

Median age for M 58 48exposure (years) F 59 47

No. of cases of IHD M 416 263F 322 105

No. of cases of stroke M 279 51F 373 41

No. of deaths M 1606 288F 1532 140

(b) The difference in estimates obtained from OC and OS will give us an idea about

the change in parameter values over calender time as OS is more recent than

OC.

(c) Taken together the lowest age available is 13, which allows us to obtain estimates

at younger ages and we have exposure up to age 90 or more, allowing us to obtain

estimates at older ages.

(d) The data have a good mix of males and females at different ages.

(e) The data enable us to infer the exact age of death and other significant events.

(f) The data record cholesterol, blood pressure and blood glucose as continuous

variables, which enable us to group them according to our requirements.

29

(g) We have data available over a long duration (40 years in the OC and 25 years

in the OS).

(h) The observations are recorded every 2 years on average in OC, which will allow

us to monitor movements more frequently. The observations in OS are less

frequent.

(i) The exact dates of examinations that an individual attended are recorded for

each individual.

Although the data are very well suited for parametrising the majority of the

model, they also have some limitations:

(a) The examinations in the OS are on average 6 years apart. We do not know

how many transitions take place between two examinations. It is possible that

for some factors the values would have increased and then come back to their

original levels and we observe that there has been no change in the factor for

the individual. Where we do notice a change in the levels of a factor, we do not

know the exact date of the change. This feature is also applicable to the OC

even though the examinations are more frequent for this cohort.

(b) We have records of the first diagnosis of a significant event. So only the date

of first heart attack will be recorded in the data for an individual with multiple

heart attacks. Thus the data are not suitable to model second and subsequent

significant events.

(c) There are missing values in the data as all individuals did not attend all the

examinations. Individuals not attending all examinations has resulted in large

gaps between consecutive recordings for some individuals.

(d) As described in Dawber et al. (1951), the population of Framingham was pre-

dominantly white and individuals in blue collar jobs. The racial and social

profile was not diverse and adjustments will be needed to the parameters when

applying the model to more diverse populations like the population of the UK.

We will use data and results from other sources to get around these limitations

and we will investigate this in Chapter 4.

30

3.4 Framingham Cohort Data

3.4.1 Availability and classification of data

In this section we describe the details of the data, specifically the variables available

in the data, how to use these variables, the examinations in which these variables

are available and how we classify them into different groups. We have categorised

some of the risk factors to simplify the analysis of these risk factors. We will also

describe how the dates of events and examinations are recorded in the data.

Date of examinations

In the OC, the exact dates of examinations are not recorded. For the time of exami-

nation, the data records the number of days from a specific date in time which is not

known. We set the time of the first examination as time 0 and calculate the number

of days to the subsequent examinations from the above data (by subtracting the

number of days to the first examination from the number of days to the subsequent

examinations).

In the OS also, the exact dates of examinations are not recorded. For the time of

examination the data records the number of days since the first examination. The

time of first examination is recorded as 0.

For both these cohorts, the number of days since the first examination to a

particular examination is divided by 365 to get the number of years since the first

examination to that particular examination. We round the number of years to the

nearest two decimal places.

All individuals did not attend all the examinations and as a result at each ex-

amination we do not have the number of days to the examination from the first

examination for all individuals. We treat these as missing data. Table 3.2 gives the

number of individuals present at the different examinations.

At the end of 20 examinations in the OC, 3138 individuals had died (Table 3.1)

and 1401 attended the last examination (Table 3.2) out of 5209 individuals who

attended the first examination. This indicates that only 670 individuals did not

attend examination number 20, which took place about 40 years after the study was

31

Table 3.2: Number of individuals at each examination.

Original CohortExamination No. of Individuals Examination No. of Individuals

1 5209 11 29552 4792 12 32613 4416 13 31334 4541 14 28715 4421 15 26326 4259 16 23517 4191 17 21798 4030 18 18259 3833 19 154110 3595 20 1401

Offspring and Spouses CohortExamination No. of Individuals Examination No. of Individuals

1 5124 4 40192 3863 5 37993 3873 6 3532

set up. The response rate is therefore very good.

In the OS, 428 individuals had died at the end of examination 6 (Table 3.1)

and 3532 attended the examination 6 (Table 3.2) out of 5134 individuals attending

the first examination, indicating a loss of 1174 individuals in about 30 years at

examination 6.

Date of significant events

We will describe the data on significant events later in this section. Here we describe

how the dates for these events are recorded.

In the OC, the exact date for the first diagnosis or occurrence of a significant event

(including death) is recorded. We do not know the exact dates of the examinations.

The time is recorded as number of days since a specific date in time and we assume

this date to be 1 January 1960. The assumption about the specific date is consistent

with the rest of the data and was also used by Wekwete (2002). To get the number

of days to the significant event from the first examination, we calculate the number

32

of days since 1 January 1960 to the date of significant event and then subtract from

this the number of days to the first examination from 1 January 1960.

In the OS, the exact dates of significant events are not recorded but the number

of days to a significant event since the first examination is recorded.

For both these cohorts, the number of days since the first examination to a

particular significant event is divided by 365 to get the number of years since the

first examination to the significant event. We round the number of years to the

nearest two decimal places. Where an individual has had a significant event before

being recruited in the study, the number of years to a significant event since the first

examination is negative.

Recall that the dates to the diagnosis and occurrence of significant events are

recorded for the first event only and the date of any subsequent occurrence of the

same event is not recorded.

Age

Age in integer numbers is recorded for the individuals at each examination that the

individual had attended. We assume that the recorded age is the age last birthday.

We assume that an individual attended their first examination on average six months

after their last birthday and their exact age at that date is 0.5 years more than the

recorded age. Although age is recorded in subsequent examinations (as integer), we

calculate the age at subsequent examinations by adding the number of years since

the first examination.

In our model we will treat age as a continuous variable which will be a proxy for

time. Age will be denoted by x.

Sex

Sex is recorded for the individuals in the first examination of OC and all examina-

tions of OS. In our model, sex will be denoted by s and s=1 for males and s=2 for

females.

33

Body mass index

Body mass index (BMI) is defined as “Weight(kgs)/(Height(mtrs))2”. Weight is

recorded in all the examinations of OC and OS, but height is not recorded in all

the examinations of the OC and OS (we describe the treatment of missing data in

Section 3.4.2). The availability of data in the two cohorts is summarised in Table

3.9.

In the OC, weight is recorded in pounds. In the OS, the weights are recorded

in groups of 5 pounds starting from individuals with a weight of more than 100

pounds, with everyone with a weight of less than 100 pounds classified in the same

group (denoted as 0). If an individual belongs to a particular weight group, we

allocate the mid point of the group as the individual’s weight (97.5 pounds for the

group denoted by 0). We convert the weight in pounds into weight in kilograms by

multiplying the weight in pounds by 0.45455.

In both OC and OS, height is recorded in full inches. We convert the height in

inches into height in metres by multiplying the height in inches by 0.02542.

In Well-Connected Reports (2007c), an individual with BMI of 25 to 29.9 is

classified as overweight. An individual with BMI greater than 30 is classified as

obese. Among the obese individuals, individuals are class II obese if they have BMI

greater than 35 and class III obese if they have BMI greater than 40.

Rogers et al. (2003) used the same guidelines in their study on the effect of obesity

on mortality and have classified individuals with BMI less than 18.5 as underweight

as they have mortality significantly different from individuals with normal BMI

(defined as BMI in the range 18.5 to 25).

We discretise BMI into five categories, as shown in Table 3.3. These categories are

consistent with those in Sproston and Primatesta (2004b) although our terminology

is slightly different. Sproston and Primatesta (2004b) use the term ‘Desirable’ for

BMI between 18.5 and 25. This seems to us to be unnecessarily emotive and so we

have used the term ‘Lightweight’ for this category. We will use the term ‘Obese’

to denote a BMI value greater than 30. Thus, using our terminology, Obese is

a combination of Moderately Obese and Morbidly Obese. Our use of Obese and

Morbidly Obese is consistent with Sproston and Primatesta (2004b), but they have

34

no special term for those with a BMI value between 30 and 40, i.e. our Moderately

Obese category. BMI categories will be denoted by b.

Table 3.3: Categories of body mass index.

Category Term BMI (kgs/(mtrs)2)0 Underweight ≤ 18.51 Lightweight 18.5 − 252 Overweight 25 − 303 Moderately Obese 30 − 404 Morbidly Obese > 40

We use body mass index (BMI), as a measure of adiposity even though some

authors, for example Solomon and Manson (1997), have suggested that waist/hip

ratio might be a better measure of adiposity. The Health Survey for England 2003

(Sproston and Primatesta (2004b)) gives prevalence data relating to waist/hip ratio

as well as BMI. However, we use BMI because the Framingham Heart Study does

not record waist/hip ratios for individuals.


Hypercholesterolaemia is the presence of high concentrations of cholesterol in the

circulating blood. We have seen in Chapter 2 that total cholesterol in the blood is

made up of LDL cholesterol, HDL cholesterol and VLDL cholesterol. The current

treatment recommendations, issued by the National Cholesterol Education Program

(NCEP), are based on four categories of LDL cholesterol. These categories and

recommendations are described in Well-Connected Reports (2007b) and the NCEP

website.

In the OC only total cholesterol was recorded for most examinations and in the

OS total cholesterol was recorded in all examinations. In the OS, HDL cholesterol

was recorded in all examinations, but LDL cholesterol was recorded only in the first

two examinations. The availability of data in the two cohorts is summarised in Table

3.9. In the Framingham cohorts, total cholesterol and its components are recorded in

mg/dL. We did not have LDL cholesterol for all examinations and absence of VLDL

35

cholesterol values prevented us calculating the LDL cholesterol from the available

data.

We did not have LDL cholesterol recorded in most examinations. A relationship

between total cholesterol and LDL cholesterol is given by the Friedwald equation.

See Well-Connected Reports (2007b). As we did not have the information necessary

to use the Friedwald equation, as an alternative we used a regression equation based

on the data in the first two examinations of the OS to formulate an approximate

relationship between total cholesterol and LDL cholesterol (as total cholesterol was

available in most examinations) and used total cholesterol as a proxy to determine

the categories for hypercholesterolaemia. The approximate relationship is given by

(in mg/dL):

LDL ≈ TC − 70

An alternative unit of measurement of concentrations of cholesterol and its com-

ponents is mmol/L and can be inferred by multiplying the mg/dL concentrations

by 0.02586.

The categories both in terms of LDL cholesterol and corresponding total choles-

terol values are shown in Table 3.4. Hypercholesterolaemia categories will be denoted

by c.

Table 3.4: Categories of hypercholesterolaemia.

Category LDL (mg/dL) LDL (mmol/L) TC (mg/dL) TC (mmol/L)0 < 130 < 3.362 < 200 < 5.171 130 − 160 3.362 − 4.138 200 − 230 5.17 − 5.952 160 − 190 4.138 − 4.913 230 − 260 5.95 − 6.723 ≥ 190 ≥ 4.913 ≥ 260 ≥ 6.72

Hypertension

Hypertension is the presence of elevated levels of blood pressure. Blood pressure

is measured in mm Hg and has two components, systolic blood pressure (sbp) and

diastolic blood pressure (dbp). We classify blood pressure into four categories which

36

are consistent with the National Heart, Lung and Blood Institute (NHLBI) recom-

mendations and are described in Well-Connected Reports (2007a). The categories

of blood pressure are shown in Table 3.5. Hypertension categories will be denoted

by p.

Table 3.5: Categories of hypertension.

Category SBP (mm Hg) DBP (mm Hg)0 < 120 < 801 120–139 80–892 140–159 90–993 ≥160 ≥100

If the measurements of sbp and dbp indicate two different categories, the individ-

ual is assigned to the higher category of hypertension.

In the OC and OS, both sbp and dbp are observed and recorded three times, once

by a nurse and twice by different physicians. In all the examinations of OC and

OS, at least one of the three readings is available for all individuals attending the

examinations. We classify an individual into a hypertension category based on the

lowest category indicated by the three readings. The availability of data in the two

cohorts is summarised in Table 3.9.

Diabetes

Diabetes is the presence of high levels of glucose in the blood. The threshold above

which an individual is usually classified as diabetic is a concentration of 126 mg/dL

or equivalently 7 mmol/L of blood glucose. The categories are shown in Table 3.6.

Diabetes categories will be denoted by d. Description of the classification can be

seen in Well-Connected Reports (2006).

In all the examinations in the OC and OS, blood glucose is recorded in mg/dL.

The availability of data in the two cohorts is summarised in Table 3.9.

37

Table 3.6: Categories of diabetes status.

Category Term Blood glucose (mg/dL) Blood glucose (mmol/L)0 Non-Diabetic ≤ 126 ≤ 71 Diabetic > 126 > 7

Smoking

In the OC and OS, smoking habit is recorded in most of the examinations as “if the

individual has smoked regularly in the year prior to the examination date”. The

data also records the number of cigarettes smoked for those individuals who were

smokers at the time of the examinations. Both these variables are self-reported.

Although the examinations were approximately two years apart in OC and 6 years

apart in OS, an individual was classified as “current smoker”, if he/she has been

smoking regularly in the year prior to the examination. The individual was classified

as “never–smoked”, if they were not current smokers in the current examination and

have not been a current smoker in any prior examinations. Otherwise an individual

was classified as “ex–smoker”. The categories are shown in Table 3.7. Smoking

categories will be denoted by n.

Table 3.7: Categories of smoking status.

Category Smoking Status0 never–smoked1 current smoker2 ex–smoker

In the OC, an individual could be classified only as “never–smoked” or “current

smoker” in the first examination, because no prior history of smoking was available

at that examination. In OS, the smoking history was recorded into the three classes

mentioned in the first examination and hence the individuals could be classified in

all the three categories.

Even though the number of cigarettes smoked by an individual was available in

38

the data, we have not classified individuals by the number of cigarettes smoked, as

the evidence of the effect of heavy smoking on the significant events was inconclusive

(as seen in Chapter 2). The availability of data in the two cohorts is summarised in

Table 3.9.

Significant events

The significant events recorded separately in both the OC and the OS are:

(a) Cardiovascular Disease (CVD)

(b) Coronary Heart Disease (CHD)

(c) Angina Pectoris (AP)

(d) Myocardial Infarction (MI)

(e) Coronary Insufficiency (CI)

(f) Heart Attack (HA)

(g) Intermittant Claudication (IC)

(h) Congestive Heart Failure (CHF)

(i) Stroke (CVA)

(j) Hard Stroke (CVM) (We denote this condition by HS)

(k) Transient Ischaemic Attack (TIA)

(l) Atherothrombotic Infarction (ABI)

According to the Framingham Heart Study definitions, some of the conditions

include some of the other conditions as its components. The relationships between

these conditions according to the definition used by Framingham Heart Study are

summarised in Table 3.8.

Table 3.8: Relationship between significant events.

Event ComponentsHA MI and AP

CVA HS, ABI and TIACHD HA and CICVD CVA, CHD, IC and CHF

39

We are interested in studying the effects of the risk factors on IHD and stroke.

According to the International Classification of Diseases (ICD-10), IHD (also CHD)

comprises MI, AP and CI (which is also known as unstable angina). Stroke is made

up of HS and TIA.

As noted before in this section, only the first diagnosis of these conditions is

recorded. There are a few conditions, which are made up of several other conditions

(Table 3.8) and for these conditions the date of event is recorded as the date of the

earliest event among its constituents.

Mortality

The other significant event recorded in the data is death and cause of death. We

are interested in death from any cause and as a result we do not classify the data

by cause of death.

The literature suggests that mortality is significantly different in the month im-

mediately following the occurrence of MI and HS (Chapter 2) and we classify the

data according to whether death has occured from any cause within one month of

these events. We call this death in the short span following MI and HS as “sudden

death”. Individuals surviving the first month following MI or HS can then die from

any cause subsequently and this is parameterised separately as long-term mortality.

3.4.2 Treatment of missing data

The majority of missing data arises from individuals not attending examinations.

Where this is the case, date of examination is not relevant. In these situations the

best option available to us is to ignore the exposure and any possible transitions

since the last time the individual attended an examination.

From Table 3.9 we see that all the variables are not recorded at all the exami-

nations even when an individual attends an examination. Also, it is possible that

the data for a particular variable for a specific individual are not recorded when the

variable is recorded for other individuals. In such cases we assume that the data for

the specific individual have not changed since the variable was last recorded. If that

particular variable is not recorded for that individual ever before, then as a second

40

choice we assume the value to be the same as that recorded for the first time at a

later examination.

3.5 Estimation of transition intensities

In the last section we have looked at the variables available in the Framingham data

sets and how these variables can be used to determine the levels of different risk

factors and significant events. The risk factors are classified into different categories.

As time progresses, individuals grow older and their risk factor categories are

likely to change. The data sets are snapshots of the levels at certain times during

their life. We may see that the levels of individuals’ risk factors have changed, but

from the data it is difficult to infer when or how many times the risk factor level

changed between two examinations.

We want to develop a Markov model incorporating different factors specified by

transition intensities between different categories of these factors. Our aim in this

section is to obtain the intensities at which individuals are moving between the

categories of the different risk factor from the Framingham Heart Study data. In

Chapter 4 we will describe the model and the parameterisation of the model based on

the transition intensities obtained by smoothing the transition intensities estimated

in this chapter.

Assumptions for the data

To obtain estimates for these transition intensities we will need some assumptions.

The assumptions mentioned below can bias the estimates of transition intensities

towards a particular level of a factor or towards a particular age. We believe that

for a data set with large number of individuals and data over a long period in time,

the bias should not be substantial. We did find that in some cases the bias was

substantial, and we have estimated the intensities using approaches to remove the

bias as can be seen in Chapter 4.

(a) There is a grading in the categories of risk factors, except smoking, with the

higher categories having higher levels of the risk factors. We define forward

41

transition as increase in the categories of risk factors and backward transition

as reduction in the categories of risk factors. Smoking has no grading in its

categories, and forward and backward transitions are not relevant. Smoking

status of individuals can change from one category to another over time as

individuals take up smoking or quit smoking.

(b) Forward or backward transitions are possible between adjacent categories only.

For example, transition from category 1 of BMI to category 3 of BMI is not

possible in a single step and will have to involve at least two transitions, one

from category 1 of BMI to category 2 of BMI and another one from category 2

of BMI to category 3 of BMI.

(c) For estimation of transition intensities, we assume that going from one level of a

risk factor to another level of a risk factor, the minimum number of transitions

is required. That is going from category 1 of a factor to category 4 of the

factor will involve three forward transitions and will not involve combinations

of forward and backward transitions leading to a higher number of transitions.

(d) As we do not know the exact time at which a transition takes place between

two examinations, we will assume that the transitions are equally spaced in the

interval between the two examinations. For example, to move from category

1 of a factor to category 2 of the factor, the transition will take place midway

through the interval.

(e) We will consider exposure and transitions between two examinations if and

only if the individual attended both the examinations at the start and the end

of the period. When a significant event (including death) is the last event, we

will consider exposure and transition from the last recorded examination to the

time of the final significant event.

(f) The same transition in a factor can take place from two different levels of a

different factor. We will calculate the transition intensities of a factor separately

for the different levels and combinations of other factors and investigate if these

intensities are different. For example, transition from category 0 to category 1 of

diabetes can occur for two groups of individuals, one with hypertension category

1 and another with hypertension category 2. In this case we will calculate

42

the transition intensity of moving from category 0 to category 1 of diabetes

separately for the two groups and investigate if having a different hypertension

category at the time of diabetes transition, affects the diabetes transition.

(g) If two factors, say a and b, change categories between two examinations at the

same time, we will assume that the transition in the factor a occurred at a

category of factor b just before the transition in factor b. For example, if both

hypertension and diabetes increased from category 0 to category 1 between

consecutive examinations for an individual, we will assume the transition from

category 0 to category 1 of diabetes occurred for hypertension category 0 and the

transition from category 0 to category 1 of hypertension occurred for diabetes

category 0.

(h) Transitions from not being diagnosed with a significant event to being diagnosed

with a significant event occur at an exact date known to us. At this point

categories of risk factors may not be recorded. We assume the categories of risk

factors relevant at the time of the transition are the later of the last recorded

categories of the risk factors or the categories determined using the assumptions

mentioned above.

Risk profile of an individual

Based on the assumptions mentioned above and the raw data that we get for the

Framingham cohorts, we manipulate and categorise the data using a “C” program

developed by us to arrange the data in a format that we can use for futher calcu-

lations. The format reflects the categories of risk factors that an individual is in at

each examination and the status of significant events. We then use the formatted

data to construct a life history for each individual. We will describe with an example

how we use the data and assumptions to develop the life history of an individual.

We start with a 9-digit code representing the risk profile of the individual at a

particular age x. Table 3.10 illustrates the factors represented by each digit.

So, a code (101000000) will represent a male, who has never–smoked, with lowest

categories of diabetes, hypercholesterolaemia and hypertension, is lightweight and

has not experienced any significant event.

43

Consider the first individual recruited in the offspring cohort. We will build up

the risk profile for this individual. The individual is a female with the recorded age

36 at the first examination. We will assume the age of the individual is 36.5 at the

first examination.

In examination 1, the individual has weight group 6, which is 125–130 pounds

and we take the midpoint, 127.5 pounds as the individual’s weight. We multiply

this by 0.45455 and get the individual’s weight as 57.96 kgs. The height is recorded

as 64.5 inches, which we multiply by 0.02542 to get a height of 1.64 mtrs. This gives

us a BMI of 21.55 kgs/(mtrs)2 and the individual is classified as category 1 of BMI.

In examination 1, the individual has a total cholesterol of 165 mg/dL and will be

classified as category 0 of hypercholesterolaemia.

In examination 1, the individual has two measurements for blood pressure. The

blood pressure measured by the nurse is a sbp of 112 mm Hg and a dbp of 72 mm

Hg which gives a classification of category 0 of hypertension and the blood pressure

by the first physician is a sbp of 104 mm Hg and a dbp of 72 mm Hg which again

gives a classification of category 0. The individual is thus classified as category 0 of

hypertension.

In examination 1, the individual has a blood glucose level of 113 mg/dL and is

classified as category 0 of diabetes.

In examination 1, the smoking status of the individual is category 0 as the indi-

vidual has never smoked.

The individual has not been diagnosed with any significant event at the time of

the first examination.

Thus the individual has a risk profile of (201000000). Table 3.11 gives the risk

profile of the individual at different examinations of the OS.

The risk profile and the intermediate transitions, based on the assumptions are

plotted on the timeline in Figure 3.1

We can obtain a similar life history for all the individuals in both the OC and

OS data using the same principles as above.

44

6

6Age Risk Profile

•

•

•

•

•

•

36.50

44.58

48.87

52.33

55.95

60.00

201000000 (Exam 1)

201000000 (Exam 2)

201000000 (Exam 3)

201010000 (Exam 4)

201000000 (Exam 5)

201020000 (Exam 6)

–

–

–

–

50.60

54.14

57.30

58.65

201010000

201000000

201010000

201020000

Figure 3.1: Life history of individual 1 in the OS data.

Estimation of transition intensities

Once we have the life history data, we know at each age the risk profile to which

an individual is exposed. We also know the age at which the individual made the

transition from one risk profile to another risk profile.

This data can be added up for all the individuals in the OC and OS and we

can get a distribution of the exposure to a particular risk profile at a particular

age and the number of transitions to another risk profile at that age. For example,

we can calculate the exposure (in person years) to risk profile 201000000 for age

greater than or equal to 56.5 and age less than 57.5 (call this E56.5) and also the

45

number of transitions from 201000000 to 201010000 between ages 56.5 and 57.5

(call this T56.5). T56.5/E56.5 is the estimate of the transition intensity of moving

from risk profile 201000000 to 201010000 midway through the ages 56.5 and 57.5 at

57, i.e., the transition intensity of moving from category 0 of hypercholesterolaemia

to category 1 of hypercholesterolaemia at age 57, for females who have never smoked,

are lightweight and have lowest categories of diabetes and hypertension and are not

diagnosed with a significant event.

Figures 3.2, 3.3, and 3.4 show the transition intensities graphically for some of

the risk profiles.

0

0.1

0.2

0.3

0.4

0.5

20 30 40 50 60 70 80 90

Transition Intensity

Age

MaleFemale

Figure 3.2: Transition intensities calculated from Framingham cohorts of transitionfrom hypercholesterolaemia category 1 to category 2 for individuals who have neversmoked, have lowest categories of diabetes, hypertenstion, are lightweight and havenot been diagnosed with any significant event.

3.6 Summary

In this chapter we have looked at different potential sources of data. Data from the

Framingham Heart Study is the best suited for parameterising our model. The data

records observations for individuals multiple times over a portion of their life history.

These data include details on age, sex, body mass index, hypercholesterolaemia,

hypertension, diabetes, smoking status and diagnosis of significant events.

46

0

0.2

0.4

0.6

0.8

1

20 30 40 50 60 70 80 90


Age

MaleFemale

Figure 3.3: Transition intensities calculated from Framingham cohorts of transitionfrom hypertension category 2 to category 1 for individuals who have never smoked,have lowest categories of diabetes, hypercholesterolaemia, are lightweight and havenot been diagnosed with any significant event.

The data can be used to build a risk profile history for the period of the study for a

particular individual. Individuals contribute to the exposure and transitions between

different risk profiles and these can be used to evaluate the transition intensities

between risk profiles.

47

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

20 30 40 50 60 70 80 90


Age

UnderweightLightweightOverweight

ObeseMorbidly Obese

Figure 3.4: Transition intensities calculated from Framingham cohorts of transitionfrom diabetes category 0 to category 1 for females, who have never smoked, havecategory 1 of hypercholesterolaemia, category 1 of hypertenstion and have not beendiagnosed with any significant event.

48

Table 3.9: Summary of the data available in the Framingham data sets.

Examinations – Original CohortFactors 1 2 3 4 5 6 7 8 9 10Smoking • • • • • • •Blood glucose • • • • • • • •Total Cholesterol • • • • • • • • •HDL CholesterolLDL CholesterolDiastolic Blood Pressure • • • • • • • • • •Systolic Blood Pressure • • • • • • • • • •Height • •Weight • • • • • • • • • •

Examinations – Original CohortFactors 11 12 13 14 15 16 17 18 19 20Smoking • • • • • • • • •Blood glucose • • • • • • • • •Total Cholesterol • • • •HDL CholesterolLDL CholesterolDiastolic Blood Pressure • • • • • • • • • •Systolic Blood Pressure • • • • • • • • • •Height • • • • • • •Weight • • • • • • • • • •

Examinations – Offspring and Spouses CohortFactors 1 2 3 4 5 6Smoking • • • • • •Blood glucose • • • • • •Total Cholesterol • • • • • •HDL Cholesterol • • • • • •LDL Cholesterol • •Diastolic Blood Pressure • • • • • •Systolic Blood Pressure • • • • • •Height • • • • •Weight • • • • • •

49

Table 3.10: Code representing the risk profile

Digit Risk factor1 Sex (1 for male and 2 for female)2 Category of diabetes3 Category of body mass index4 Category of hypertension5 Category of hypercholesterolaemia6 Category of smoking7 IHD status (0 if no IHD and 1 if IHD)8 Stroke status (0 if no stroke and 1 if stroke)9 Death status (0 if alive and 1 if dead)

Table 3.11: Risk profile of individual 1 in the OS data

Examination Age Risk Profile1 36.50 2010000002 44.58 2010000003 48.87 2010000004 52.33 2010100005 55.95 2010000006 60.00 201020000

50

Chapter 4

The Model

4.1 Introduction

In Chapter 3, we have selected the Framingham data sets to parameterise our model.

We have also seen how to estimate transition intensities of moving from one risk

profile to another using the Framingham data sets. These transition intensities can

be calculated in respect of a variety of risk profiles based on sex, hypertension,

hypercholesterolaemia, diabetes, smoking, BMI and some significant events.

We have also seen that the transitions can be calculated separately for different

categories of other factors. These models for different factors can be associated with

each other to get an individual life history model which will be described in Section

4.2.

The transition intensities obtained using the approach in Chapter 3 are subject to

random errors from the data. We will smooth these transition intensities in Section

4.3.

4.2 Structure of the model

We discussed the risk profile for an individual in Chapter 3. We divide this risk

profile into three parts based on whether a factor is deterministic or stochastic and

if the factors are modifiable or not.

Individuals have choice in their smoking habit. They determine the smoking

51

status for themselves and hence this is unlikely to be affected by any of the risk

factors that we have considered for our model. An individual may decide to quit

smoking based on some risk factor, for example, after having a heart attack. Even

then, it is a choice within the individual’s control and could be built into the model.

We look at some of these possible choices and we treat smoking as deterministic

by specifying such a choice for the individual over their lifetime. For example, we

can specify that an individual starts smoking at the age of 19 and continues till

age 38 and then the person quits smoking forever. We can obtain results from the

model based on different smoking profiles. Sex is a deterministic factor and does not

change over an individual’s lifetime. We will call these deterministic risk factors.

There are other risk factors like hypertension, hypercholesterolaemia, diabetes

and body mass index, that are modifiable over time and hence can move up and

down between the levels of their categories. We will call these modifiable risk factors.

IHD, stroke and death are not modifiable and can only move up in their categories.

We will call these non-modifiable conditions.

So an individual’s risk profile is made up of three components, namely, determin-

istic risk factors, modifiable risk factors and non-modifiable conditions.

Our aim is to build a model for each combination of the deterministic risk factors,

for example, separate models for males and females. Each such model will have

many states representing a category of each of the modifiable risk factors and non-

modifiable conditions and can be parameterised as a multiple state model.

Modifiable risk factors

The modifiable risk factors in our model are shown in Table 4.12.

Table 4.12: Modifiable risk factors.

Risk factors Number of categoriesBody mass index 5

Hypertension 4Hypercholesterolaemia 4

Diabetes 2

52

We note from Table 4.12, that it is possible to have 5× 4× 4× 2 = 160 different

combinations of modifiable risk factors for each combination of the non-modifiable

conditions.

Non-modifiable conditions

We can determine the age at which significant events are diagnosed for the indi-

viduals in the Framingham data. If we consider a particular age for an individual,

we know the conditions that have been diagnosed for the individual by that age.

Based on conditions already diagnosed by a particular age, we can classify the in-

dividual into a category of non-modifiable condition at that age. The categories of

non-modifiable conditions in our model are listed below:

(a) No significant event or Event Free (EF)

(b) Angina Pectoris (AP)

(c) Coronary Insufficiency (CI)

(d) Transient Ischaemic Attack (TIA)

(e) Myocardial Infarction (MI)

(f) Hard Stroke (HS)

(g) Myocardial Infarction and Hard Stroke (MI+HS)

(h) Dead

In our model we assume that if an individual is diagnosed with MI or HS, we do

not need to record their history of diagnosis of AP, CI or TIA because future events

for these individuals depend on if they are diagnosed with MI or HS only and not

dependent on the diagnosis of other events.

We will calculate the occupancy probabilities in Chapter 5 using a recursive

algorithm. We will start with an initial distribution of individuals in different states

and then calculate the distribution of these individuals in different states after a

small period of time. We will refer to this small time period as the “computational

time period”. There is a discrete probability of death (sudden death probability)

following a myocardial infarction and stroke. To apply the sudden death probability,

we will need to count the number of myocardial infarction and stroke cases that have

occurred in the most recent computational time period. As a result, in addition to

53

the conditions mentioned above, we need some more categories for computational

purposes. These conditions are listed below:

(a) Myocardial Infarction occurring in the most recent computational time period

(MI∗)

(b) Hard Stroke occurring in the most recent computational time period (HS∗)

(c) Myocardial Infarction occurring in the most recent computational time period

for an individual having HS (HS+MI∗)

(d) Hard Stroke occurring in the most recent computational time period for an

individual having MI (MI+HS∗)

Based on our definition of conditions, an individual can be in any of the 12

conditions for each of the 160 different states as obtained from the modifiable risk

factors.

The model

The total number of states in our model is equal to 160×12 = 1920. For the “Dead”

state, the different risk factor states are irrelevant and can be represented by only 1

state. This will result in 160 × 11 + 1 = 1761 states in our model (we will use the

model with 1920 states in some of our calculations for easier numerical formulation).

Our model is represented diagramatically in Figure 4.5. Some notes on the model

are listed below:

(a) Two transitions are not allowed in our model in a single instant of time. For ex-

ample, it is not possible for an individual to go from the state with hypertension

category 1 and hypercholesterolaemia category 1 to a state with hypertension

category 2 and hypercholesterolaemia category 2 in a single instant of time.

(b) In our model, the significant events are MI, AP, CI, HS, TIA and Death.

(c) The box marked “Event Free” refers to the condition where an individual does

not have any form of IHD or stroke.

(d) The double lined boxes indicate that it is possible to make transitions between

the risk factors, hypertension, hypercholesterolaemia, body mass index and di-

abetes.

(e) The transitions can be both forward and backward between the modifiable risk

54

factors.

(f) In one computational time period (generally small, say 0.1 years), a transition

from one significant event to another is allowed only once.

(g) The “*” in some of the boxes indicates the significant event resulting in the

transition. The boxes marked with “*” allow us to count the new cases of the

event indicated by the “*”.

(h) Individuals in the “dotted” boxes can die within one computational time period

with a fixed probability of sudden death, described later in this chapter.

(i) We apply the sudden death probability to the individuals in the “dotted” boxes.

(j) Everyone remaining alive in the “dotted” boxes moves to the corresponding

“solid” boxes at the end of each computational time period indicated by the

“dotted” line, thus allowing for multiple events to take place in a lifetime.

(k) Long-term mortality can occur at any time from any of the “solid” boxes in the

model, indicated by the “dashed” box.

4.3 Parameterisation of the model

We parameterise the model by parameterising the transition intensities between

different states in the model. We have assumed that the instantaneous rate of two

or more transitions is 0. This will mean we can assume that when transition in one

factor or from one condition to another is taking place, we know the categories of

other factors and other conditions.

This enables us to parameterise transitions between different categories of each

factor and between different conditions separately. Effects of different categories of

other factors on a particular transition can then be determined by obtaining the

transition intensities separately for different categories of other factors.

55

Event Free

HS

TIA

CI

AP

MI

HS∗

MI+HS

MI∗

HS+MI∗

MI+HS∗

Dead-

-

-

-

-

-

-

�

�

?

6

-

-

-

-

?

6

-

6

?

6

?

-

-

6

?

�

�6

6

6

?

?

?

?

?

?

?

6

-

-

-

-

-

-�

�

�

�

�

�

�

�

�

�

Figure 4.5: Individual life history model terminating in death.

56

We have calculated the raw transition intensities using the approach described in

Chapter 3 and our aim is to smooth the transition intensities using Generalised Lin-

ear Models (GLMs) to obtain functional forms for the transition intensities between

different states in our model.

4.3.1 Generalised Linear Models

Generalised Linear Models (GLM) are a broad class of linear models (introduced by

Nelder and Wedderburn (1972)) that are specified by three components. The random

component consists of independent observations Yi from a natural exponential family

with probability density function of the form

f(yi, θi) = a(θi)b(yi) exp[yiQ(θi)]. (4.1)

The values of θi can change depending on the values of explanatory variables.

Here a(θi) and Q(θi) are functions in θi and b(yi) is a function in yi. The systematic

component relates a linear predictor ηi to the set of explanatory variables through

a linear model

η = Xβ. (4.2)

β is the vector of modelled parameters and X is the matrix consisting of the values

of the explanatory variables for the different observations. The third component

is the link function, which is the functional relationship between the systematic

component and the expected value of the random component. Therefore,

ηi = g(λi). (4.3)

Here, g is the link function that relates the linear predictor ηi to λi = E(Yi).

A GLM can be interpreted as a linear model for a transformed mean of a variable

having a distribution in the natural exponential family. Details about GLMs can be

found in Agresti (1990).

We will now look at two members of the exponential family, the “Bernoulli dis-

tribution” and the “Poisson distribution” and see how they fit into the generalised

linear model setup.

57

Bernoulli distribution

The probability function of an observation Yi from a Bernoulli distribution with

parameter λ is given by

f(yi, λ) = λyi(1 − λ)1−yi (4.4)

where, yi = 0, 1 and 0 < λ < 1. This can also be written as

f(yi, λ) = (1 − λ) exp[yi log(λ/(1 − λ))]. (4.5)

So, the natural link function is

η = log(λ/(1 − λ)) (4.6)

and the GLM using this link is given by

log(λ/(1 − λ)) =∑

j

βjxj. (4.7)

Poisson distribution

The probability function of an observation Yi from a Poisson distribution with pa-

rameter λ is given by

f(yi, λ) = exp(−λ)(λ)yi/yi! (4.8)

where, yi = 0, 1, ... and λ > 0. This can also be written as

f(yi, λ) = exp(−λ)(1/yi!) exp[yi log(λ)]. (4.9)

So, the natural link function is

η = log(λ) (4.10)

and the GLM using this link is given by

log(λ) =∑

j

βjxj. (4.11)

58

Fitting a GLM

We will be using the “R” statistical package to fit the generalised linear models. To

calculate a transition intensity, we observe a group of individuals over some time

(say K) and count the number of transitions taking place (say n) in the time period

K. The number of transitions is a counting process and is assumed to follow the

Poisson distribution.

We will specify the family of the distribution as “Poisson” in the GLM. Our

observations are the number of specified transitions from each state. The variables

identifying the risk profile for each state will be the set of explanatory variables.

Let us define the random variable X as counting the number of transitions within

a year. Let us assume this follows a Poisson(λ) distribution.

We observe from the data the number of transitions (n) for an exposure of K

years. Let λ̂ denote the estimate for the parameter λ and β̂ denote the estimate for

the parameter β.

We note that

n = K × λ̂

log(n) = log(K) + log(λ̂)

log(n) = log(K) +∑

j β̂jxij.

While modelling the intensities using a GLM to estimate the β’s using the equa-

tion above, we use the log of exposure (log(K) in the equation) as an offset variable.

Not all explanatory variables are likely to impact each transition and we will use

the “step function” to select significant explanatory variables. When investigating

the significance of a particular factor, we will not use that particular variable as a

potential explanatory variable because all the transitions will take place from the

same category of that variable.

The “step function” starts with the smallest model possible and then includes

the explanatory variable which results in maximum reduction in AIC (Akaike’s In-

formation Criterion). The process will keep on including explanatory variables as

long as the reduction in AIC is significant.

We will explain the selection procedure with an example. Consider the transition

from category 2 of hypertension to category 3 of hypertension. Let nj be the number

59

of transitions from state j which is specified by the levels of other risk factors. Also

let Ej be the exposure for state j. We start with the smallest model given by

log(nj) = log(Ej).

The possible explanatory variables are:

(a) Age

(b) Age2

(c) Sex

(d) Smoking

(e) Cholesterol level

(f) Diabetes status

(g) Cohort

(h) Body mass index

(i) IHD status

(j) Stroke status

Note that “Blood pressure” is not a possible explanatory variable.

The “step” function in the GLM will calculate the reduction in AIC from includ-

ing each of these variables one at a time. This step will also calculate the results for

a model that does not add any variable in that particular step and is referred to in

the R GLM computing process as “none”. The results are shown in Table 4.13

From Table 4.13 we note that adding “Cohort” as an explanatory variable results

in the maximum reduction in AIC. We add “Cohort” to our present model and we

get

log(nj) = log(Ej) + β̂cohort.

This will now be our “none” model. We then proceed to the next step with

“Cohort” removed from the set of possible explanatory variables listed above. We

continue this process until the maximum reduction in AIC results from the “none”

model. The results in the last step of our example are given in Table 4.14.

Table 4.14 shows that diabetes and stroke are not significant factors for transitions

from category 2 to category 3 of hypertension as they cannot reduce the AIC any

further.

60

Table 4.13: Results from the first step of the GLM process for transition fromcategory 2 to category 3 of hypertension.

Factors Degrees of freedom (df) Residual Deviance AICCohort 1 6780.5 11681.6

Age 1 7146.6 12047.7Age2 1 7161.7 12062.8

Cholesterol 3 7164.9 12070.0Sex 1 7178.6 12079.7IHD 1 7214.5 12115.6

Smoking 2 7218.4 12121.5none – 7225.0 12124.1

Diabetes 1 7224.4 12125.6Stroke 1 7225.0 12126.1BMI 4 7223.5 12130.6

Table 4.14: Results from the last step of the GLM process for transition fromcategory 2 to category 3 of hypertension.

Factors df Residual Deviance AICnone – 6680.8 11607.9

Diabetes 1 6678.9 11608.0Stroke 1 6680.8 11609.9

We now look at the ANOVA of the accepted model (Table 4.15) .

Table 4.15 also gives the order in which the factors were added to the model

as explanatory variables. For all the transitions we decided to accept factors as

explanatory variables if they were very significant (p-value less than 0.001). We

chose to accept factors based on a p-value of 0.001 because in all cases the relative

levels of the factor made medical sense at this level of sigificance. As a result we

discard some more factors from our model and in our final model we have “Cohort”,

“Sex”, “Age” and “Age2”. We include “Age” in our model because “Age2” is a

significant variable. Our final model for transition from category 2 to category 3 of

hypertension at age x is

log(nj) = log(Ej) + β̂1x + β̂2x2 + β̂Cohort + β̂Sex.

61

Table 4.15: ANOVA of the accepted model for transition from category 2 to category3 of hypertension.

Factors df Deviance Residual df Residual Deviance p-valueNULL - – 11262 7225.0 –Cohort 1 444.5 11261 6780.5 0.000000

Sex 1 15.0 11260 6765.6 0.000109Cholesterol 3 14.4 11257 6751.2 0.002452

BMI 4 14.0 11253 6737.2 0.007230Age 1 7.2 11252 6729.9 0.007139Age2 1 38.5 11251 6691.4 0.000000IHD 1 5.0 11250 6686.5 0.026050

Smoking 2 5.7 11248 6680.8 0.100000

For a Poisson family of distributions the residual deviance should approximately

have a chi-squared distribution with the degrees of freedom equal to the residual

degrees of freedom. Thus, the model is a good fit if the value of the residual degrees

of freedom is not in the tail of the related chi-squared distribution, which can be

seen from Table 4.15.

For some transitions the fitting procedure results in significant explanatory vari-

ables which do not have sound medical grounding. In those cases we have removed

these variables from the list of potential explanatory variables. We will look at some

specific examples of such cases in the next section.

4.3.2 Smoothed transition intensities

In general terms, our intensities for transitions between different categories of risk

factors and from one condition to another have the following form:

λ = exp(αint+β1x+β2x2+γsex+γBMI +γsmok+γbp+γchol+γdiab+γMI +γHS+γcohort).

(4.12)

Formula (4.12) allows for an Age2 term but not for any interactions. We found

some significant interaction terms and they will be noted in the relevant sections.

In this formula:

62

αint is an intercept term;

x denotes exact age and β1 and β2 are the coefficients of x and x2, respectively;

γsex is the adjustment for females; the value for males is 0;

γcohort is the adjustment for estimates based on the OS data; the value for the OC

data is 0;

γBMI , γsmok, γbp, γchol and γdiab are the adjustments for the different categories of

BMI, smoking, hypertension, hypercholesterolaemia and diabetes, respectively,

with the lowest category (never–smoked in the case of smoking) having the value

0;

γMI and γHS are the adjustments for presence of MI and HS respectively with a

value of 0 for a state without these conditions;

αint and γcohort are added together to get the intercept term as we want to use a set

of parameters consistent with the more recent OS data.

For transitions between different categories of hypertension, the γbp adjustment

would be excluded from formula (4.12). The corresponding statement applies to

each of BMI, hypercholesterolaemia and diabetes.

We have assumed that two transitions cannot take place at the same instant of

time. Thus when calculating the transition intensity for one factor, we assume that

the transition takes place from the initial category of the other factor. See Section

3.5. Due to this assumption, in all cases where multiple transitions take place we

will bias the estimates towards the initial category of the factors. This bias cancels

out approximately for middle categories, but underestimates or overestimates at the

highest and the lowest categories of the factors. To avoid introducing a bias in the

estimates, we obtain estimates for transition intensities for a factor by considering

exposure and transition for the factor where the categories of other factors have not

changed between two examinations. We will look at specific examples later in this

section.

Body Mass Index

We noted in Chapter 2 that quitting smoking is associated with weight gain. In most

cases the maximum weight gain takes place within a year of quitting smoking. We

63

want to model this effect of smoking on the transitions between categories of BMI. In

the OC, the examinations are approximately 2 years apart. For certain individuals,

we note that they have quit smoking in a period between two examinations, but the

effect of quitting smoking (weight gain) occurs in the subsequent adjacent period

between the corresponding examinations. This results in estimates for the effect of

smoking on BMI which are inaccurate.

As a result we parameterise the transition intensities of moving between categories

of BMI using OS data alone. For transitions between different categories of BMI,

the γcohort adjustment would be excluded from formula (4.12). We set out in Table

4.16 the parameters of these models.

The transition intensities between BMI categories depend on smoking status, in

particular on any change in smoking status within the past year. In our modelling

of BMI transitions we used as explanatory variables any change in smoking status

between ‘Never’, ‘Current’ and ‘Ex’ within the year preceding the change in BMI

category. For all but two of the seven values of this explanatory variable, the tran-

sition intensities did not depend on smoking status. For these cases, the intensities

are shown in Table 4.16 under the heading ‘Smoking: Base case’. The two excep-

tions were ‘Current to Ex-smoker’ and ‘Ex to current smoker’. Put simply, giving

up smoking carries an increased risk of putting on weight and resuming smoking

increases the chance of losing weight in the following year. More precisely, for in-

dividuals who gave up smoking within the last year, the intensities of moving up

a category are higher in some cases (1→2 and 2→3). For those former smokers

who have started smoking again within the last year, the intensity of moving down

a category (2→1) is higher. The full sets of parameters for these two groups are

labelled ‘Current to Ex–smoker’ and ‘Ex to Current smoker’ in Table 4.16.

For the transition from category 1 to category 2 of BMI, at early ages the base

case had a higher transition intensity when compared to the ‘Current-Ex smoker’.

This is an inconsistency and in the practical implementation we set the transition

intensities for ‘Current-Ex smoker’ equal to the base case where they are smaller.

Hypertension was a significant factor for some transitions between BMI categories

statistically, but was excluded from the potential list of explanatory variables as hy-

64

pertension was not significant medically for the transitions between BMI categories.

Table 4.16: Parameters for the models for body mass index.

Smoking: Base caseFactor 0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −2.7725 −3.7188 −5.9188 −3.0350 −3.5036 −3.9435 −7.5065

Age – −0.002208 – – – – – –

Sex: Female – −1.4913 0.5096 1.7403 – – 0.2752 1.5701

Age × Sex:Age × Female – 0.02321 – – – – – –

Smoking: Current to Ex0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −3.4373 −3.2610 −5.9188 −3.0350 −3.5036 −3.9435 −7.5065

Age – 0.02177 – – – – – –

Sex: Female – −0.5367 0.6245 1.7403 – – 0.2752 1.5701

Smoking: Ex to Current0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −2.7725 −3.7188 −5.9188 −3.0350 −3.5036 −3.3230 −7.5065

Age – −0.002208 – – – – – –

Sex: Female – −1.4913 0.5096 1.7403 – – – 1.5701

Age × Sex:Age × Female – 0.02321 – – – – – –

Hypertension

The models for hypertension are parameterised using both the OC and OS data.

The parameters of the model for transitions between the different categories of

hypertension are shown in Table 4.17. Note that:

(i) Diabetes, hypercholesterolaemia and smoking are not significant explanatory

variables for movements between categories of hypertension. Of these variables

hypercholesterolaemia was significant statistically in some cases, but was ex-

cluded from the hypertension models as it is not significant medically as seen

in Chapter 2.

65

(ii) The intensities of moving to a higher category of hypertension increase with age

up to about age 65 (about age 60 for 0 → 1 for males).

(iii) Increasing BMI increases the intensities for 0 → 1 and 1 → 2, and decreases

the intensities for 3 → 2 and 1 → 0.

Table 4.17: Parameters for the model for hypertension.

TransitionsFactor 0→1 1→2 2→3 3→2 2→1 1→0

Intercept −5.2250 −6.7559 −6.1070 −1.4509 −1.5793 −2.0782

Age 0.06934 0.1102 0.09007 −0.007570 −0.01088 −0.009779Age2 −0.0005662 −0.0008271 −0.0006924 – – −0.00002555

Sex: Female −2.2040 −0.1456 0.1204 – – 0.3378

Age × Sex:Age × Female 0.06351 – – – – –

Age2 × Sex:Age2 × Female −0.0004287 0.00006362 – – – −0.00008308

BMI: Lightweight 0.2573 0.01070 – −0.0001575 – −0.002701Overweight 0.6218 0.2145 – −0.02764 – −0.2324

Moderately Obese 0.8785 0.3865 – −0.1198 – −0.4527Morbidly Obese 1.1050 0.6849 – −0.5250 – −0.7060


The models for hypercholesterolaemia are parameterised using both the OC and OS

data. The parameters of the model for transitions between the different categories

of hypercholesterolaemia are shown in Table 4.18.

Features of this model are:

(i) BMI, smoking and hypertension are not included as explanatory variables for

transitions between categories of hypercholesterolaemia. In fact, these factors

were statistically significant for some of the transitions but they have been

excluded since their inclusion is not supported by medical evidence as discussed

in Chapter 2.

66

Table 4.18: Parameters for the models for hypercholesterolaemia.


Intercept −6.1141 −4.9372 −6.2556 −3.2804 −3.5572 −5.2261

Age 0.1499 0.1109 0.1555 0.04828 0.05368 0.09142Age2 −0.001643 −0.001279 −0.001710 −0.0004436 −0.0004721 −0.0007403

Sex: Female −3.2676 −3.0015 −0.5949 −0.4248 −0.2666 2.9518

Age × Sex:Age × Female 0.1147 0.1120 0.01491 – – −0.1051

Age2 × Sex:Age2 × Female −0.0008875 −0.0009411 – – – 0.0008393

Diabetes

The models for diabetes are parameterised using both the OC and OS data. The

parameters for the models for transition intensities for diabetes are shown in Table

4.19.

Table 4.19: Parameters for the models for diabetes.

TransitionsFactor 0→1 1→0

Intercept −13.1194 −5.7628

Age 0.2251 0.08451Age2 −0.001430 −0.0007309

Sex: Female −0.3632 –

BMI: Overweight 0.2369 –Moderately Obese 0.8942 –

Morbidly Obese 1.6080 –

We note that:

(i) The forward transition intensity increases with age up to around age 78 and is

67

lower for females.

(ii) Increased BMI is a significant risk factor for diabetes – see

Well-Connected Reports (2006). In our model the lowest two categories

of BMI, underweight and lightweight, have been combined since their effects on

diabetes are not significantly different. Raw intensities for transitions between

categories of diabetes were calculated from exposure and transitions with BMI

categories unchanged between two consecutive examinations.

(iii) Smoking, hypertension and hypercholesterolaemia are not included as ex-

planatory variables for transitions between categories of diabetes. This is

because they were not statistically significant in our modelling. However,

Well-Connected Reports (2006) says, ‘Smoking increases the risk for diabetes’.

First diagnosis of IHD and stroke

The Framingham data record the exact dates of the first diagnosis of MI, CI, AP,

TIA and HS, but not second or subsequent diagnoses. This allows us to parameterise

the models for transitions corresponding to the first diagnosis of these conditions.

The parameters are set out in Table 4.20. Note that:

(i) Smoking is a (direct) risk factor for MI and HS. The parameters for current

smoker and ex-smoker are shown in Table 4.20; the parameters for never–

smoked, the default category, are zero. We will consider a detailed model for

the effects of giving up smoking in Chapter 8.

(ii) BMI is not a direct risk factor for IHD or stroke. However, BMI is an indirect

risk factor for IHD since it is a direct risk factor for hypertension and diabetes

which, in turn, are direct risk factors for stroke and/or IHD.

From Table 4.20 we can see that smoking is a significant risk factor for MI and for

HS. Based on the OS data, the intensities of MI and HS for smokers are increased by

factors of 3.436 (= exp(1.2343)) and 2.158 (= exp(0.7693)), respectively, compared

to the intensities for those who have never smoked.

68

Table 4.20: Parameters for the models for the first diagnosis of IHD or stroke.

ParametersFactor MI AP CI HS TIA

Intercept −9.8973 −15.8300 −10.9729 −13.1289 −21.1800

Age 0.06167 0.3003 0.04473 0.09979 0.3201Age2 – −0.002252 – – −0.001708

Sex: Female −1.0907 −0.4767 −0.7155 – –

Smoking: Ex 0.05230 – – 0.2050 –Current 1.2343 – – 0.7693 –

Hypertension: Category 1 0.2248 0.3820 – 0.1714 0.9223Category 2 0.6133 0.6534 – 0.4026 1.1290Category 3 0.6957 0.8135 – 1.1907 1.4340

Hyperchol: Category 1 0.2152 – 0.3499 – –Category 2 0.3998 – 0.8898 – –Category 3 0.7914 – 1.3566 – –

Diabetes 0.5635 – 0.8100 – –

Long-term Mortality

The parameters for the model for mortality are given in Table 4.21. This model

is separate from the model for mortality within 30 days of MI or HS (discussed in

Section 4.3.4). Points to note are:

(i) Several interactions are included in the model.

(ii) Prior MI and HS increase the intensity of mortality significantly, although, be-

cause of the negative age interactions, with decreasing effect as age increases.

(iii) The (direct) effect of BMI on mortality is interesting. The default category, Un-

derweight, has parameter 0, which gives it a much higher intensity of mortality

than any of the other categories.

(iv) We will consider a detailed model for the effects of giving up smoking in Chapter

8.

69

The interactions between age and hypertension, prior MI and prior HS shown in

Table 4.21 imply that for certain ages the effect of having a higher level of any of

these factors results in a lower force of mortality. This is a clear inconsistency. In

the practical implementation of our model we eliminate these inconsistencies in a

pragmatic way. For example, at age 90 the relative risk of mortality for increasing

levels of hypertension is 1 for Category 0, 0.86 for Category 1, 0.79 for Category 2

and 0.74 for Category 3. These relative risks are all set to 1 in practice. As a further

example, above age 94.5 the relative risk of mortality from prior HS is less than 1.

This would be set equal to 1.

Figure 4.6 shows the relative risk of mortality at selected ages for each of the five

categories of BMI. The striking features of Figure 4.6 are:

(a) at younger ages, where absolute values of the intensity of mortality are very

low, the relative risk for underweight is far greater than for any other category

of BMI,

(b) at older ages, the relative risk has a U shape as a function of BMI.

From the parameters in Table 4.21 it can be seen that:

(i) Underweight gives the highest relative risk of mortality for all ages up to 83,

(ii) Morbidly obese gives a higher relative risk than moderately obese for all ages

greater than 40,

(iii) Morbidly obese gives a higher relative risk than overweight for all ages greater

than 52, and,

(iv) Morbidly obese gives a higher relative risk than lightweight for all ages greater

than 67.

The observations above are consistent with the evidence in the literature given

in Chapter 2.

4.3.3 Modelling second and subsequent MI and HS

For applications of our model in later chapters, we need to model not only the first

diagnosis of any of our events classified as IHD or stroke but also subsequent MI and

HS. The Framingham data sets record the exact date of first diagnosis of each of CI,

70

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mor. ObeseMod. ObeseOverweightLightweightUnderweight

Relative risk

Body Mass Index

30507090

Figure 4.6: Relative risks of mortality for selected ages and each category of BMI.

AP, MI, TIA and HS so that we can use these data sets to estimate, for example,

the intensity of the transition AP → MI. The results of this modelling are shown in

Table 4.22. For each of the transitions in Table 4.22, no explanatory variables are

significant, not even age or sex, and so the transition intensities are constants, equal

to the exponential of the intercept. To a large extent this somewhat minimal model

is the result of relatively little data for each of these transitions.

The model shown in Table 4.22 for the transition CI → HS has been set equal

to the model for the transition AP → HS, i.e. exp(−5.6925) = 0.00337. This is

because the Framingham data contained no cases of transitions from CI to HS so

that the estimate of the transition intensity from the data was zero. We have set

this intensity equal to the intensity for the transition AP → HS since CI and AP

are related conditions.

The intensities for the transitions MI → MI and HS → HS cannot be estimated

from the Framingham data since only the first event for each of these is recorded.

However, we can estimate these intensities from information provided by Caro et al.

(2005). They report that prior MI is a predictor for subsequent MI (hazard ratio =

1.53), prior HS is a predictor of subsequent MI (hazard ratio 1.26) and that prior HS

71

is a predictor of subsequent HS (hazard ratio = 2.23). (Prior MI is not a predictor

of subsequent HS.) We conclude that:

(i) the transition intensity from MI to the next MI is 1.53 times the intensity given

by the individual’s risk profile, i.e. given by the intensity of the first MI with

parameters as in Table 8.57, with this intensity increased further by a factor

1.26 if the individual has already had a hard stroke, and,

(ii) the transition intensity from HS to the next HS is 2.23 times the intensity given

by the individual’s risk profile, i.e. given by the intensity of the first HS with

parameters as in Table 8.57.

Tables 8.57 and 4.22 set out the parameters for the transition intensities to IHD

and to stroke. From these tables it can be seen that for higher ages the transition

intensity of a first diagnosis of MI is higher than the transition intensity to MI from

AP, CI , HS or TIA. This is an obvious inconsistency. As a result, we assume that

the transition intensity to MI from different conditions is equal to the transition

intensity for a first diagnosis of MI whenever the latter is higher. We make similar

assumptions when determining the transition intensity from different conditions to

HS.

An important feature of our model can be illustrated by considering two individ-

uals who have identical risk profiles – age, sex, smoking pattern, categories of BMI,

diabetes, hypertension and hypercholesterolaemia – and who have both previously

suffered a myocardial infarction. They will both be in the box labelled MI and the

model will treat them identically in terms of transition intensities for future move-

ments. Suppose now that they had reached the MI box via different routes: one

entering from the Event Free box and the other entering from the AP box. For the

latter individual, the prior diagnosis with AP is now irrelevant. In particular, the

intensity of a further MI is the same for these two individuals and equal to 1.53

times the intensity for a first MI for their given risk profile. Note that for some risk

profiles this value will be lower than the value for AP→MI, exp(−4.273), taken from

Table 5.30. We will ignore this apparent inconsistency since the estimates in Table

5.30 are subject to considerable uncertainty and since to allow for it would increase

the number of states in our model, thereby increasing computer run times, and have

72

a negligible effect on any numerical calculations.

4.3.4 Modelling sudden death

There is a significant risk of death immediately following, or soon after, IHD or

stroke. Since the Framingham data record the exact date of death, it is possible to

model this probability, at least for death following a first diagnosis of IHD or stroke.

We consider death (from any cause) within 30 days of the diagnosis of IHD or stroke

and model the probability of this event using a binomial model with the other risk

factors as possible explanatory variables. The model for the probability of death

within 30 days of MI and HS is given in Table 4.23.

These models are broadly in line with summary statistics reported by Caro et al.

(2005).

The probability of death within 30 days of the diagnosis of AP, CI or TIA is not

significantly different from 0.

4.4 Summary

In this chapter we have described the structure of a model which includes transi-

tions between different risk factors and transitions from one condition to another.

Individuals can go up as well down the categories of risk factors, but are not allowed

to move back to certain conditions once they leave that condition.

We have parameterised the model using the Framingham data sets. We did not

have complete information from the Framingham data sets to parameterise the full

model and as a result we had to use some other sources of data to complete the

model.

Table 4.24 summarises the sigificant risk factors for the transition intensities

between risk factors and from one condition to another. ‘*’ indicates the factors

excluded as potential explanatory variables when parameterising a particular tran-

sition intensity. The figures in the brackets indicate the order of significance ( in

terms of reduction in deviance) of the factors in explaining the variability in the

transitions. A superscript “2” in the column for factor Age indicates Age square is

73

also a significant factor. The last column in the Cohort effect gives the exponential

of the coefficient of the Cohort effect obtained from the GLM and is the factor which

when multiplied to the OC transition intensities, gives the transition intensities for

the OS.

74

Table 4.21: Parameters for the model for mortality.

Factor ParametersIntercept −5.9281

Age −0.01475Age2 0.0007460

Sex: Female −0.4099

Smoking: Ex 0.1455Current 0.5689

BMI : Lightweight −1.7760Overweight −2.5030

Moderately Obese −3.3130Morbidly Obese −3.5640

Age × BMI: Age × Lightweight 0.01585Age × Overweight 0.02248

Age × Moderately Obese 0.03635Age × Morbidly Obese 0.04252

Hyperchol: Category 1 −0.2117Category 2 −0.2564Category 3 −0.1145

Hypertension: Category 1 0.2891Category 2 1.0740Category 3 2.7800

Age × Hypertension: Age × Category 1 −0.004866Age × Category 2 −0.01443Age × Category 3 −0.03381

Diabetes 0.2824

Prior MI 3.2340

Age × Prior MI −0.03133

Prior HS 4.2000

Age × Prior HS −0.04398

75

Table 4.22: Parameters for the models for the second and subsequent Events.

Transitions InterceptMI→HS −4.8670

AP→MI −4.2730

AP→HS −5.6925

CI→MI −4.0841

CI→HS −5.6925

HS→MI −4.4166

TIA→MI −4.6734

TIA→HS −4.0856

Table 4.23: Probability of sudden death following MI and HS consistent with theEnglish population.

Event ProbabilityMI exp(−5.9254 + 0.05290 × Age)/(1 + exp(−5.9254 + 0.05290 × Age))

HS exp(−1.9394)/(1 + exp(−1.9394))

76

Table 4.24: Significant risk factors.

FactorTransition Age Sex Smoking BMI H’tens H’chol Diab MI HS Cohort effect

First Event MI (1) (2) (4) (5) (3) (6) (7) 1.60AP (1)2 (3) (2) – 1.00CI (1) (3) (2) (5) (4) 0.36HS (1) (3) (2) (4) 2.05

TIA (1)2 (2) – 1.00

Second Event MI→MI (1) (2) (4) (5) (3) (6) (7) 1.60MI→HS – 1.00AP→MI – 1.00AP→HS – 1.00CI→MI – 1.00CI→HS – 1.00HS→MI – 1.00HS→HS (1) (3) (2) (4) 2.05

TIA→MI – 1.00TIA→HS – 1.00

MI+HS→MI+HS+MI (1) (2) (4) (5) (3) (6) (7) 1.60MI+HS→MI+HS+HS (1) (3) (2) (4) 2.05

H’tens 0→1 (2)2 (4) (3) * (1) 0.331→2 (2)2 (4) (3) * (1) 0.402→3 (2)2 (3) * (1) 0.383→2 (2) (1) * (3) 0.772→1 (2) * (1) 0.581→0 (3)2 (4) (2) * (1) 0.55

H’chol 0→1 (2)2 (3) * (1) 0.411→2 (2)2 (3) * (1) 0.482→3 (2)2 (3) * (1) 0.463→2 (2)2 (1) * – 1.002→1 (2)2 (1) * (3) 0.861→0 (2)2 (1) * (3) 0.90

Diab 0→1 (1)2 (3) (2) * (4) 0.661→0 (2)2 * (1) 0.20

BMI 0→1 * *1→2 (3)2 (1) (2) * *2→3 (1) (2) * *3→4 (1) * *4→3 * *3→2 * *2→1 (2) (1) * *1→0 (1) * *

Mortality (1)2 (6) (5) (7) (2) (10) (9) (3) (4) (8) 0.59

77

Chapter 5

Occupancy Probabilities

5.1 Introduction

In the previous chapter we described the structure of the model and parameterised

the model by specifying the transition intensities between different states. We want

to use the model with transition intensities consistent with the OS and we do this

by adding the coefficient of cohort effect to the intercept.

We want to use this model to calculate conditional occupancy probabilities. Con-

ditional occupancy probabilities are the probability of an individual occupying a

certain state after a fixed amount of time, conditional on the individual starting

from a particular state at a certain age. The sort of calculations we will be inter-

ested in will be the probability (p) that an individual has a MI event by age 60 if

the individual has the lowest risk profile at age 20. This will enable us to measure

the difference in p if the transition intensities change due to some intervention and

we can determine the effect of the intervention on an individual having a MI. We

describe the approach to calculating the occupancy probabilities in Section 5.2.

We will use this approach to calculate the prevalence rates of different conditions

using the model parameterised in Chapter 4. These prevalence rates can be com-

pared to the published prevalence figures for England. We look at the comparisons

and the adjustments needed to the parameters so that the calculated prevalence

rates are consistent with the English prevalence figures in Section 5.3.

78

5.2 Calculation of occupancy probabilities

In mathematical terms the model described in Chapter 4 is Markov – an individual’s

future movements between the states of the model depend only on the current state,

with the individual’s age playing the role of time. We believe the Markov assumption

used in the model is reasonable. The effects of hypertension are likely to depend on

the current level, rather than the build up over time. This is consistent with the

Markov assumption. However, the effects of a given level of hypercholesterolaemia

could possibly build up over time and so the Markov assumption is less reasonable

in this case. An important consideration is that the Markov assumption simplifies

the model considerably in terms of parameterisation and calculation of occupancy

probabilities. The model is almost a continuous time model – the minor exception

to this is the fact that there is a discrete probability of death within 30 days of MI

or HS.

The model has been parameterised by specifying the transition intensities be-

tween states. We need to be able to calculate probabilities from the model; for

example, the probability that a woman aged 20, with a given risk profile at that

age, will have suffered a stroke within the next 50 years. This probability will depend

on the woman’s future smoking pattern. We discussed in Section 4.2 that we will

treat smoking deterministically and obtain results for some specified future smoking

patterns and as a result we assume the woman’s future smoking pattern is known.

The model has 1,761 separate states – there are 160 different combinations of

the risk factors (BMI, diabetes, hypertension and hypercholesterolaemia), for each

of these there are 11 combinations of IHD and/or stroke (including neither IHD nor

stroke) as in Figure 4.5, and finally there is ‘Dead’.

5.2.1 Kolmogorov Forward Equations

Let i and j represent different states, where 0 ≤ i, j ≤ n (= 1, 760). Let µijx denote

the transition intensity from i to j at age x and let tpijx denote the probability that

an individual who is in state i at age x will be in state j at age x+ t, where x, t ≥ 0.

Then, ignoring for the moment the discrete probability of death within 30 days

79

following MI or HS, the Kolmogorov forward equations for this process starting in

state a are:

t+hpajx = tp

ajx hp

jjx+t +

n∑

k=0,k 6=j

tpakx hp

kjx+t j = 0, 1, . . . , n

= tpajx

(

1 − h

n∑

k=0,k 6=j

µjkx+t

)

+

n∑

k=0,k 6=j

tpakx

(

hµkjx+t

)

+ o(h).

Rearranging the terms and then taking the limit as h tends to 0 we get,

∂

∂ttp

ajx = −

n∑

k=0,k 6=j

(

tpajx µjk

x+t − tpakx µkj

x+t

)

j = 0, 1, . . . , n

= tpa0x µ0j

x+t + tpa1x µ1j

x+t + . . . + tpanx µnj

x+t

where we have written:

µiix+t

def= −

n∑

k=0,k 6=i

µikx+t.

We can re-write these equations as:

∂

∂ttp

ajx = fj(t; tp

a0x , tp

a1x , . . . , tp

anx )

where:

fj(t; tpa0x , tp

a1x , . . . , tp

anx ) = tp

a0x µ0j

x+t + tpa1x µ1j

x+t + . . . + tpanx µnj

x+t.

Details on Kolmogorov Forward equations can be found in Hoem (1988).

5.2.2 Solutions to the Kolmogorov Forward Equations

This system of simultaneous, linear, first–order differential equations can be solved

by standard methods, in particular the Runge-Kutta method of order 4. See, for

example, Burden and Fiares (2001). This method involves choosing a step size h

years – in our applications we will use h = 0.1 – and, given {tpijx }

ni,j=0, calculating

{t+hpijx }

ni,j=0. Given an initial distribution over the states at some initial age x0,

probabilities can then be calculated recursively for ages x0 + h, x0 + 2h, x0 + 3h, . . ..

80

Specifically the proportion in state a at age x0 and for states j = 0, 1, . . . , n we

calculate successively:

k1,j = hfj(t; tpa0x0

, tpa1x0

, . . . , tpanx0

)

k2,j = hfj(t + h/2; tpa0x0

+ k1,0/2, tpa1x0

+ k1,1/2, . . . , tpanx0

+ k1,n/2)

k3,j = hfj(t + h/2; tpa0x0

+ k2,0/2, tpa1x0

+ k2,1/2, . . . , tpanx0

+ k2,n/2)

k4,j = hfj(t + h; tpa0x0

+ k3,0, tpa1x0

+ k3,1, . . . , tpanx0

+ k3,n)

Then:

t+hpajx0

= tpajx0

+ (k1,j + 2k2,j + 2k3,j + k4,j)/6

At the conclusion of each recursive step, the probabilities of new cases of MI and

HS can be noted and multiplied by the appropriate probability of death within 30

days as given in Table 4.23. The resulting probabilities can then be subtracted from

those for the MI or HS state and added to probability of being dead. This adjusts

for the discrete probability of death within 30 days following MI or HS with the

simplification that such deaths are assumed to occur within duration h of MI or HS.

5.3 A model consistent with English prevalence

The occupancy probabilities calculated by solving the Kolmogorov forward equations

can be compared to the prevalence rates published for the English population. The

mix of individuals in the English population is very different from the Framingham

population in terms of social class and ethnicity. As a result, the transition intensities

that we have obtained in Chapter 4 are consistent with the Framingham data, but

are unlikely to be consistent with the English population. We will have to adjust

the transition intensities in Chapter 4 to obtain occupancy probabilites that are

consistent with English prevalence.

5.3.1 Health Survey for England

Health Surveys for England (HSE) are a series of surveys organised by the Depart-

ment of Health in England since 1991. These surveys were commissioned to provide

81

regular information on various aspects of health in England. The surveys have cov-

ered the adult population over the age of 16 living in private households in England.

Children have been included in the surveys since 1995.

In each year the survey has had a different focus. The focus of the 2003 survey

was cardiovascular diseases and its risk factors. Details of the methodology can be

found in Sproston and Primatesta (2004c). The prevalence of IHD and stroke can

be found in Sproston and Primatesta (2004a) and the prevalence of different risk

factors are available in Sproston and Primatesta (2004b). We will refer to the survey

as Health Survey for England (2003) (HSE (2003)) and this will include details from

the reports mentioned above. HSE (2003) also gives the prevalence of different risk

factors, IHD and stroke for 1994 and 1998.

The prevalence rates are available for HSE (2003) in different age groups, 16-24,

25-34, 35-44, 45-54, 55-64, 65-74 and 75 and over, for both males and females. We

have the prevalence from HSE (2003) for all the dynamic risk factors that we have

included in our model as well as IHD and stroke. The prevalence for the dynamic

risk factors at age 20 are set out in Table B.64.

5.3.2 Adjustments to the model

We have calculated the occupancy probabilities in each state of our model at all

ages starting at age 20. We want to compare the occupany probabilities obtained

from our model to the prevalence from HSE (2003). To compare like with like, we

calculate the weighted average of the occupancy probabilities over all ages in each

of the age groups in HSE (2003). We denote each age group with the mid-point in

each age group.

We compare the prevalence rates obtained from the model with the English preva-

lence rates at ages 30 (25-34), 40 (35-44), 50 (45-54), 60 (55-64), 70 (65-74) and 80

(75 and over). The English prevalence rates for different risk factors and IHD and

stroke are obtained from the HSE (2003) for the years 1994, 1998 and 2003.

The starting conditions for these calculations are the prevalence rates from the

HSE (2003) for age 20 (16-24). We use the prevalence rates from 2003 for all risk

factors except for cholesterol levels. The prevalence rates used for cholesterol are

82

taken from 1994 as we believe that statins will not have had any significant effects

on the prevalence of hypercholesterolaemia by that time. We want to parameterise

a model for a population unaffected by statins, which were introduced in the early

1990’s. Details are given in Chapter 6.

For hypertension and hypercholesterolaemia, our categories do not match exactly

the levels used in the HSE (2003). We compare the prevalence rates for the model

with the HSE (2003) prevalence using our categories which are the closest match

between the two. For example, categories 1, 2 and 3 of cholesterol combine to give

us total cholesterol greater than or equal to 5.17 mmol/l, which we compare with

hypercholesterolaemia defined in the Health Survey for England as total cholesterol

greater than or equal to 5 mmol/l.

Smoking is treated deterministically in our model. We calculate the prevalence for

two different populations, identified by their smoking habits. The two populations

are:

(a) Never–Smoked

(b) Current Smoker: Smoking from before age 19 and throughout life.

On comparing the prevalence rates to the occupancy probabilities, we observe

that they are not consistent. Looking at the differences between the two sources,

we decided to adjust the parameters for the transition intensities that we obtained

in Chapter 4.

The adjustments were done by trial and error. We started by using the transition

intensities obtained from the Framingham data to calculate the prevalence rates of

different factors. When compared to the English prevalence we saw that there was

either a constant difference in the prevalence rates over all ages or the difference in-

creased by age. We adjusted the intercept and Age coefficients to match the English

prevalence. We had to try different adjustments in an iterative manner before we

found an approximate match. We defined an adjustment giving a good match if the

prevalence rates were within the confidence limits of the English prevalence.

It is interesting to note that the adjustments to the intensities in this section

are mostly to the intercept (a multiplicative factor affecting the overall level of the

intensity) and coefficients of age, age squared and sex. This shows that the English

83

experience in recent years is consistent with the Framingham experience in terms

of the similar increase in the transition intensities from similar changes in the levels

of risk factors like hypertension, hypercholesterolaemia, diabetes, smoking status,

body mass index, prior IHD and prior stroke.

We also note that in the Framingham cohorts the same individuals are followed for

several years resulting in an increase in the average age. A result of this observation

is that estimates for younger ages are obtained from earlier examinations and for

older ages from the later examinations. If there is a calendar time effect, i.e., the

intensities change over time, we will see that the prevalence rates are higher than

expected if the calendar time effect is increasing, and lower when the calendar time

effect is decreasing.

We will describe the adjustments needed for each risk factor transition and from

one condition to other, display graphically the comparison between the occupancy

probabilities obtained from adjusted parameters and list the adjusted parameters.

The adjusted model thus obtained is consistent with the English population preva-

lence. The graphs plot the upper confidence limit (estimate plus 2 standard errors)

and the lower confidence limit (estimate minus 2 standard errors) for the English

prevalence estimates for year 1994 for hypercholesterolaemia and year 2003 for all

other factors.

Body Mass Index

Our aim is to produce transition intensities so that the modelled probabilities of

different levels of BMI are consistent with the English prevalence for the year 2003.

For the purpose of this comparison we combine the underweight and lightweight

BMI as lightweight and we also combine moderately obese and morbidly obese as

obese.

The prevalence rates for obesity at higher ages based on the initial parameter

estimates were a little lower than those for 2003 reported in HSE (2003). These

differences are reduced by adjusting the following terms:

(i) The intercept term for category 1 to category 2 and for category 2 to category

3 transition intensity.

84

(ii) The sex coefficient for category 1 to category 2 transition intensity.

(iii) The age term for males for category 1 to category 2 and for category 2 to

category 3 transition intensity.

(iv) The age term for females for category 1 to category 2 (different adjustment from

males) and category 2 to category 3 (different adjustment from males) transition

intensity.

(v) The age squared term for males for category 1 to category 2 and for category 2

to category 3 transition intensity.

(vi) The age squared term for females for category 1 to category 2 (different ad-

justment from males) and category 2 to category 3 (different adjustment from

males) transition intensity.

Table 5.25 sets out the parameters relevant in England for the transition inten-

sities between different levels of BMI. We infer from the table that for lower ages,

the transition intensity of going from lightweight to overweight is lower for those

who have quit smoking in the last year. For these individuals we assume that the

transition intensity of lightweight to overweight is equal to the transition intensities

from other smoking profiles. The same is true for overweight to obese transition

intensities. Figures 5.7 – 5.12 show the modelled probabilities after adjustments

and raw prevalence rates for each sex and each level of BMI.

85

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994

Never SmokedCurrent Smoker

Figure 5.7: Prevalence rates of male individuals with lightweight, from HSE (2003)

and those calculated from the model for different smoking profiles.

0.1

0.2

0.3

0.4

0.5

0.6

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.8: Prevalence rates of male overweight individuals, from HSE (2003) and

those calculated from the model for different smoking profiles.

86

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.9: Prevalence rates of male obese individuals, from HSE (2003) and those

calculated from the model for different smoking profiles.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.10: Prevalence rates of female individuals with lightweight, from HSE

(2003) and those calculated from the model for different smoking profiles.

87

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.11: Prevalence rates of female overweight individuals, from HSE (2003)

and those calculated from the model for different smoking profiles.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.12: Prevalence rates of female obese individuals, from HSE (2003) and

those calculated from the model for different smoking profiles.

88

Hypertension


different categories of blood pressure are consistent with the English prevalence for

the year 2003.

HSE (2003) gives prevalence rates for two different definitions of hypertension.

Before making any adjustments, for both sexes, the modelled probability of cate-

gories 2 and 3 of blood pressure combined (SBP ≥140 mmHg and DBP ≥90 mmHg),

is lower than the English prevalence of hypertension defined as SBP ≥140 mmHg

and DBP ≥90 mmHg for the year 2003 reported in HSE (2003).

Also the modelled probability of category 3 of blood pressure (SBP ≥160 mmHg

and DBP ≥100 mmHg), is lower than the English prevalence of hypertension defined

as SBP ≥140 mmHg and DBP ≥95 mmHg for the year 2003 reported in HSE (2003).

Our definition of category 3 hypertension does not match exactly with the second

definition of hypertension given in HSE (2003) and we will expect our definition to

produce a slightly lower prevalence of hypertension compared to HSE (2003).

These differences are reduced by adjusting the following terms:

(i) The intercept term for category 1 to category 2 transition intensity.

(ii) The age term for category 2 to category 3 transition intensity.


sities between different categories of blood pressure. Figures 5.13 – 5.16 show the

modelled probabilities after adjustments and raw prevalence rates for each sex and

each category of blood pressure.



different levels of cholesterol are consistent with the English prevalences for the year

1994.

89

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.13: Prevalence rates of blood pressure for males, from HSE (2003) (SBP

≥140 mmHg and DBP ≥90 mmHg) and those calculated from the model (SBP ≥140

mmHg and DBP ≥90 mmHg) for different smoking profiles.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.14: Prevalence rates of blood pressure for males, from HSE (2003) (SBP



90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.15: Prevalence rates of blood pressure for females, from HSE (2003) (SBP



0

0.1

0.2

0.3

0.4

0.5

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.16: Prevalence rates of blood pressure for females, from HSE (2003) (SBP



91

HSE (2003) gives prevalence rates for two different definitions of hypercholestero-

laemia. Before making any adjustments, for both sexes, the modelled probability of

categories 1, 2 and 3 of total cholesterol combined (total cholesterol ≥5.17 mmol/l),

is lower than the English prevalence of hypercholesterolaemia defined as total choles-

terol ≥5 mmol/l for the year 1994 reported in HSE (2003). The categories do not

match exactly and we will expect our definition of hypercholesterolaemia to produce

a lower probability than HSE (2003).

Also the modelled probability of category 3 of total cholesterol (total cholesterol

≥6.66 mmol/l), is lower than the English prevalence of hypertension defined as total

cholesterol ≥6.5 mmol/l for the year 2003 reported in HSE (2003). The categories

do not match exactly and we will expect our definition of hypercholesterolaemia to

produce a lower probability than HSE (2003).

These differences are reduced by adjusting the following terms:

(i) The intercept term for category 0 to category 1 and for level 2 to level 3 transition

intensity.

(ii) The sex coefficient for category 0 to category 1 and for category 2 to category

3 transition intensity.

(iii) The age term for males for category 0 to category 1 and for category 2 to

category 3 transition intensity.

(iv) The age term for females for category 0 to category 1 (different adjustment from

males), category 1 to category 2 (different adjustment from males) and category

2 to category 3 (different adjustment from males) transition intensity.

(v) The age squared term for males for category 2 to category 3 transition intensity.

(vi) The age squared term for females for category 0 to category 1 (different adjust-

ment from males), category 1 to category 2 (different adjustment from males)

and category 2 to category 3 (different adjustment from males) transition in-

tensity.


sities between different levels of cholesterol. Figures 5.17 – 5.20 show the modelled

probabilities and raw prevalence rates for each sex and each level of cholesterol.

92

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.17: Prevalence rates of cholesterol level for males, from HSE (2003) (total

cholesterol ≥5 mmol/l) and those calculated from the model (total cholesterol ≥5.17

mmol/l) for different smoking profiles.

0

0.1

0.2

0.3

0.4

0.5

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.18: Prevalence rates of cholesterol level for males, from HSE (2003) (total

cholesterol ≥6.5 mmol/l) and those calculated from the model (total cholesterol

≥6.66 mmol/l) for different smoking profiles.

93

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.19: Prevalence rates of cholesterol level for females, from HSE (2003) (total

cholesterol ≥5 mmol/l) and those calculated from the model (total cholesterol ≥5.17

mmol/l) for different smoking profiles.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.20: Prevalence rates of cholesterol level for females, from HSE (2003) (total

cholesterol ≥6.5 mmol/l) and those calculated from the model (total cholesterol

≥6.66 mmol/l) for different smoking profiles.

94

Diabetes

Our aim is to produce transition intensities so that the modelled probability of being

diabetic is consistent with the English prevalence for the year 2003.

For both sexes, the modelled probabilities (before making any adjustments) were

higher than the English rates for 2003 reported in HSE (2003). These differences

are reduced by adjusting the following terms:

(i) The sex coefficient for non-diabetic to diabetic transition intensity..

(ii) The age term for non-diabetic to diabetic transition intensity.


sities between non-diabetics and diabetics. Figures 5.21 – 5.22 show the modelled

probabilities after adjustments and raw prevalence rates for each sex.

0

0.05

0.1

0.15

0.2

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.21: Prevalence rates of diabetic males, from HSE (2003) and those calcu-

lated from the model for different smoking profiles.

95

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.22: Prevalence rates of diabetic females, from HSE (2003) and those cal-

culated from the model for different smoking profiles.

In the figures above, we note that current smokers have lower prevalence of dia-

betes compared to never smoked even though smoking does not affect diabetes. We

see that the prevalence rates for current smokers is different to the never smoked in

other risk factors like hypertension and body mass index. These are second order

effects due to effects of smoking on mortality and have not been explored further in

this thesis.

IHD and stroke

Our aim is to produce transition intensities so that the modelled probability of

having IHD or a stroke is consistent with the English prevalence for the year 2003.

For the purpose of this comparison we combine myocardial infarction and angina

pectoris as IHD and consider hard stroke as stroke which is consistent with HSE

(2003).

We would expect the weighted average of never–smoked (weight: 0.7) and current

smoker (weight: 0.3) to produce probabilities of IHD that are consistent with the

English rates. Before making any adjustments the weighted average was higher for

96

IHD and lower for stroke. These differences are reduced by adjusting the following

terms:

(i) The intercept term for transition to MI and transition to HS.

(ii) The sex coefficient for transition to HS.

(iii) The age term for males for transition to MI and transition to HS.

(iv) The age term for females for transition to MI (different adjustment from males)

and transition to HS (different adjustment from males).

Tables 5.29 and 5.30 set out the parameters relevant in England for the transition

intensities to IHD and to stroke. From these tables we note that for higher ages,

the transition intensity of having an MI from no significant events is higher than the

transition intensity of MI from AP, CI , HS or TIA. As a result, we assumed that

the transition intensity to MI from different conditions is equal to the transition

intensity to MI from no significant events, whenever this is higher. For example,

consider an 80 year old male who is a current smoker but has the lowest category

of all other risk factors. The transition intensity of MI for this individual if he does

not have a prior AP is 0.0167 and is 0.0139 if he has a prior AP. In this case we

will set the intensity for this individual of having an MI following a prior AP to

0.0167. We make similar assumptions when determining the transition intensity

from different conditions to HS. Figures 5.23 – 5.26 show the modelled probabilities

after adjustments and raw prevalence rates for each sex and for IHD and stroke.

97

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.23: Prevalence rates of IHD among males, from HSE (2003) and those


0

0.05

0.1

0.15

0.2

0.25

0.3

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.24: Prevalence rates of IHD among females, from HSE (2003) and those


98

0

0.05

0.1

0.15

0.2

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.25: Prevalence rates of stroke among males, from HSE (2003) and those


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994


Figure 5.26: Prevalence rates of stroke among females, from HSE (2003) and those


99

Mortality

Our aim is to produce transition intensities so that the modelled probability of

death is consistent with English Life Table Number 15 (ELT15). We would expect

the probability of death to be uniformly higher than that of the never–smoked and

uniformly lower than that of the current smoker and similar to the weighted aver-

age of modelled probabilities for never–smoked (weight: 0.7) and current smokers

(weight: 0.3). The modelled probabilities are consistent with ELT15 and do not

need any adjustment.


sities to death and Table 5.31 sets out the probability of sudden death relevant in

England.

For mortality we look at mortality at all ages as given by ELT15. We do not

need to group the rates over age groups. We compare the total probability of death

until a specified age from the model and from ELT 15.

Figures 5.27 – 5.28 show the modelled cumulative probabilities of death and the

ELT15 cumulative probabilities of death for each sex.

0

0.2

0.4

0.6

0.8

1

20 40 60 80 100

Cumulative probability of death

Age

ELT15Never Smoked

Current Smoker

Figure 5.27: Probability of death for males, from ELT15 and those calculated from

the model for different smoking profiles.

100

0

0.2

0.4

0.6

0.8

1

20 40 60 80 100

Cumulative probability of death

Age

ELT15Never Smoked

Current Smoker

Figure 5.28: Probability of death for females, from ELT15 and those calculated from

the model for different smoking profiles.

5.3.3 Futher adjustments

For some extreme combinations of age and risk factors, the adjusted transition

intensities, notably for mortality, can have unrealistically large values. For example,

a 20-year old male with prior MI and HS who is a current smoker and has the

highest categories of diabetes and hypertension and the lowest categories of BMI

and hypercholesterolaemia, would, from the figures in Table 5.32, have an intensity

of mortality equal to:

exp(−5.9281 − 0.01475× 20 + 0.000746× 202 + 0.5689 + 2.78 − 0.03381× 20

+0.2824 + 3.234 − 0.03133 × 20 + 4.2 − 0.04398 × 20) = exp(2.9642) = 19.379

This risk profile is not realistic. From Tables B.63 and B.64 we can see that the

prevalence of IHD and stroke in England at age 20 is virtually zero. To avoid this

unrealistic feature, we have capped all transition intensities at 10 which effectively

results in a transition probability very close to 1. This also results in consistent

sets of probabilities (approximately equal to the step size times the intensity) when

101

step size used is less than 0.1. We will cap the transition intensities to 10 whenever

some adjustment to the intensities, for example the calendar time effect in Chapter

7, results in a transition intensity greater than 10.

5.3.4 Patterns in English Prevalence

Prevalence rates for the different categories of risk factors in the English population

are given in HSE (2003). We note that the prevalence decreases over time at all

ages for hypertension and hypercholesterolaemia. This is consistent with the obser-

vation that the forward transition intensities have decreased at a faster rate than

the backward transition intensities in the Framingham Heart Study data (see the

cohort effects in Table 4.24). Conversely, the prevalence of diabetes has increased

in England at all ages as seen from HSE (2003). This is consistent with the obser-

vation that the forward transition intensities have decreased at a slower rate than

the backward transition intensities in the Framingham Heart Study data (see the

cohort effects in Table 4.24).

We also notice that the intensities of having IHD/stroke have increased over time

in the Framingham Heart Study data (see the cohort effects in Table 4.24), but

the transition intensities between risk factor categories have decreased. The change

in prevalence rates will depend on the balance between the relative changes in the

transition intensities. In England we note that the prevalence of IHD/stroke as seen

in HSE (2003) is fairly unchanged over time at all ages.

5.4 Accuracy in obtaining transition intensities

The model described in Chapter 4 has a total of 198 parameters, each of which,

before adjustment, is a maximum likelihood estimate. For each part of the model,

for example, transitions from hypertension Category 3 to Category 2, there is a

variance/covariance matrix for the estimates of the parameters which we get as an

ouput from “R”. We will show the expected values and the variance–covariance ma-

trix for the different transition intensities in Appendix C. The transition intensities

before and after adjustment are given in Chapters 4, 5 and 8. Appendix A gives a

102

summary of the table numbers.

Asymptotically, these estimates will have a multivariate normal distribution and

we can assess the impact of parameter uncertainty by sampling from the parameter

space a large number of times, calculating the probability or other item of interest

for the given set of parameters and then calculating the standard deviation of this

item. We simulate a set of parameters based on the expected values and variance

– covariance matrix using “R” and we can repeat the process to generate multiple

sets of parameters. Table 5.33 shows the results of such calculations based on 100

simulations. For these calculations the starting points are HSE 2003 profiles at

age 20 and age 40 as given in Table B.64. The items calculated are the expected

future life time, the expected future “Event Free” lifetime and the prevalence of IHD

and/or stroke at ages 60 and 80. Note that “Event Free” here is consistent with the

usage in HSE (2003) – it means the person has not been diagnosed with IHD or HS,

but could have suffered a TIA.

The sampling from the parameter space has been based on three assumptions:

(a) The parameter estimates have a multivariate normal distribution.

(b) Estimates of parameters for different transitions are independent.

(c) Adjusting parameters, as described in this chapter, affects only the mean and not

the variance or covariances which results in a slight inaccuracy in the variance

and covariance.

The information in Table 5.33 is:

(1) The item calculated using the estimates of the parameters set out in this chapter

– labelled ‘Fixed parameters’.

(2) The mean of the 100 simulated values of the item – labelled ‘Sampled parame-

ters, Mean’.

(3) The standard deviation of the 100 simulated values of the item – labelled ‘Sam-

pled parameters, St. Dev.’.

103

5.5 Summary

In this chapter we have calculated the occupancy probabilities for each state starting

from a distribution of the population at age 20. We have found that the occupancy

probabilities calculated using transition intensities from Framingham data were in-

consistent with the English population as published in HSE (2003) and we have

adjusted the transition intensities and used them to obtain occupancy probabilities

that are consistent with the English population.

We have smoothed the transition intensities obtained from the Framingham Heart

Study data and adjusted them to match the English prevalence. We simulate dif-

ferent sets of parameters to reproduce results multiple number of times and find

that the results have low standard errors showing that the smoothing procedure

introduces only a small error in the parameter estimates.

104

Table 5.25: Parameters consistent with the English population for the models forbody mass index.

Smoking: Base caseFactor 0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −2.5725 −3.3188 −5.9188 −3.0350 −3.5036 −3.9435 −7.5065

Age – −0.005208 −0.004250 – – – – –

Age2 – −0.000075 −0.000075 – – – – –

Sex: Female – −1.3913 0.5096 1.7403 – – 0.2752 1.5701

Age × Sex:Age × Female – 0.02196 −0.007000 – – – – –

Age2 × Sex:Age2 × Female – 0.000025 0.000025 – – – – –

Smoking: Current to Ex0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −3.4373 −3.2610 −5.9188 −3.0350 −3.5036 −3.9435 −7.5065

Age – 0.02177 – – – – – –

Sex: Female – −0.5367 0.6245 1.7403 – – 0.2752 1.5701

Smoking: Ex to Current0→1 1→2 2→3 3→4 4→3 3→2 2→1 1→0

Intercept −2.0093 −2.5725 −3.3188 −5.9188 −3.0350 −3.5036 −3.3230 −7.5065

Age – −0.005208 −0.004250 – – – – –

Age2 – −0.000075 −0.000075 – – – – –

Sex: Female – −1.3913 0.5096 1.7403 – – – 1.5701

Age × Sex:Age × Female – 0.02196 −0.007000 – – – – –

Age2 × Sex:Age2 × Female – 0.000025 0.000025 – – – – –

105

Table 5.26: Parameters consistent with the English population for the model forhypertension.


Intercept −5.2250 −5.4559 −6.1070 −1.4509 −1.5793 −2.0782

Age 0.06934 0.1102 0.09257 −0.007570 −0.01088 −0.009779Age2 −0.0005662 −0.0008271 −0.0006924 – – −0.00002555

Sex: Female −2.2040 −0.1456 0.1204 – – 0.3378

Age × Sex:Age × Female 0.06351 – – – – –

Age2 × Sex:Age2 × Female −0.0004287 0.00006362 – – – −0.00008308

BMI: Lightweight 0.2573 0.01070 – −0.0001575 – −0.002701Overweight 0.6218 0.2145 – −0.02764 – −0.2324

Moderately Obese 0.8785 0.3865 – −0.1198 – −0.4527Morbidly Obese 1.1050 0.6849 – −0.5250 – −0.7060

Table 5.27: Parameters consistent with the English population for the models forhypercholesterolaemia.


Intercept −5.6141 −4.9372 −4.0056 −3.2804 −3.5572 −5.2261

Age 0.1699 0.1109 0.1305 0.04828 0.05368 0.09142Age2 −0.001643 −0.001279 −0.001360 −0.0004436 −0.0004721 −0.0007403

Sex: Female −0.7676 −3.0015 −1.3449 −0.4248 −0.2666 2.9518

Age × Sex:Age × Female 0.01470 0.06200 −0.01509 – – −0.1051

Age2 × Sex:Age2 × Female −0.00003750 −0.00004110 0.0007500 – – 0.0008393

106

Table 5.28: Parameters consistent with the English population for the models fordiabetes.

TransitionsFactor 0→1 1→0

Intercept −13.1194 −5.7628

Age 0.2171 0.08451Age2 −0.001430 −0.0007309

Sex: Female −0.4632 –

BMI: Overweight 0.2369 –Moderately Obese 0.8942 –

Morbidly Obese 1.6080 –

107

Table 5.29: Parameters consistent with the English population for the models forthe first diagnosis of IHD or stroke.


Intercept −10.8973 −15.8300 −10.9729 −11.8289 −21.1800

Age 0.06967 0.3003 0.04473 0.08779 0.3201Age2 – −0.002252 – – −0.001708

Sex: Female −1.0907 −0.4767 −0.7155 1.7000 –

Smoking: Ex 0.05230 – – 0.2050 –Current 1.2343 – – 0.7693 –



Diabetes 0.5635 – 0.8100 – –

Age × Sex:Age × Female 0.002000 – – −0.03200 –

108

Table 5.30: Parameters consistent with the English population for the models forthe second and subsequent events.

Transitions InterceptMI→HS −4.8670

AP→MI −4.2730

AP→HS −5.6925

CI→MI −4.0841

CI→HS −5.6925

HS→MI −4.4166

TIA→MI −4.6734

TIA→HS −4.0856

Table 5.31: Probability of sudden death following MI and HS consistent with theEnglish population.

Event ProbabilityMI exp(−5.9254 + 0.05290 × Age)/(1 + exp(−5.9254 + 0.05290 × Age))

HS exp(−1.9394)/(1 + exp(−1.9394))

109

Table 5.32: Parameters consistent with the English population for the model formortality.


Age −0.01475Age2 0.0007460


Smoking: Ex 0.1455Current 0.5689








Diabetes 0.2824

Prior MI 3.2340


Prior HS 4.2000


110

Table 5.33: Results of calculations using simulated parameters.

Sex Smoking Fixed Sampled parametersstatus parameters Mean St. Dev.

Expected future lifetime from age 20Male Never 58.6 58.4 0.6

Current 51.6 51.4 0.6Female Never 62.4 62.3 0.6

Current 56.1 56.0 0.6

Expected future “Event Free” lifetime from age 20Male Never 53.2 53.0 0.6


Current 51.4 51.3 0.6

Expected future lifetime from age 40Male Never 39.3 39.2 0.6


Current 37.2 37.1 0.6

Expected future “Event Free” lifetime from age 40Male Never 34.0 33.9 0.5


Current 32.7 32.7 0.6

Prevalence of IHD/stroke at age 60 starting from age 20Male Never 10.19% 10.39% 0.71%

Current 16.75% 16.96% 1.18%Female Never 6.23% 6.35% 0.41%

Current 9.60% 9.75% 0.64%

Prevalence of IHD/stroke at age 80 starting from age 20Male Never 29.79% 30.11% 1.99%

Current 44.45% 44.62% 3.14%Female Never 18.87% 19.10% 1.27%

Current 29.34% 29.53% 2.22%

111

Chapter 6

Treatments

6.1 Introduction

In previous chapters we parameterised a model that produces occupancy probabili-

ties consistent with the prevalence rates for different conditions in England.

Over the years, the risk factors we have considered, and many more, have been

associated with cardiovascular diseases, renal diseases, cancers and other diseases.

There are many studies which indicate that the prevalence of diseases can be reduced

by simply reducing the prevalence of harmful levels of these risk factors. Guidance

has been issued about the levels of the risk factors that are desirable for everyone.

Details of the guidance and the categorisation of factors are described in Chapter 3.

Many drugs have been developed that have a significant impact in reducing the

levels of risk factors from higher levels to lower levels. New drugs have been devel-

oped which are more potent and have greater benefits above and beyond the effects

of earlier drugs.

We will discuss the effect of some of these drugs in Section 6.2. We will describe

in greater detail the class of drugs called “Statins” in Section 6.3 and finally we will

describe a model to measure the effects of different treatments in Section 6.5.

112

6.2 Treatment for conditions

We have noted that some of the risk factors are modifiable. See Chapter 4. The

risk factors may be modified by changes in lifestyle, like diet or exercise. When the

levels are significantly higher than the desirable levels, individuals may need drug

therapy or surgical interventions.

In the OS data of the Framingham cohorts, the data records the drugs taken by

the participants in each exam. These drugs include cholesterol-lowering drugs and

blood-pressure-lowering drugs.

Here we will look at the drugs available for the conditions hypercholesterolaemia

and hypertension. We will also describe the effect these drugs have on the conditions

and the effect they can have on cardiovascular diseases.

6.2.1 Cholesterol-lowering drugs

We have described the effect of cholesterol on cardiovascular diseases in Chapter 2.

A reduction in cholesterol can reduce the risk of cardiovascular diseases. Different

classes of cholesterol lowering drugs are listed below:

(a) Statins

(b) Nicotinic acid or Niacin

(c) Fibrates

(d) Bile acid-binding resins

Statins are the most commonly used cholesterol reducing drug in use now and we

will discuss this class of drugs in more detail in Section 6.3. More details on drug

therapy for reducing cholesterol can be found in Well-Connected Reports (2007b).

According to Burke et al. (1997), the reduction in cholesterol does not reduce

the narrowing of arteries but is assumed to stabilise the plaques resulting in lower

frequency of plaque rupture.

According to Law et al. (1994), cohort studies show the effect of age – a decrease

in LDL cholesterol concentration of 0.6 mmol/l in men is associated with a decrease

in the risk of ischaemic heart disease of about 50% at age 40, 40% at age 50, 30%

at 60 and 20% at 70 and over. The trials also show that little reduction in risk of

113

ischaemic heart disease occurs in the first two years after lowering cholesterol, but

the full reduction in risk of ischaemic heart disease is achieved within five years.

Wannamethee et al. (2000) have found that the role of blood cholesterol in stroke

prevention is unclear. Most prospective studies have failed to find a relation between

total cholesterol and risk of stroke. This is also supported by the fact that cholesterol

is not a significant factor for stroke. See Chapter 4.

In the Framingham cohorts some of the participants were prescribed cholesterol

lowering drugs like fibrates or niacin but these drugs did not include statins as they

were not widely available at the time of the study.

6.2.2 Blood pressure lowering drugs

We described the effect of blood pressure on cardiovascular diseases in Chapter 2. A

reduction in blood pressure can reduce the risk of cardiovascular diseases. Different

classes of blood pressure lowering drugs are listed below:

(a) Diuretics

(b) Beta-blockers

(c) Angiotensin converting enzyme (ACE) inhibitors

(d) Calcium-channel blockers

(e) Angiotensin-receptor blockers

(f) Vasolidators

In the Framingham cohorts some of the participants were prescribed with blood-

pressure-lowering drugs which included most of the drugs mentioned above. The

data used to parameterise the models in Chapter 5 already have the effects of blood-

pressure-lowering drugs. As a result, we will not attempt to measure the effects of

blood-pressure-lowering drugs in this thesis.

6.2.3 Other drugs

Wald and Law (2003) have proposed a cocktail of drugs known as the “Polypill ”,

and they estimate that the drug can reduce IHD events by 88% and stroke events

by 80%. The “Polypill” aims to reduce the risk of cardiovascular events by reducing

114

cardiovascular risk factors like hypercholesterolaemia, hypertension and the effects

of serum homocysteine and platelet function. The drug is a combination of six

drugs and is made up of a statin, three of the first five blood pressure lowering

drugs mentioned in the previous section, aspirin and folic acid. We are unable to

measure the effects of such a drug as we do not have the data on risk factors like

serum homocysteine and platelet function.

There are other drugs for the risk factors like diabetes and obesity, but lifestyle

changes are more likely to be used in prevention or reduction in the risks from these

factors.

6.3 Statins

6.3.1 Classes of statins

Statins are a class of lipid-lowering drugs. New statins have been developed in

recent years which are more potent than some earlier statins. The different classes

of statins are listed below:

(a) Pravastatin

(b) Simvastatin

(c) Lovastatin

(d) Fluvastatin

(e) Atorvastatin

(f) Rosuvastatin.

6.3.2 Effect on cholesterol

Many studies have been carried out to measure the effect of statins on the reduction

of cholesterol levels and their effect on cardiovascular diseases. Table 2 in Law et al.

(2003) gives the absolute reduction in LDL cholesterol using different forms of statins

in varying doses.

Law et al. (2003) also show that the reduction in LDL for a standard dose of a

statin is 1.8 mmol/l. The standard doses (given in Law et al. (2003)) for different

115

statins are given in Table 6.34.

Table 6.34: Standard dosage for different statins.

Statin Daily dosage in mgRosuvastatin 5Atorvastatin 10Lovastatin 40Simvastatin 40

6.3.3 Effect on cardiovascular diseases

Studies measuring the effect of statins on reduction in risk of cardiovascular dis-

eases have reported a reduction in the risk of cardiovascular events following treat-

ment with statins, both in individuals with IHD/stroke and those without prior

IHD/stroke.

The reduction in risk of IHD is not immediate and can take between 2 to 9 years

before the full effect can be seen (see Vaughan et al. (1996)). In a meta-analysis,

Law et al. (2003) have determined the percentage reduction in risk by duration of

treatment. Their figures are given in Table 6.35. They also report that the reduction

in the relative risk of IHD is independent of the risk factors, including the baseline

levels of LDL concentration.

Table 6.35: Percentage reduction in risk of fatal and non-fatal MI by duration oftreatment.

% Reduction in IHD risk forDuration of treatment a reduction in LDL of

1 mmol/l 1.8 mmol/l1st year 11 192nd year 24 39

3rd-5th years 33 516th and subsequent years 36 55

IHD in Table 6.35 actually refers to fatal and non-fatal MI. The reduction in risk

116

mentioned in Law et al. (2003) is for a reduction of 1 mmol/l in LDL cholesterol.

The reduction in risk of IHD for reduction in LDL different from 1 mmol/l can be

derived from risk reduction values for 1 mmol/l. We will demonstrate how this is

done through an example.

Let us assume the reduction in LDL is 1.8 mmol/l (the reduction for a standard

dose). Then the reduction in risk of IHD in the second year of treatment is given

by 1 − (1 − 0.24)(1.8/1.0) which is equal to 0.39. Here, 0.24 is the reduction in risk

in year 2 for 1 mmol/l reduction in LDL cholesterol. The reduction in risk of

IHD at different durations for 1.8 mmol/l reduction in LDL calculated from the

corresponding reduction in risk figures for 1 mmol/l reduction in LDL is given in

Table 6.35.

The same meta-analysis also shows that the reduction in risk of stroke is 10% for

1 mmol reduction in LDL cholesterol and 17% for a reduction in LDL cholesterol of

1.8 mmol/l. The reduction in risk of stroke is the same for all durations of treatment.

We have seen in Chapter 4 that cholesterol is not a risk factor for incidence of

stroke and Law et al. (2003) find it paradoxical that there is reduction in stroke risk

due to the use of statins. According to Wannamethee et al. (2000), despite the lack

of association between serum total cholesterol and risk of stroke in observational

epidemiological studies, the results of lipid-lowering trials with statins suggest ben-

efit for stroke reduction. It has been suggested that the beneficial effects of statins

on clinical events may involve mechanisms independent of lipid-lowering.

There are effects of statins which are not related to lipid lowering and they have a

beneficial effect on cardiovascular diseases (both myocardial infarction and stroke).

These effects are listed below:

(a) Modification of the arterial walls (endothelium).

(b) Stabilising the vulnerable plaques and making them less prone to rupture.

(c) Affecting the formation of blood clots and breaking up the blood clots.

(d) Changing the inflammatory responses on the walls of arteries.

(e) Inhibiting the spread of harmful cells and help in programmed cell death.

The details on beneficial effects of statins other than lipid lowering can be found

in Vaughan et al. (1996), Palinski (2001) and Wannamethee et al. (2000).

117

6.3.4 Adverse effects of statins

Statins have some adverse effects as well as the beneficial effects we have seen so

far. According to Well-Connected Reports (2007b), “Side effects may include gas-

trointestinal discomfort, headaches, skin rashes, muscle aches, sexual dysfunction,

drowsiness, dizziness, nausea, constipation and numbness or tingling in the hands

and feet”. The report also mentions that statins may result in an uncommon con-

dition which results in muscle damage and a special form of the condition may lead

to kidney failure.

We do not model the adverse effects of statins in this thesis.

6.4 Treatment recommendations

Different guidelines based on levels of cholesterol and presence of other risk factors

have been developed for the prescription of statins for cholesterol reduction. In

this section we will describe these recommendations and also describe how these

recommendations can be incorporated into our model.

6.4.1 Description

We will describe some of the recommendations for prescribing treatment with statins.

National Cholesterol Education Programme (NCEP)

According to the NCEP guidelines, as described in NCEP Expert Panel (2001),

the initiation of treatment for high cholesterol is given in terms of levels of LDL

cholesterol. The levels are different for the different risk categories as shown in

Table 6.36.

We note the following points about the NCEP recommendations:

(a) The recommendations use Framingham projections of 10–year absolute CHD

risk for risk classification purposes. See NCEP Expert Panel (2001) for the

details of the Framingham 10–year risk calculation.

(b) Diabetes is considered as a CHD risk equivalent.

(c) Major risk factors for risk classification are:

118

Table 6.36: NCEP guidelines regarding levels at which to consider treatment.

LDL level at which to LDL level at which toRisk Category initiate therapeutic consider drug

lifestyle changes therapyin mg/dL in mg/dL

CHD orCHD risk equivalent ≥ 100 ≥ 130

or 10 year risk > 20%

2+ risk factors and ≥ 130 ≥ 13010 year risk 10%–20%

2+ risk factors and ≥ 130 ≥ 16010 year risk <10%

0–1 risk factor ≥ 160 ≥ 190

(a) Cigarette smoking

(b) Hypertension (blood pressure ≥140/90 mm Hg or on antihypertensive med-

ication)

(c) Low HDL cholesterol (<40 mg/dL)

(d) Family history of premature CHD

(e) Age (men ≥45 years; women≥55 years)

(f) HDL cholesterol ≥60 mg/dL counts as one negative factor.

First Joint British Societies (JBS 1)

The JBS 1 recommend use of a statin based on 10–year risk of fatal and non-fatal

myocardial infarction and new angina calculated from equations in Anderson et al.

(1991). A statin treatment is then recommended if the person’s risk is ≥ 15% and

total cholesterol is ≥ 5 mmol/l or LDL cholesterol ≥ 3 mmol/l. Details can be found

in McElduff et al. (2006).

119

National Service Framework (NSF)

The recommendations of the NSF are as those of JBS, but the risk must be ≥ 30%

over a 10-year period to receive treatement with a statin. Details are in McElduff

et al. (2006).

Fourth British Hypertension Society (BHS IV) and second JBS (JBS 2)

Recommendations from BHS IV and JBS 2 are based on a 10–year risk of fatal or

non-fatal myocardial infarction, new angina and stroke estimated from the equations

in Anderson et al. (1991). There are some modifications to the equations: the age

is projected forward to 49 years if the current age is < 50, to 59 if the current age

is 50-59 and to 69 if the current age is ≥ 60. The charts for the recommendations

are shown in Williams et al. (2004) and Wood et al. (2005). A statin is then rec-

ommended if the patient’s risk is ≥20% and total cholesterol ≥4 mmol/l or LDL

cholesterol ≥2 mmol/l. Details about these recommendations can also be found in

McElduff et al. (2006).

Third Joint Task Force for European and other Societies on Cardiovas-

cular Disease Prevention in Clinical Practice (European)

The European recommendations are based on 10–year risk of a fatal CVD event

estimated from the charts in De Backer et al. (2004). A statin will be recommended

if the risk is ≥5% and total cholesterol ≥5 mmol/l or LDL cholesterol ≥3 mmol/l

or regardless of calculated risk if serum cholesterol is ≥8mmol/l or LDL cholesterol

≥6mmol/l. Details are in McElduff et al. (2006).

Other recommendations

There are other recommendations that are based on age only. Wald and Law (2003)

suggest that everyone over the age of 55 should be given the “Polypill” and a stan-

dard dose of a statin is a component of the “Polypill”. Recently there were claims

in the popular press (Curtis (2007)) that statins should be recommended to all men

over the age of 50 and women over the age of 60.

120

6.4.2 Incorporating the recommendations in our model

From the description of the different treatment criteria, we note that they are based

on levels of LDL and the overall levels of risk of myocardial infarction or stroke

based on the levels of other risk factors. Some recommendations are also based on

attaining a specific age.

Recommendation based on risk

A living individual, in our model, can be in any of the 1760 states. Based on the

risk profile given by the levels of risk factors for that state we can calculate the risk

of stroke and myocardial infarction according to the recommendation (for example,

10–year absolute CHD risk for the NCEP guidelines). We also know the level of LDL

cholesterol for that state. Given the level of LDL cholesterol and the risk calculation

we can decide whether individuals in that state will be treated or not.

For some of the recommendations, our categorisation of risk factors does not

match exactly the categorisation needed to measure the risk, although the categories

are approximately the same. Approximate risks and LDL levels can be obtained for

each state for each recommendation.

In the NCEP guidelines, diabetes is considered a CHD equivalent. So the indi-

viduals in the state with diabetes and hypercholesterolaemia category 1 or more will

be treated with a statin.

Recommendation based on age

When a recommendation is based on age alone, we do not need to know the state

an individual is in; once the individuals reach a specified age in the model, they are

treated with a statin.

6.4.3 Proportion of population treated

McElduff et al. (2006) considered a population of 1653 men aged between 49 and

65 and checked how many of them should be treated with statins for the different

treatment recommendations. The proportions treated for each recommendation are

given in Table 6.37.

121

Table 6.37: Proportion treated at each age based on different treatment recommen-dations.

Recommendation Proportion treatedNCEP 0.58JBS 1 0.62NSF 0.14BHS IV & JBS 2 0.77European 0.46

We see from Table 6.37 that a significant proportion of the population considered

by McElduff et al. (2006) were eligible for treatment with the highest proportion

given by BHS IV & JBS 2. We have to note that these proportions are at a single

point in time and as the levels of risk factors move dynamically over time, more

people become eligible for statin treatment.

In our model, we consider a simple example where everyone with hycholestero-

laemia category 3, diabetes, IHD or stroke will be treated with a statin. We start

with a 20 year old individual and assume that the categories of risk factors are dis-

tributed as in Table B.64 for age 20. We will consider separately both males and

females and never–smoked and current smokers. The proportions of these popula-

tions who should be receiving treatment at 10–year intervals are given in Table 6.38.

We will describe how to calculate these proportions in Section 6.5.

Table 6.38: Percentage treated at each age based on their risk profile starting at age20.

Male FemaleAge Never–Smoked Current Smoker Never–Smoked Current Smoker30 18.6 18.9 10.1 10.340 41.6 42.3 18.7 19.350 64.1 65.0 39.4 40.360 78.0 79.3 66.7 67.870 85.6 87.2 85.0 85.980 89.9 91.9 92.8 93.590 92.8 95.2 95.6 96.3

122

Here also we notice that a significant proportion of the population should be

receiving treatment by the age of 50 and around 90% of the population should be

receiving treatment with a statin by the age of 80.

In both Tables 6.37 and 6.38, we give the proportion of the population that should

actually be treated with a statin. According to Walley et al. (2005), the compliance

by individuals in taking statins is about 72.3% and hence the effects that we observe

in a population will be lower than what we will predict using the recommendations

above.

6.5 Model for treatment effects

In this chapter we have discussed the use of statins to reduce levels of LDL cholesterol

and the beneficial effects on the risk of myocardial infarction and stroke. We can

use our model developed in Chapter 5 to measure these beneficial effects. We note

that the model developed in Chapter 5 is for a population without the influence of

statins.

Relative risk of an event

Let us denote the relative risk of an event in the treated individuals when compared

to the untreated individuals by RR and the reduction in relative risk by (1−RR).

Table 6.35 shows the values of (1−RR) at different durations for MI. Let us denote

by δd the factor (1−RR) at duration of treatment d for MI for a reduction of 1.8

mmol/l. Then if µkjx is the untreated transition intensity for the states k and j, the

transition intensity of having an MI, then the treated transition intensity for the

same states is given by

µkjx,d = δd × µkj

x (6.13)

We denote by δ0 the constant factor (1−RR) at all durations of treatment for

HS. Then if µkjx is the untreated transition intensity of having an HS for the states

k and j, the treated transition intensity for the same states is given by

123

µkjx,d = δ0 × µkj

x (6.14)

6.5.1 Model for treatment recommendations based on risk

Our model is specified by the transition intensities between different states at each

age. At each step to specify the transition intensities we need to know the current

state that the individuals are in, their current age and if the individuals are treated

or not. To know if the individuals are treated or not, it is not sufficient to know

their current state because the individuals may not be eligible for treatment in the

current state, but in the past they may have been in a state where treatment was

recommended and they started getting treatment. Once an individual starts getting

treatment, they get the treatment for life and we will need to know their movement

history to know if they have been receiving treatment or not. Hence the model is

semi-Markov.

We need to calculate the probabilities P [alive at age x], for all ages x > x0 to

calculate the expected future lifetime from age x0, and P [Event Free at age x], for

all ages x > x0 to calculate the expected future “Event Free” lifetime from age x0.

In the calculation of an “Event Free” lifetime we will include TIA within “Event

Free” because this is consistent with HSE (2003). The way to do these calculations

will be to condition on when the treatment starts, but it is difficult to do such a

conditioning in continuous time. We approximate these probabilities by assuming

that the treatments can start at integer ages only. So, we can write

P [alive at age x] =

x−x0∑

k=0

P [alive at age x|treatment = k] × P [treatment = k]

(6.15)

where P [treatment = k] is the probability that an individual has been treated

for duration k and P [alive at age x|treatment = k] is the probability that an

individual is alive at age x with duration of treatment k, starting from age x0.

We can calculate probabilites of the type P [alive at age x|treatment = k] using

the transition intensities adjusted for treatment as in Equations 6.13 and 6.14 using

the procedure to calculate the occupancy probabilities in Section 5.2.2.

124

We consider the example in the previous section where individuals get treatment

if they have hycholesterolaemia category 3, are diabetic or they have IHD or stroke

and calculate the expected future lifetime and expected “Event Free” lifetime from

age 20. The results are given in Table 6.39.

Table 6.39: Effect of treatment with statins based on risk profile on expected futurelifetime and expected future “Event Free” lifetime.

Male FemaleNever–Smoked Current Smoker Never–Smoked Current Smoker

Expected future 59.2 52.6 62.8 56.8lifetime from age 20

Expected future“Event Free” 53.8 47.3 58.3 52.2

lifetime from age 20

6.5.2 Model for treatment recommendations based on age

If the treatment recommendations are based on a specified age, to know if the

individuals are treated or not, it is sufficient to know their current age irrespective

of the state they are in or they have been in. The current age will also tell us the

duration of treatment (current age − specified age of treatment). So the model

is Markov and we can calculate the expected future lifetime from the probabilities

calculated using the approach in Section 5.2.2 by adjusting the transition intensities

using Equations 6.13 and 6.14.

Let us consider the English population at age 20 (see Table B.64) in 2003. We

investigate the effect of treating everybody with a statin after reaching a specific

age (xT ). So, the population is untreated up to age xT and on attaining age xT the

whole population is treated with duration 0 at age xT . We investigate the effect of

statins on the population through the beneficial effects on expected future lifetime

and expected future “Event Free” lifetime. The results are given in Table 6.40.

From Table 6.40 we note that the incremental benefits can be achieved both

125

Table 6.40: Effect of treatment with statins on expected future lifetime and expectedfuture “Event Free” lifetime from age 20 by age of treatment.

Future Expected future lifetime from age 20Male Female

Never–Smoked Current Smoker Never–Smoked Current SmokerTreated at age 20 59.3 53.0 62.9 57.0Treated at age 30 59.3 52.9 62.9 57.0Treated at age 40 59.2 52.8 62.9 56.9Treated at age 50 59.2 52.5 62.8 56.8Treated at age 60 59.0 52.2 62.7 56.7Untreated 58.6 51.6 62.4 56.1

Expected future “Event Free” lifetime from age 20Male Female

Never–Smoked Current Smoker Never–Smoked Current SmokerTreated at age 20 54.6 48.3 59.2 53.2Treated at age 30 54.6 48.2 59.1 53.1Treated at age 40 54.5 47.9 59.1 53.0Treated at age 50 54.3 47.5 59.0 52.8Treated at age 60 54.0 46.8 58.8 52.4Untreated 53.2 45.8 58.2 51.4

in terms of expected future lifetime and expected future “Event Free” lifetime by

treating individuals earlier rather than later. But the increments become smaller as

age of starting treatment (xT ) becomes lower. The effect of treating everyone from

age 20 is only marginally better than treating everyone from age 30 which is only

marginally better than treating everyone from the age of 40.

We note that significant improvement in expected future lifetime and expected

future “Event Free” lifetime can be obtained by treating everyone over the age

of 50. Treating everyone from the age of 50 will increase the life expectancy for

male smokers by about a year and male non-smokers by about half a year. The

corresponding figures for females are a little lower, about half a year and quarter of

a year respectively.

These improvements are bounded at 0 for the untreated population and by the

improvements of 20 year olds at the other end (considering the population of cur-

rent 20 year olds). If we then compare these effects with the effects of treatment

126

recommendations based on risk, they will lie within these bounds. We refer to the

expected future lifetime of 59.2 for a male who has never smoked given in Table 6.39

and note that it lies between 59.3 and 58.6 given in Table 6.40 and hence the effects

of treatment recommendation based on risk will be bounded by recommendation

based on age (the expected future lifetime for the untreated population is the same

whatever the treatment recommendation).

We assume that statins are prescribed for everyone from the age of 50 in the

remainder of this chapter. We now want to look at the benefits of statin treatment

for an average individual from England. We start with the English profile for age

50 from HSE (2003) given in Table B.64.

Let us consider the average English population with the profile given in Table

B.64 at age 50. We calculate the expected future lifetime and expected future “Event

Free” lifetime for this population for both males and females and for both never–

smoked and current smokers. We also calculate coresponding figures for two other

populations in which the perecntages in different categories of risk factors remain

the same as the average English population, but the percentages of the population

with significant events is different. In one population everyone has MI at the start

(percentage of MI is set as 100 in Table B.64 so that the proportion of other events is

0) and another in which everyone is “Event Free” at the start (percentage of “Event

free” is set as 100 in Table B.64 so that the proportion of other events is 0). The

results are given in Table 6.41.

We note the following points from Table 6.41:

(a) Expected future “Event Free” lifetime for the population with MI is 0 as every-

one starts with at least one event.

(b) Benefits for men are greater than the benefits for women.

(c) Benefits for current smokers are higher than benefits for those who never smoke.

This is due to the higher risk for current smokers when compared to those who

never smoke.

(d) Benefits are lower for individuals with MI at the start when compared to indi-

viduals without MI at the start because individuals without MI benefit from the

effects on the first event as well as the second and subsequent events, whereas

127

the individuals with MI benefit only from the effects on second and subsequent

events. The effect on a population with a proportion of the starting popula-

tion with MI will lie between the benefits for the populations with and without

significant events.

Body mass index has effects on mortality as well some of the risk factors (hyper-

tension and diabetes) but does not have a direct effect on IHD or stroke (see Table

4.24). We want to investigate the effct of treatment if we start with individuals

in different categories of body mass index. We start at age 50 with the starting

profile given in Table B.64 except that the population is “Event Free” and we look

at different populations based on their BMI categories at the start. The results are


From Table 6.42 we note that the difference in the expected future lifetime and

expected future “Event Free” lifetime is not substantially different for the different

categories of BMI. The lowest difference can be seen in the underweight category

when compared to the other categories and can be due to relatively high mortality

at earlier ages for underweight people. We can conclude that the different categories

of BMI have a small impact on the benefits from treatment with statins from age

50.

We noticed that the difference in the beneficial effects for populations with dif-

ferent categories of BMI is small. We can then look at individuals with specific risk

profiles at age 50 and calculate the beneficial effects of treatment with statins from

age 50. For these calculations we will consider an individual with the BMI profile

given in Table B.64. We want to consider individuals with a low risk profile for IHD

given by the lowest categories of hypertension, hypercholesterolaemia and diabetes

and correspondingly a high risk profile for IHD by considering the highest categories

of the factors. We will also consider some intermediate risk profiles for IHD based

on a combination of highest and lowest categories of the factors. The results are


128

Table 6.41: Effect of treatment with statins on expected future lifetime and expected future “Event Free” lifetime for differentcategories of the English population.

Expected future lifetime from age 50 Expected future “Event Free” lifetime from age 50Male Female Male Female

Never Current Never Current Never Current Never CurrentSmoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker

Average English Treated 30.5 25.1 33.9 28.8 26.0 21.0 30.5 25.4population Untreated 29.9 24.1 33.5 28.1 24.9 19.1 29.6 24.0

Difference 0.6 1.0 0.4 0.7 1.1 1.9 0.9 1.4English population Treated 21.7 16.7 25.3 20.0 0.0 0.0 0.0 0.0

with MI Untreated 21.4 16.4 24.9 19.7 0.0 0.0 0.0 0.0Difference 0.3 0.3 0.4 0.3 0.0 0.0 0.0 0.0

“Event Free” Treated 30.9 25.5 34.2 29.1 27.2 21.9 31.3 26.1English population Untreated 30.3 24.5 33.8 28.4 26.0 20.0 30.4 24.6

Difference 0.6 1.1 0.4 0.7 1.2 1.9 0.9 1.5

129

Table 6.42: Effect of treatment with statins on expected future lifetime and expected future “Event Free” lifetime for differentcategories of BMI.


Never Current Never Current Never Current Never CurrentSmoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker

Treated 29.3 23.4 33.3 27.6 26.0 20.3 30.6 25.0Underweight Untreated 28.8 22.4 32.9 26.9 24.9 18.7 29.8 23.6

Difference 0.5 1.0 0.4 0.7 1.0 1.6 0.8 1.4Treated 30.8 25.2 34.3 29.1 27.1 21.8 31.4 26.2

Lightweight Untreated 30.2 24.2 33.9 28.3 26.0 19.9 30.6 24.7Difference 0.6 1.0 0.4 0.8 1.1 1.9 0.8 1.5

Treated 31.1 25.8 34.5 29.4 27.3 22.1 31.5 26.4Overweight Untreated 30.5 24.7 34.1 28.7 26.1 20.1 30.6 24.8


Mod. Obese Untreated 30.1 24.4 33.5 28.2 25.8 19.8 30.1 24.4Difference 0.6 1.1 0.4 0.8 1.2 2.0 0.9 1.5

Treated 29.7 24.5 33.1 28.1 26.1 21.0 30.2 25.2Mor.Obese Untreated 29.1 23.4 32.6 27.4 24.9 19.1 29.3 23.7

Difference 0.6 1.1 0.5 0.7 1.2 1.9 0.9 1.5

130

Table 6.43: Effect of treatment with statins on expected future lifetime and expected future “Event Free” lifetime for individuals withdifferent risk profiles from age 50.


Never Current Never Current Never Current Never CurrentDiab. H’Chol. H’tens. Smoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker

Treated 31.3 26.2 34.5 29.6 28.1 23.1 31.9 26.9Low Low Low Untreated 30.8 25.3 34.1 28.9 27.1 21.4 31.1 25.6


Low Low High Untreated 29.4 23.2 32.9 27.1 24.9 18.8 29.3 23.2Difference 0.6 1.0 0.5 0.8 1.1 1.7 0.9 1.4

Treated 31.3 26.1 34.4 29.5 27.8 22.6 31.7 26.6Low High Low Untreated 30.7 25.0 34.0 28.7 26.6 20.6 30.8 25.1


High Low Low Untreated 29.8 24.0 33.2 27.7 25.9 20.0 30.1 24.3Difference 0.5 1.0 0.4 0.8 1.2 1.8 0.8 1.5

Treated 29.9 24.0 33.3 27.8 25.7 19.9 29.9 24.3Low High High Untreated 29.2 22.7 32.9 26.9 24.3 17.8 28.9 22.6


High Low High Untreated 28.1 21.5 31.8 25.6 23.6 17.1 28.1 21.7Difference 0.7 1.2 0.5 0.9 1.2 2.0 1.0 1.6

Treated 30.3 24.8 33.5 28.3 26.6 21.1 30.6 25.3High High Low Untreated 29.6 23.6 33.1 27.5 25.2 18.9 29.7 23.6


High High High Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9Difference 0.8 1.4 0.5 1.0 1.5 2.4 1.1 1.9

131


(a) For a higher category of a factor that has a positive effect on myocardial infarc-

tion or stroke transition intensity, the beneficial effect of treatment is higher.

(b) Statins seem to have a higher beneficial effect for individuals with higher abso-

lute risk of myocardial infarction or stroke.

(c) Individuals with higher categories of more than one factor will have greater

benefits compared to individuals with a higher category of only one factor.

The effects though are not additive with an indication that the benefit from

higher levels of two factors is more than the sum of the beneficial effects of the

individual factors.

(d) The greatest benefit from statin treatment in absolute terms is for male current

smokers with their expected future lifetime increased by about one and a half

years and their expected future “Event Free” lifetime increased by about two

and a half years.

(e) The smallest benefit from statin treatment in absolute terms is for the female

never–smoked population with their expected future lifetime increased by half

a year and their expected future “Event Free” lifetime increased by about one

and a three quarters of a year.

(f) The conclusions in the points above are valid for both expected future lifetime

and expected future “Event Free” lifetime.

6.5.3 Uncertainty in treatment effects

Uncertainty in the reduction in risk

The effect of treatments considered in Section 6.5 are for the effect of a standard

dose of a statin which are based on the risk reduction figures given in Law et al.

(2003). We also investigate what the effects of treatments would be if the effects

for a standard dose were different from the effects reported in Law et al. (2003),

especially since their results are based on studies with a follow-up period of about 5

years. We consider two scenarios, one with 30% higher risk reduction of myocardial

infarction and stroke and the other with 30% lower risk. The duration dependent

132

reductions in risk of myocardial infarction and stroke for these scenarios are given

in Table 6.44.

Table 6.44: Percentage reduction in risk by duration of treatment–non standarddose scenarios.

% Reduction in riskEvent Duration of treatment High scenario Standard Low scenarioMyocardial 1st year 25 19 13Infarction 2nd year 51 39 27

3rd-5th years 66 51 366th and 72 55 39subsequent years

Stroke All durations 22 17 12

Based on these reductions in risk we can recalculate the effects for the individuals

with the highest categories of the risk factors hypercholesterolaemia, hypertension

and diabetes, for both males and females and for never–smoked and current smokers.

These results are given in Table 6.45. We notice that a greater reduction in risk

of IHD and stroke results in a greater increase in the expected future lifetime and

expected future “Event Free” lifetime and vice versa compared to the base scenario.

Uncertainty in absolute risk

The reduction in relative risk of IHD or stroke on treating someone with a statin

is independent of baseline characteristics, but the absolute risk of IHD or stroke is

not independent of baseline characteristics, as seen in Table 4.24. The uncertainty

in the absolute risk will result in uncertainty in the effect of treatment with statins.

The absolute risk of IHD and stroke in England is given by the model described

in Chapter 5. In Section 5.4 we have shown the accuracy of the model giving the

absolute risks of events and other transitions.

133

Table 6.45: Effect of treatment with statins on expected future lifetime and expected future “Event Free” lifetime for individuals withdifferent risk profiles from age 50.


Never Current Never Current Never Current Never Current. Smoked Smoker Smoked Smoker Smoked Smoker Smoked Smoker

Treated 29.0 23.0 32.4 26.7 24.8 19.2 29.1 23.5High Scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9


Base Scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9Difference 0.8 1.4 0.5 1.0 1.5 2.4 1.1 1.9

Treated 28.5 22.0 32.1 26.0 23.8 17.5 28.4 22.2Low Scenario Untreated 27.9 21.0 31.7 25.3 22.8 15.8 27.6 20.9

Difference 0.6 1.0 0.4 0.7 1.0 1.7 0.8 1.3

134

The uncertainty in treatment effects due to uncertainty in absolute risk is given

in Tables 6.46 and 6.47. The information in Tables 6.46 and 6.47 is:

(1) The item calculated using the estimates of the parameters set out in Chapter 5

– labelled ‘Fixed parameters’.

(2) The mean of the 100 simulated values of the item – labelled ‘Sampled parame-

ters, Mean’.

(3) The standard deviation of the 100 simulated values of the item – labelled ‘Sam-

pled parameters, St. Dev.’.

(4) The calculations show the effect of treatment with statins. This is obtained by

calculating the items for the same set of simulated parameters for the treated

model and the untreated model and then taking the difference.

(5) The starting population in Table 6.46 are 20 years old with distribution of risk

factors as in Table B.64 and everyone gets treatment with a standard dose of

statin on reaching age 50 for the rest of their lives.

(6) The starting population in Table 6.47 are 50 years old with the highest cate-

gory of hypertension, hypercholesterolaemia and diabetes, do not have IHD or

stroke and BMI distributed as in Table B.64 and everyone gets treatment with

a standard dose of statin from the start for the rest of their lives.

Table 6.46: Effect of treatment from age 20 using fixed parameters estimated fromthe data and simulated parameters sampled from the adjusted asymptotic distribu-tion of the corresponding estimates.

Sex Smoking Increases in expected Fixed Sampled parametersstatus parameters Mean St. Dev.

Male Never future lifetime 0.6 0.6 0.08future “Event Free” lifetime 1.1 1.1 0.14

Current future lifetime 1.0 1.0 0.09future “Event Free” lifetime 1.6 1.6 0.14

Female Never future lifetime 0.4 0.4 0.05future “Event Free” lifetime 0.8 0.8 0.11


135

Table 6.47: Effect of treatment from age 50 using fixed parameters estimated fromthe data and simulated parameters sampled from the adjusted asymptotic distribu-tion of the corresponding estimates.

Sex Smoking Increases in expected Fixed Sampled parametersstatus parameters Mean St. Dev.

Male Never future lifetime 0.8 0.9 0.13future “Event Free” lifetime 1.5 1.5 0.23


Female Never future lifetime 0.6 0.6 0.08future “Event Free” lifetime 1.1 1.2 0.17


6.6 Summary

In this chapter we have seen that drugs have been developed to reduce the levels

of risk factors for myocardial infarction and stroke, such as hypercholesterolaemia

and hypertension. We have described the effect of statins and measured its effects

on the expected future lifetime, which increases by about one and a half years for

individuals with very high risk of myocardial infarction. We note that the treat-

ment recommendations can be based on risk, which makes the model semi-Markov,

or based on age, under which the model remains Markov. The results show that

the overall life expectancy in England can be increased if statins are prescribed to

everyone over a certain age.

136

Chapter 7

Modelling and forecasting Body

Mass Index

7.1 Introduction

In Chapter 2 we discussed the effect of body mass index on risk factors such as

hypertension and diabetes. In the same chapter we also discussed the effect of body

mass index on the significant events such as IHD, stroke and death. In Chapter 5 we

obtained a model for transitions between categories of body mass index consistent

with the English population in 2003.

In this chapter we will look at how the prevalence of BMI has changed over time

(Section 7.2) and how we can obtain adjusted models that are consistent with these

changes (Section 7.3). We will also calculate the effects on the expected future

lifetimes and the prevalence of other factors using the different models for body

mass index (Section 7.4). We do not calculate the standard errors for the results

obtained in this chapter as we believe that they should be of the same order as the

standard errors calculated for the results in Chapter 5.

7.2 Increasing prevalence of obesity

Figures 7.29 and 7.30 show the prevalence rates by age for obesity (moderately obese

and morbidly obese combined) for males and for females in England in 1994, 1998

137

and 2003. These rates are taken from HSE (2003) and are based on a sample of

the population of England. Also shown are approximate 95% confidence limits for

the 2003 rates. A marked feature of these rates is the increase in the prevalence of

obesity for both sexes over the period 1994 to 2003. This increase has been achieved

by decreases in the prevalence of lightweight and underweight combined for both

sexes and at all ages over this period. The prevalence of overweight shows no strong

trend over this period. Details can be found in HSE (2003).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994

Figure 7.29: Prevalence of obesity for males in England.

Figures 7.31 and 7.32 show the prevalence rates by age for obesity for males and

for females calculated from each of the six examinations for the Offspring & Spouses

(OS) data from the Framingham Heart Study. These figures can be compared with

Figures 7.29 and 7.30 but they relate to different time periods. Examination 1 took

place around 1971 and Examination 6 took place around 1998. Figures 7.31 and

7.32 show the same trend towards increasing prevalence of obesity as we observe in

Figures 7.29 and 7.30, though at a slower rate.

A feature not apparent from Figures 7.31 and 7.32 is that, since the Framingham

Heart Study uses a fixed population, the number of people at the younger ages

decreases with each examination.

138

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

20 30 40 50 60 70 80

Prevalence

Age

UK2003UK1998UK1994

Figure 7.30: Prevalence of obesity for females in England.

7.3 Models for BMI

7.3.1 Models with calendar time effect

We have obtained a model for the transitions between the categories of BMI in

Chapter 5 and we will refer to this model as Model I.

Model I is specified by a set of transition intensities for movements between the

five different categories of BMI. We will use the following abbreviated notation for

these intensities:

λ(ab)I a, b = 0, 1, 2, 3, 4

where a and b denote categories of BMI, as specified in Table 3.3, and λ(ab)I denotes

the intensity of moving from category a to category b. Note that a and b must be

neighbouring categories since, for example, transitions from lightweight directly to

morbidly obese are not permitted. Note also that these intensities are functions of

age, sex and change in smoking status (see Table 5.25).

The intensities specifying Model I do not include any explicit allowance for

changes over calendar time. However, Figures 7.29, 7.30, 7.31 and 7.32 show that

139

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 20 30 40 50 60 70 80

Prevalence

Age Group

Exam 1Exam 2Exam 3Exam 4Exam 5Exam 6

Figure 7.31: Prevalence of obesity for males in the Framingham Heart Study, Off-spring & Spouses data.

the prevalence of obesity for both males and females has increased over the period

1994 to 2003 in England and over the period 1971 to 1998 in Framingham. We used

the Framingham Heart Study data to investigate this effect by including an extra

explanatory variable in our models. This explanatory variable is a single factor in-

dicating whether the data comes from observations between examinations 1 and 2,

2 and 3, 3 and 4, 4 and 5 or 5 and 6. The conclusions from this modelling exercise

were as follows:

(a) The ‘examination factors’ for the backward transitions, those where a > b, and

for some of the forward transitions were not significantly different from zero,

indicating no calendar time trend for these intensities.

(b) The ‘examination factors’ for the remaining forward transitions, which were

lightweight to overweight ((ab) ≡ (12)) and overweight to moderately obese

((ab) ≡ (23)), were significantly different from zero. In these cases, the factors

indicated that these two transition intensities had increased by about 1.5% each

year over the period from examination 3 to examination 6. The annual rate of

increase between the earlier examinations was slightly higher.

140

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 20 30 40 50 60 70 80

Prevalence

Age Group

Exam 1Exam 2Exam 3Exam 4Exam 5Exam 6

Figure 7.32: Prevalence of obesity for females in the Framingham Heart Study,Offspring & Spouses data.

Given these conclusions we investigated the suitability of models of the following

form for applicability to the English population:

λ(ab)(t) = λ(ab)I for (ab) 6= (12), (23)

λ(ab)(t) = (1 + r)tλ(ab)I for (ab) = (12), (23)

where t is time in years measured from some starting point and r is an annual rate

of increase. Note that our notation makes the dependence on calendar time explicit.

HSE (2003) give prevalence rates for different categories of BMI by age group

and sex for the population of England in both 1994 and 2003. To determine a value

for r we calculated for different starting ages, separately for males and females, for

HSE 1994 profiles (see Table B.63), the conditional probability of being in each

BMI category nine years later. The chosen value of r, 0.06, was the value such that

these conditional probabilities best matched the 2003 prevalence rates for the BMI

categories.

Table 7.48 shows how well r = 0.06 models the changes in BMI prevalence for

the population of England between 1994 and 2003. This table shows the following

141

information:

(i) 1994: the figures in these rows are the prevalence rates for the five categories of

BMI in England in 1994 for the age range including the age indicated. These

values are consistent with HSE (2003).

(ii) 2003: the figures in these rows are the prevalence rates for the five categories of

BMI in England in 2003 for the age range including the age indicated. These

values are are consistent with HSE (2003).

(iii) r = 0.06: the figures in these rows are the predicted prevalences for the five

BMI categories at the end of the age range starting nine years earlier with the

HSE 1994 profile. These values have been calculated using r = 0.06, with t = 0

at 1994 assuming the individual never smokes.

The ability of r = 0.06 to match the changes in BMI prevalence from 1994 to

2003 can be seen by comparing the values for HSE 2003 with the values for r = 0.06

in the adjacent row.

142

Table 7.48: The changing prevalence of BMI in England between 1994 and 2003.

Sex Profile/Model Age/range U’weight L’weight O’weight Mod. Obese Morb. Obese% % % % %

1994 20 6.8 62.6 24.9 5.5 0.22003 29 0.7 40.6 41.2 16.7 0.8r = 0.06 20 → 29 2.1 36.7 44.6 16.3 0.3

1994 40 0.6 37.7 46.2 15.1 0.4Male 2003 49 0.4 23.7 47.7 26.8 1.5

r = 0.06 40 → 49 0.3 26.6 48.3 24.2 0.6

1994 60 0.5 30.3 51.4 17.4 0.42003 69 0.4 22.3 48.6 27.7 1.0r = 0.06 60 → 69 0.2 25.6 50.0 23.6 0.61994 20 7.2 64.6 20.3 7.1 0.82003 29 1.9 51.8 28.3 15.1 3.0r = 0.06 20 → 29 2.9 54.2 25.8 15.3 1.8

1994 40 1.0 54.2 27.9 15.1 1.8Female 2003 49 1.0 39.8 32.8 22.4 3.9

r = 0.06 40 → 49 0.9 40.8 34.0 21.1 3.2

1994 60 0.9 34.9 38.7 23.2 2.32003 69 0.9 27.6 41.5 27.5 2.6r = 0.06 60 → 69 0.6 27.2 42.0 26.0 4.2

143

We regard an annual rate of increase of 6% for an indefinite period starting in

2003 as somewhat extreme so we have specified a model where this rate of increase

is limited to a period of 20 years from 2003, with the intensities remaining constant

from that time. Hence our two further models are specified as functions of t, the

time in years from 2003, as follows:

Model II:

λ(ab)II (t) = λ

(ab)I for (ab) 6= (12), (23)

λ(ab)II (t) = 1.06t+9λ

(ab)I for (ab) = (12), (23), 0 ≤ t ≤ 20

λ(ab)II (t) = 1.0629λ

(ab)I for (ab) = (12), (23), t > 20

Model III:

λ(ab)III (t) = λ

(ab)I for (ab) 6= (12), (23)

λ(ab)III (t) = 1.06t+9λ

(ab)I for (ab) = (12), (23), t ≥ 0

7.3.2 Comments on the models

Table 7.49 shows prevalence rates for obese (BMI > 30) males and females at dif-

ferent ages in England in 2003, labelled ‘HSE 2003’, together with the conditional

probabilities of being obese at these ages, as calculated using Models I, II and III

starting from the age indicated with an HSE 2003 profile (see Table B.64) at that

age. We make the following comments about Table 7.49:

(a) The values labelled ‘HSE 2003’ are consistent with HSE (2003).

(b) The conditional probabilities have been calculated assuming the individuals

never smoke. Smoking affects the transition intensities for moving between

BMI categories only marginally, but it does have an effect on mortality and

hence a small effect on the conditional probabilities.

(c) The conditional probability of being obese at ages 60 or 80 calculated from ages

20 or 40 using Model I are significantly higher than the HSE 2003 rates for both

males and females. This may seem surprising since the parameters for Model I

were adjusted from the initial Framingham estimates so that these conditional

probabilities would match the HSE 2003 prevalence rates. However, it should

144

be borne in mind that the HSE 2003 prevalence rates for obesity at age 80

relate to individuals who were age 20 in 1943 whereas the Model I conditional

probabilities are predictions for a population who were aged 20 in 2003.

(d) It can be seen that Model III produces extreme results. For example, starting

from age 20, it predicts that over 96% of men reaching age 80 will be obese.

(e) The values in these tables have been calculated using the model described in

detail in Chapter 5, together with the specified model for movements between

BMI categories. This model has a large number of parameters. Standard errors

for values calculated using the model are discussed in Chapter 5.

The UK Department of Health commissioned a report, Zaninotto et al. (2006),

which forecasts the prevalence of obesity in England in 2010 starting from the pop-

ulation in 2003. It is of some interest to compare their forecasts with prevalence

rates predicted by our Models II and III. Table 7.50 shows for males and females

and for selected ages in 2010:

(a) the forecast prevalence of overweight and obese given by Table 1 in Zaninotto

et al. (2006), and,

(b) the predicted prevalence of overweight and obese using Models II or, equiva-

lently, III, and starting with an individual in 2003 with the HSE 2003 profile,

seven years younger than the age in 2010 and who never smokes. It can be seen

that, in general, Models II and III predict higher prevalence of overweight and

obesity in 2010 than Zaninotto et al. (2006).

7.4 Applications of these models

Tables 7.51 and 7.52 show for males and females separately the expected future life-

time and the prevalence at ages 70 and 80 of diabetes, hypertension and IHD/stroke

for starting ages 20, 40 and 60. At the starting age the individual has the HSE

2003 profile and never smokes. All these values are calculated using Models I, II

and III for movements between BMI categories. For these tables, hypertension is

defined as systolic blood pressure greater than 140 mmHg or diastolic blood pressure

greater than 90 mmHg. This definition is in line with HSE (2003) and corresponds

145

to categories 2 and 3 for hypertension in the discretisation for our model. See Table

3.5.

The interesting features of Tables 7.51 and 7.52 are:

(a) Smoking has a considerable impact on expected future lifetime. The effect of

smoking on IHD, stroke and mortality will be discussed in detail in Chapter 8.

(b) The effect on expected future lifetime of the three different BMI models is far

less than the effect of smoking. Model III, which may be considered somewhat

extreme, reduces life expectancy from age 20 by less than one year and by less

than this starting from higher ages.

(c) The effect of the BMI models on the prevalence of diabetes and hypertension is

considerably greater than their effect on the prevalence of IHD and/or stroke.

146

Table 7.49: Actual and modelled prevalence of obesity.

Sex Starting Profile/ Ageage Model 20 40 60 80

% % % %Male HSE 2003 8.6 25.3 26.7 20.9

20 I 8.6 22.8 29.9 28.3II 8.6 63.5 78.9 74.3III 8.6 63.5 91.3 96.6

40 I 25.3 31.5 29.1II 25.3 62.7 72.3III 25.3 62.7 87.4

60 I 26.7 27.1II 26.7 53.2III 26.7 53.2

Female HSE 2003 13.1 22.2 27.9 26.320 I 13.1 23.3 29.9 30.7

II 13.1 60.4 82.3 80.0III 13.1 60.4 93.5 97.5

40 I 22.2 30.1 30.9II 22.2 63.2 77.3III 22.2 63.2 90.4

60 I 27.9 29.5II 27.9 57.8III 27.9 57.8

147

Table 7.50: Forecasts of obesity in England in 2010.

Sex Age in Model Prevalence %2010 Overweight Obese

Male 27 Zaninotto et al. (2006) 32.0 16.0Models II & III 45.03 22.7

47 Zaninotto et al. (2006) 46.0 38.0Models II & III 45.8 36.9


Female 27 Zaninotto et al. (2006) 22.0 22.0Models II & III 25.0 24.3



148

Table 7.51: Expected future lifetime and prevalence of diabetes, hypertension and IHD/stroke – males.

Starting Model Expected Prevalence % of Prevalence % of Prevalence % ofage future lifetime diabetes at age hypertension at age IHD/stroke at age

(years) 70 80 70 80 70 80Never–Smoked

20 I 58.6 12.6 16.5 56.0 59.7 19.2 29.8II 58.2 17.4 22.4 64.1 67.2 20.1 30.8III 57.9 18.5 24.3 65.4 68.9 20.2 30.9

40 I 39.3 13.2 16.9 57.1 60.4 19.3 29.9II 38.9 16.2 21.5 62.0 66.0 19.7 30.4III 38.7 16.4 22.3 62.2 66.8 19.7 30.3

60 I 20.8 12.9 16.6 56.6 60.2 20.1 29.3II 20.6 13.2 18.0 57.2 62.1 20.1 29.3III 20.5 13.2 18.0 57.2 62.1 20.1 29.3

Current Smoker

20 I 51.6 12.1 14.3 55.0 57.6 30.3 44.5II 51.5 16.7 19.5 63.2 65.3 31.7 45.6III 51.3 17.7 21.2 64.5 67.1 31.8 45.3

40 I 32.9 12.6 14.6 56.1 58.3 30.2 44.5II 32.7 15.5 18.7 61.0 64.1 30.9 45.0III 32.6 15.7 19.5 61.2 64.9 30.9 44.8

60 I 15.9 12.4 14.5 55.8 58.3 26.8 41.8II 15.8 12.8 15.8 56.5 60.2 26.9 41.7III 15.8 12.8 15.8 56.5 60.2 26.9 41.7

149

Table 7.52: Expected future lifetime and prevalence of diabetes, hypertension and IHD/stroke – females.

Starting Model Expected Prevalence % of Prevalence % of Prevalence % ofage future lifetime diabetes at age hypertension at age IHD/stroke at age

(years) 70 80 70 80 70 80Never–Smoked

20 I 62.4 8.9 12.0 56.4 64.9 11.8 18.9II 61.7 13.2 17.8 67.6 74.4 12.5 19.8III 61.4 14.0 19.1 69.1 76.0 12.6 19.9

40 I 43.0 8.9 12.0 58.2 65.8 11.8 19.0II 42.4 11.5 16.3 64.9 73.0 12.1 19.5III 42.1 11.6 16.8 65.1 73.7 12.1 19.5

60 I 24.3 8.3 11.5 57.6 65.8 12.5 18.9II 23.9 8.6 12.8 58.4 68.3 12.5 18.9III 23.8 8.6 12.8 58.4 68.3 12.5 18.9

Current Smoker

20 I 56.1 8.6 11.0 55.9 63.9 18.3 29.3II 55.8 12.9 16.3 67.1 73.5 19.4 30.6III 55.6 13.7 17.5 68.6 75.2 19.5 30.5

40 I 37.2 8.7 11.0 57.7 64.8 18.3 29.6II 36.8 11.2 14.9 64.4 72.1 18.8 30.2III 36.7 11.3 15.5 64.6 72.9 18.8 30.1

60 I 19.5 8.2 10.7 57.3 64.9 16.4 27.8II 19.3 8.4 11.8 58.1 67.4 16.5 27.9III 19.3 8.4 11.8 58.1 67.4 16.5 27.9

150

The three BMI models predict increasing prevalence of obesity in the order I, II

and then III. See Table 7.49. However, the direct influence of BMI on mortality is

not monotonic at all ages, so that increasing BMI does not necessarily lead to higher

mortality rates. See Section 4.3.2 and, in particular, Figure 4.6. This is the reason

why the effect on expected future lifetime of the different BMI models is not much

larger.

BMI does have an increasing influence on the incidence of both diabetes and

hypertension (see Section 4.3.2), and this can be seen in the prevalence rates for

these conditions in Tables 7.51 and 7.52. These conditions in turn have a direct

influence on mortality (see Section 4.3.2) and so, through them, BMI has an indirect

increasing influence on mortality.

BMI also has an indirect increasing influence on mortality through IHD and/or

stroke: increasing BMI → increased risk of diabetes and/or hypertension → in-

creased risk of IHD and/or stroke → increased risk of mortality. However, the

influence through this route of increasing BMI on mortality is marginal since its

influence on the prevalence of IHD and/or stroke is marginal. For example, starting

from age 20, Model I predicts 28.3% of males will be obese at age 80, whereas Model

III predicts 96.6%. Despite this difference, the two models predict almost identical

prevalence of IHD and/or stroke at age 80, 29.8% and 30.9%, respectively.

The calculations for Tables 7.51 and 7.52 assume an HSE 2003 profile for the

individual at the starting age. For example, for 20 year old males, it is assumed

that 62.4% are lightweight, 22.6% are overweight, and so on. See Table B.64. For

the calculations for Table 7.53 we assume that our 20-year olds have the HSE 2003

risk profile in every respect except BMI. The calculations start from a given BMI

category at age 20, but allow for the individual’s BMI category to change in the

future according to Model I. The figures in parentheses are the corresponding results

where changes in the individual’s BMI category are not allowed in the future. These

calculations give insight into the effect of changes in the prevalence of BMI at age

20.

151

Table 7.53: Expected future lifetime and prevalence of diabetes, hypertension and IHD/stroke, starting at age 20 with given BMI fornever–smoked. Figures in brackets are the corresponding values when BMI does not change over lifetime.

Sex BMI at Expected Prevalence % of Prevalence % of Prevalence % ofage 20 future lifetime diabetes at age hypertension at age IHD/stroke at age

(years) 70 80 70 80 70 80

Male Underweight 57.5 (49.5) 11.6 (8.1) 15.5 (10.3) 53.1 (35.6) 57.7 (39.7) 18.7 (15.1) 29.3 (23.2)Lightweight 58.6 (57.7) 12.2 (8.3) 16.1 (11.0) 54.9 (41.7) 59.0 (46.0) 19.0 (17.5) 29.6 (27.2)Overweight 58.8 (59.7) 13.2 (10.5) 17.1 (14.0) 57.7 (56.4) 60.9 (60.2) 19.4 (19.4) 30.1 (30.4)Mod. Obese 58.8 (58.1) 14.9 (18.9) 18.6 (24.3) 60.7 (66.5) 63.1 (69.3) 19.9 (20.5) 30.6 (31.1)Morb. Obese 58.4 (56.1) 18.6 (33.9) 21.8 (41.6) 64.8 (77.7) 65.9 (79.4) 20.6 (21.7) 31.3 (32.2)

Female Underweight 61.8 (54.9) 7.6 (5.4) 10.7 (7.2) 52.6 (36.1) 62.4 (44.9) 11.4 (9.4) 18.4 (14.9)Lightweight 62.4 (62.1) 8.0 (5.6) 11.1 (7.5) 54.0 (42.5) 63.3 (51.6) 11.6 (10.8) 18.6 (17.3)Overweight 62.5 (63.9) 9.8 (7.0) 13.1 (9.5) 59.8 (57.8) 67.3 (66.0) 12.1 (12.0) 19.2 (19.4)Mod. Obese 62.5 (62.0) 11.7 (12.7) 15.0 (17.0) 64.2 (68.6) 70.3 (74.8) 12.5 (12.8) 19.7 (20.0)Morb. Obese 62.2 (60.0) 13.9 (23.7) 17.1 (30.6) 68.0 (80.0) 72.8 (84.0) 12.9 (13.6) 20.2 (20.9)

152

Table 7.54: Expected future lifetime and prevalence of diabetes, hypertension and IHD/stroke, starting at age 20 with given BMI forcurrent smokers. Figures in brackets are the corresponding values when BMI does not change over lifetime.

Sex BMI at Expected Prevalence % of Prevalence % of Prevalence % ofage 20 future lifetime diabetes at age hypertension at age IHD/stroke at age

(years) 70 80 70 80 70 80

Male Underweight 50.0 (41.2) 11.1 (7.5) 13.5 (8.5) 52.2 (33.6) 55.7 (36.4) 29.6 (21.5) 43.8 (31.9)Lightweight 51.6 (50.5) 11.7 (7.9) 14.0 (9.6) 54.0 (40.5) 56.9 (43.5) 30.0 (27.2) 44.2 (40.3)Overweight 51.9 (52.7) 12.6 (10.0) 14.8 (12.3) 56.7 (55.4) 58.8 (58.3) 30.7 (30.9) 44.8 (45.5)Mod. Obese 52.0 (51.7) 14.2 (18.1) 16.1 (21.3) 59.7 (65.6) 61.0 (67.6) 31.4 (32.3) 45.4 (45.7)Morb. Obese 51.7 (49.8) 17.6 (32.5) 18.6 (36.8) 63.7 (76.9) 63.7 (77.9) 32.3 (33.6) 46.1 (45.6)

Female Underweight 55.1 (47.2) 7.5 (5.2) 9.9 (6.4) 52.1 (35.1) 61.4 (43.2) 17.7 (13.4) 28.8 (21.5)Lightweight 56.1 (55.6) 7.8 (5.4) 10.2 (7.0) 53.5 (41.8) 62.4 (50.4) 17.9 (16.6) 29.0 (26.8)Overweight 56.4 (57.6) 9.6 (6.8) 11.9 (8.9) 59.3 (57.3) 66.3 (65.2) 18.7 (18.8) 29.8 (30.5)Mod. Obese 56.4 (56.2) 11.4 (12.4) 13.6 (15.7) 63.7 (68.1) 69.2 (74.1) 19.4 (19.8) 30.5 (30.8)Morb. Obese 56.2 (54.3) 13.5 (23.1) 15.5 (28.2) 67.5 (79.5) 71.7 (83.4) 19.9 (20.8) 31.0 (31.2)

153

The interesting features of Table 7.53 are as follows:

(i) Increasing the starting category of BMI increases the prevalence, at later ages,

of diabetes and hypertension quite considerably and of IHD and/or stroke, but

only slightly. These effects are due to BMI having a direct effect on diabetes

and hypertension but only an indirect effect on IHD and stroke.

(ii) The effect of the starting category of BMI on expected future lifetime is very

small. For males, underweight gives the lowest expected future lifetime by about

one year for non–smokers and one and a half years for current smokers, with

almost no differences between the other categories. The comments following

Tables 7.51 and 7.52 about the direct and indirect effects of BMI on mortality

apply equally here.

(iii) As was the case in Tables 7.51 and 7.52, the effect of smoking on expected

future lifetime is far greater than the effect of the starting category for BMI.

(iv)The results are significantly different if BMI categories are not allowed to

change in future. In this scenario the expected future lifetime and prevalence

of IHD/stroke are significantly different for the different categories of BMI. The

low life expectancy reflects the high mortality for underweight individuals at

younger ages as seen in Figure 4.6.

7.4.1 Comparison with other studies

The UK government’s comprehensive report on obesity, Butland et al. (2007), has

on page 38 the ‘headline’ figures of 13 and 8 years for: the maximum number of

years of life lost for white men and women aged 20–30 with a severe level of obesity

(BMI > 45).

These figures are taken from Figure 1 of Fontaine et al. (2003), a study based

on data from the USA which used methods very different from ours. The figures

in Figure 1 of Fontaine et al. (2003) for the ‘years of life lost’ for white men and

women due to obesity are broadly in line with our figures in parentheses in Tables

7.53 and 7.54 for expected future lifetime, i.e. the case where the category of BMI is

not allowed to change over an invidual’s lifetime. For example, for a 20-year old the

difference in expected future lifetimes between an overweight and a morbidly obese

154

male (resp. female) is 3.6 (resp. 3.9) years in Table 7.53. The figure in Figure 1 of

Fontaine et al. (2003) for the difference in ‘years of life lost’ between someone with

a BMI value of 28 and someone with a BMI value of 41 is approximately 5 (resp.

3.5) years.

A feature of Tables 7.51 and 7.52 is that increasing the prevalence of obesity

(Models II and III) has relatively little effect on expected future lifetime. It is

interesting to note the following comment in page 38 of Butland et al. (2007) in

relation to the effect of increasing obesity in the UK over the next 50 years: The

role of the increase in obesity will have surprisingly little impact (less than a year) on

the life expectancy of the population .... This statement is followed by the comment

on page 38 of Butland et al. (2007): Such a modest impact on average population

life expectancy ... conceals the significant increase in healthcare costs associated with

additional years of obesity–related ill health and the associated impact on quality of

life.

Our figures in Tables 7.51, 7.52, 7.53 and 7.54 for the prevalence of diabetes, hyper-

tension and IHD/stroke support this.

7.5 Summary

In this chapter we have described two more models for obesity. In these models the

forward transition intensities from lightweight to overweight and from overweight

to moderately obese increase with calendar time as well as with the other factors.

These models predict a rising trend in obesity to very high levels in 60 years’ time.

We have calculated the expected future lifetime, future prevalence of IHD/stroke

and future prevalence of diabetes and hypertension starting with different categories

of BMI. The results indicate that the different categories have significant effects on

future prevalence of diabetes and hypertension, but do not affect the expected future

lifetime or the future prevalence of IHD/stroke significantly.

155

Chapter 8

Effect of changes in smoking

behaviour

8.1 Introduction

Smoking was banned in enclosed public places in England from 31 July 2007. The

aim of the ban is to reduce the harmful effects of smoking in the English population.

In the previous chapters we have seen that smoking affects the transition intensities

between different categories of BMI and transitions to IHD, stroke and mortality. We

have used Framingham data to obtain the transition intensities for current smokers

in relation to the never–smoked. We have also obtained the transition intensities for

individuals who have given up smoking in relation to the never–smoked.

The risks of different events do not go down to the levels of the never smoked on

quitting smoking and the reduction in risk takes time. It is difficult to obtain the

reduction in the risk of different events for different durations of giving up smoking

from the Framingham data.

We will discuss the smoking ban and smoking habits in England in this chapter

and we will model the reduction in risk of different events by the duration of giving

up smoking. We do not calculate the standard errors for the results obtained in this

chapter as we believe that they should be of the same order as the standard errors

calculated for the results in Chapter 5.

156

8.2 Effect of smoking ban in public places

8.2.1 Smoking ban

Table 8.55 gives the prevalence of smoking from 1974 to 2003 for different age groups

in Great Britain. We notice that the prevalence of smokers has been relatively

constant since 2000 for both males and females in all age groups. The smoking ban

is likely to reduce the prevalence of smoking, but we will need to wait a few more

years to find out the magnitude of any reduction.

Table 8.55: Prevalence of smoking (%) in Great Britain. Source: Rickards et al.(2004).

Age 1974 1982 1992 1998 2000 2001 2002 2003Male16-19 42 31 29 30 30 25 22 2720-24 52 41 39 41 35 40 37 3825-34 56 40 34 38 39 38 36 3835-49 55 40 32 33 31 31 29 3250-59 53 42 28 28 27 26 27 26

60 and over 33 21 29 16 16 16 17 16All aged 16 and over 51 38 29 30 29 28 27 28

Female16-19 38 30 25 32 28 31 29 2520-24 44 40 37 39 35 35 38 3425-34 46 37 34 33 32 31 33 3135-49 49 38 30 29 27 28 27 2850-59 48 40 29 27 28 25 24 23

60 and over 26 23 19 16 15 17 14 14All aged 16 and over 41 33 28 26 25 26 25 24

Table 8.56 gives the age of starting to smoke for both current smokers and ex-

smokers. We notice that the majority of individuals start smoking before the age of

25.

Many countries have imposed a smoking ban in enclosed public places. Among

these are England and Wales, Scotland, the Republic of Ireland and Norway. Figure

8.33 gives the 12-month moving average of prevalence of smokers for all ages as a

percentage of population in the Republic of Ireland which was one of the first to

157

Table 8.56: Percentages of smokers and ex-smokers in 2003 in Great Britain, classi-fied by age at which they started smoking regularly. Source: Rickards et al. (2004).

Age Current Smoker Ex–SmokerMale

Under 16 45 3816-17 25 2818-19 14 1820-24 11 12

25 and over 5 4Female

Under 16 39 2916-17 25 2718-19 17 2120-24 12 15

25 and over 7 8

ban smoking in enclosed public spaces. The smoking ban in the Republic of Ireland

was effected from 29 March 2004.

Figure 8.33 indicates a decrease in the prevalence of smokers as soon as the

smoking ban came into effect. The percentage of smokers decreased till about March

2005 and then it started to increase again. Detailed results show that the prevalence

of smoking was reduced for people over the age of 70 but was increased in people

under the age of 25.

The results from the Republic of Ireland are inconclusive in giving a pattern

about the smoking habits since the ban. The ban has not been in force in other

countries for durations long enough for the patterns to emerge. As a result it is not

possible to model the population effects of the smoking ban in England.

In Section 8.3 we will measure the effect of giving up smoking for an individual and

we can use these results to obtain population effects once we get credible patterns

about the changes in smoking habits due to a smoking ban.

158

Figure 8.33: Prevalence rates of smokers in Ireland. Source: Office of TobaccoControl, Republic of Ireland.

8.3 Effect of giving up smoking

8.3.1 Risk factors

In Chapter 4, we modelled the transition intensities for the transitions between

different levels of risk factors. Smoking was not found to be direct risk factor for

any transitions except transitions between the levels of BMI. We have described

the method of fitting a model for BMI transition intensities based on the change in

smoking profile in Section 4.3.2 and we have also given the model consistent with

the English population in Table 5.25.

8.3.2 Cardiovascular diseases

We have seen in Chapter 2 that the relative risk of MI and HS decreases with

increasing duration since giving up smoking. Lightwood and Glantz (1997) modelled

the fall in relative risk for ex-smokers over time and found that exponential decay

159

in the relative risk best described their data. The models that they proposed are:

Acute myocardial infarction:

RR(t) = [(RR0 + RR0F .F ) − (RR∞ + RR∞F F )]e−t/τ + (RR∞ + RR∞F .F )

where,

t is the time in years since giving up smoking,

RR(t), the relative risk of MI for duration t since given up smoking,

RR0 = 2.88, the relative risk for current smokers,

RR0F = 0.97, the extra relative risk for females who are current smokers,

RR∞ = 1.17, the residual risk for long time ex-smokers,

RR∞F = 0.23, the extra residual risk for female long time ex-smokers,

τ = 1.592 years; this determines the rate of decay of the relative risk for ex-smokers,

F = 1 for females and 0 otherwise.

Stroke:

RR(t) = [RR0 − RR∞]e−t/τ + RR∞

where,


RR(t), the relative risk of stroke for duration t since given up smoking,

RR0 = 2.80, the relative risk for current smokers,

RR∞ = 1.42, the residual risk for long time ex-smokers,

τ = 1.35 years.

We note that the model proposed by Lightwood and Glantz (1997) takes no

account of the number of cigarettes smoked or of how long the individual smoked.

We have used the results of our modelling of the Framingham data, as in Table

4.20 and Table 5.29, to reparameterise Lightwood and Glantz’s model. Our model

for the relative risk of MI for current and ex-smokers, relative to those who have

never smoked, is as follows:

RR(t) = (3.436 − 1.1)e−t/1.592 + 1.1 (8.16)

and the model for the relative risk of HS is:

RR(t) = (2.158 − 1.1)e−t/1.35 + 1.1 (8.17)

160

where t is the time in years since giving up smoking.

Note that:

(a) These models do not depend on sex or on age.

(b) The parameters 3.436 and 2.158 are taken from Table 5.29 and are the relative

risks for current smokers estimated from the Framingham data and appropriate

to the OS cohort.

(c) The parameters 1.1 correspond to RR∞ in Lightwood and Glantz’s model. The

value has been chosen taking account of Lightwood and Glantz’s own values,

the values reported in the literature (see Chapter 2), and our own values for the

relative risk for ex-smokers estimated from the Framingham data. These last

values, which do not take account of time since giving up smoking, are 1.054

(MI) and 1.227 (HS).

(d) The parameters 1.592 and 1.35, which control the rate of decay of the relative

risk, are taken directly from Lightwood and Glantz’s model.

Numerically, formulae (8.16) and (8.17) tell us that the relative risks of MI and

HS for current and ex-smokers are:

1. independent of age, sex and all other explanatory variables,

2. higher by a factor 3.436 (resp. 2.158) for current smokers in respect of MI (resp.

HS),

3. ultimately higher by a factor 1.1 for ex-smokers who stopped smoking a long

time ago,

4. higher by factors 2.346, 1.765 and 1.455 in respect of MI (resp. 1.604, 1.340 and

1.215 for HS) for someone who stopped smoking 1, 2 or 3 years ago.

The revised parameters for the first events (revised from Table 5.29) are set out

in Table 8.57.

8.3.3 Mortality

We have also seen in Chapter 2 that the relative risk of mortality decreases with

duration since giving up smoking. The literature also does not seem to suggest

any difference between the pattern in the reduction of mortality risk among men

161

and women. Table 5.32 which gives the transition intensity of mortality obtained

from the Framingham data and adjusted to the English population also does not

have an interaction term between sex and smoking, indicating that the pattern for

smoking is the same for men and women. Kawachi et al. (1993) give the reduction

in mortality risk by duration since giving up smoking in women. We assume that

this pattern of risk reduction is also valid for men.

Kawachi et al. (1993) give the relative risk of mortality by duration of quitting

smoking with respect to current smokers. We divide this relative risk by the relative

risk of mortality for those who have never smoked to get the relative risk of mortality

for current and former smokers relative to never–smoked. The relative risks are given

in Table 8.58.

The relative risk of mortality for current smokers relative to never–smoked is 1.79

which is very close to the relative risk for mortality for current smoker relative to

never–smoked obtained from the Framingham data (=exp(0.5689)) which we have

seen in Table 4.21 and Table 5.32.

We have modelled the relative risks in Table 8.58 using an exponential decay

model similar to the one used in Section 8.3.2. In the case of MI and stroke, there

was a very significant risk reduction in earlier years followed by smaller reductions

later on. In the case of mortality we see very small reductions in earlier years

followed by larger reductions after some time. The model that approximately fits

this pattern of relative risk is given by

RR(t) = (exp(0.5689) − 1.09)e−0.000322t4 + 1.09 (8.18)

where,


RR(t), the relative risk of death for duration t since giving up smoking.

The relative risk in Table 8.58 and the relative risk given by Equation 8.18 are

plotted in Figure 8.34.

162

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Relative risk

Duration

ObservedFitted

Figure 8.34: Risk of mortality relative to never–smoked for different durations of

giving up smoking.

Note that:

(a) These models do not depend on sex or on age.

(b) The parameter 0.5689 is taken from Table 5.32 and is the relative risk for current

smokers estimated from the Framingham data and appropriate to the OS cohort.

(c) The parameter 1.09 is the residual relative risk after giving up smoking for a

long time. The value has been chosen from Table 8.58 from the relative risk of

mortality of individuals who have given up smoking more than 15 years ago.

(d) The parameter 0.000322 controls the rate of decay of the relative risk, and is

obtained by investigating the fit of the graph to the data in Table 8.58.

The revised parameters for mortality (revised from Table 5.32) are set out in

Table 8.59.

8.4 Numerical results

We use the models in Section 8.3 for MI, HS and mortality for individuals who have

quit smoking to calculate the expected future lifetime and expected future “Event

163

Free” lifetime for populations of ex-smokers. For the calculation of “Event Free”

lifetime we include TIA with “Event Free” which is consistent with HSE (2003).

Let us start with a population of 20-year old current smokers who have taken

up smoking before the age of 19. For this population we will assume the English

prevalence at age 20 for the other factors, as given in Table B.64. Also consider

a population starting at age 40 who started smoking before the age of 19 and are

distributed as the English prevalence at age 40 for the other factors, as given in

Table B.64. We then investigate the effects for these populations if they give up

smoking at ages 20, 30, 40, 50, 60, 70 and 80. The results are given in Table 8.60.

Table 8.60 also gives the results for a population at the start that had never smoked

and will never smoke in the future.


(a) Men aged 20 years who never smoke are expected to live 7 years longer and

men aged 40 years who never smoke are expected to live 6.4 years longer than

men at coresponding ages who start smoking before the age of 19 and smoke

throughout their lifetime.

(b) Women aged 20 years who never smoke are expected to live 6.3 years longer

and women aged 40 years who never smoke are expected to live 5.8 years longer

than women at coresponding ages who start smoking before the age of 19 and

smoke throughout their lifetime.

(c) The lower the number of years smoked after age 20 the higher the expected

future lifetime and the expected future “Event Free” lifetime at age 20. Quitting

smoking sooner rather than later can have significant impact on the expected

future lifetime.

(d) The magnitude of the effects on expected future “Event Free” lifetime is similar

to the magnitude of the effects on expected future lifetime.

164

Table 8.57: Revised parameters for the models consistent with the English popula-tion for the first diagnosis of IHD or stroke.


Intercept −10.8973 −15.8300 −10.9729 −11.8289 −21.1800

Age 0.06967 0.3003 0.04473 0.08779 0.3201Age2 – −0.002252 – – −0.001708

Sex: Female −1.0907 −0.4767 −0.7155 1.7000 –

Smoking: Ex f(t)∗ – – g(t)# –Current 1.2343 – – 0.7693 –



Diabetes 0.5635 – 0.8100 – –

Age × Sex:Age × Female 0.002000 – – −0.03200 –

∗ f(t) = log([exp(1.2343) − 1.1]e−t/1.592 + 1.1)# g(t) = log([exp(0.7693) − 1.1]e−t/1.35 + 1.1)

165

Table 8.58: Relative risk of mortality for different smoking profiles. Source: Kawachiet al. (1993)

Smoking profile Duration Relative to Relative to(years) Current smoker Never–smoked

Current smoker 1.00 1.79Given up smoking < 2 1.19 2.13

2–4 1.00 1.795–9 0.79 1.41

10–14 0.53 0.95≥15 0.61 1.09

Never–smoked 0.56 1.00

166

Table 8.59: Revised parameters consistent with the English population for the modelfor mortality.


Age −0.01475Age2 0.0007460


Smoking: Ex log([exp(0.5689) − 1.09]e−0.000322t4 + 1.09)Current 0.5689








Diabetes 0.2824

Prior MI 3.2340


Prior HS 4.2000


167

Table 8.60: Effect on lifetime on giving up smoking at different ages.

Expected future lifetime Expected future “Event Free” lifetimestarting population age 20 age 40 age 20 age 40

Smoking profile Age of giving up Male Female Male Female Male Female Male FemaleNever–smoked 58.6 62.4 39.3 43.0 53.2 58.2 34.0 39.0

Given up smoking 20 57.5 61.4 38.5 42.3 52.3 57.3 33.3 38.230 57.2 61.2 38.5 42.3 51.8 56.9 33.3 38.240 56.6 60.8 38.2 42.0 51.1 56.5 33.0 38.050 55.8 60.2 37.3 41.4 50.0 55.7 31.8 37.260 54.4 59.2 35.9 40.3 48.4 54.5 30.1 35.970 52.8 57.8 34.2 38.9 46.8 53.0 28.4 34.480 51.7 56.5 33.1 37.6 46.0 51.8 27.5 33.1

Current smoker 51.6 56.1 32.9 37.2 45.8 51.4 27.4 32.7

168

Table 8.61: Effect on prevalence on giving up smoking at different ages.

starting population age 20 age 40 age 20 age 40Smoking profile Age of giving up Male Female Male Female Male Female Male Female

Prevalence of IHD at age 60 Prevalence of IHD at age 80Never–smoked 8.7 4.6 8.7 4.5 22.4 13.8 22.5 13.9

Given up smoking 30 9.2 4.8 8.9 4.6 22.9 14.1 22.9 14.160 14.2 6.7 13.8 6.5 25.2 15.2 25.1 15.3

Current smoker 14.2 6.7 13.8 6.5 34.0 21.3 34.1 21.5

Prevalence of stroke at age 60 Prevalence of stroke at age 80Never–smoked 1.7 1.8 1.7 1.8 8.3 5.8 8.4 5.8

Given up smoking 30 1.9 2.1 1.8 1.9 8.8 6.1 8.9 6.160 3.0 3.3 2.9 3.1 9.2 6.7 9.2 6.7

Current smoker 3.0 3.3 2.9 3.1 13.1 9.2 13.1 9.2

Prevalence of IHD/stroke at age 60 Prevalence of IHD/stroke at age 80Never–smoked 10.2 6.2 10.2 6.1 29.8 18.9 29.9 19.0

Given up smoking 30 10.8 6.6 10.5 6.3 30.7 19.5 30.8 19.660 16.8 9.6 16.3 9.3 33.2 21.1 33.1 21.2

Current smoker 16.8 9.6 16.3 9.3 44.5 29.3 44.5 29.6

169

Table 8.61 shows the prevalence of IHD and stroke for the populations considered

above and for giving up smoking at ages 30 and 60.


(a) Prevalence of IHD and stroke is significantly higher for current smokers when

compared to never–smoked.

(b) Prevalence of IHD and stroke decreases on giving up smoking. Giving up smok-

ing earlier rather than later decreases the prevalence of IHD and stroke to a

greater extent. People who have smoked since age 20 and gave up at age 60

have IHD/stroke prevalence of 33.2% at age 80 compared to the 44.5% for those

that do not give up smoking till age 80.

8.5 Summary

In this chapter we have modelled the effect of giving up smoking on cardiovascular

diseases and mortality. We note that on quitting smoking the risk of significant

events never goes down to the levels of risk of significant events for lifelong non-

smokers. The expected future lifetime and “Event free” lifetime is significantly

increased for lifelong non-smokers compared to lifelong smokers. Giving up smoking

increases the expected future lifetime and “Event free” lifetime compared to lifelong

smokers with greater increases seen for individuals quitting smoking sooner than

later.

170

Chapter 9

Conclusions and further research

9.1 Conclusions

The major conclusions of this thesis are:

(a) IHD and stroke are multifactorial diseases affected by risk factors like age, sex,

hypertension, hyperchoelsterolaemia, smoking, and diabetes. See Section 4.3.2.

(b) Smoking is a direct risk factor for myocardial infarction and hard stroke, with

minimal effect on other risk factors whereas body mass index is an indirect

risk factor for IHD, myocardial infarction and stroke and has a secondary effect

through hypertension and diabetes. See Section 4.3.2.

(c) All the risk factors considered for cardiovascular diseases and the cardiovascular

diseases themselves are risk factors for mortality. Body mass index and hyperc-

holesterolamia have a U shaped relationship with mortality but the other factors

have a monotonically increasing relationship with mortality. See Section 4.3.2.

(d) The cohort factor was less than or equal to 1 in all the transitions between risk

factor categories. See Table 4.24. This indicates that individuals are less likely

to change categories of risk factors over time.

(e) The cohort factor for forward transitions decreased at a higher rate compared to

the backward transitions for hypertension and hypercholesterolaemia indicating

decrease in prevalence of higher categories of these factors and the converse is

true for diabetes. See Section 5.3.4.

(f) The cohort factor was greater than or equal to 1 in most of the intensities of

171

having an IHD/stroke. See Table 4.24. This indicates that over time individuals

are more likely to have an IHD/stroke from causes unrelated to the factors that

we have considered.

(g) Statins, which lower cholesterol levels, can increase the expected future lifetime

by about one and a half years for individuals with the highest risk and have

beneficial effects in terms of life expectancy for low risk individuals. See Section

6.5.

(h) If we assume that the current level of increase in the prevalence of obesity will

continue in the future, 95% of the population aged 20 years now will be obese by

the time they are 80. Although, we note that such levels of increase are unlikely

to be sustainable in the future and we consider the effects of increases for the

next 20 years, which produces a considerable obese population in the future as

well. See Section 7.3.

(i) Body mass index does not have a significant impact on expected future lifetime.

See Section 7.4.

(j) The highest impact on expected future lifetime is from quitting smoking. The

difference in the expected future lifetime between current smokers and individ-

uals who have never smoked is about 7 years and quitting smoking can increase

expected future lifetime significantly. See Section 8.4.

9.2 Contribution

The major contributions of thesis are:

(a) The model describes an individual’s life history allowing them to move between

different levels of the risk factors.

(b) This model incorporates many risk factors where transition between categories

of risk factors may depend on the categories of other risk factors. We can

therefore measure the impact of changing one factor on some other factor as

well the overall impact on IHD/stroke prevalence and mortality.

(c) The risk factors are dynamic and they can go up as well as down. The model

can therefore measure how the risk of IHD or stroke moves up and down over

172

the individual’s lifetime.

(d) The model can measure the coverage and impact of different treatment recom-

mendations both based on risk profile and on age.

(e) The model measures the long-term effects of treating individuals with statins

and measures the impact on the individuals expected future lifetime.

(f) The model is not restricted to statins alone and can be used to measure the

impact of medicines over and above the ones available presently.

(g) The model is flexible and allows incorporation of other risk factors and events

in the model. This model therefore has use in measuring the impact of other

interventions for different factors to the ones considered here.

(h) It has a broader definition of cardiovascular diseases when compared to some

similar studies.

(i) The model has been adjusted to produce results for the English population, but

can be adjusted to produce results for a different population easily.

(j) The model is caliberated to the current conditions but can be used to forecast

prevalence of different factors in the future.

9.3 Further research

The model is very extensive and has a significant amount of detail built into it. But

there is still a lot of scope for further research based on this model.

We have used data from the USA and adjusted it to parameterise a model for

England. If longitudinal data is made available in England in the future, similar

to the Framingham data, a similar model could be parameterised using the ap-

proach used here. The set of adjustments to obtain the English prevalence from the

model parameterised using Framingham Heart Study data is not unique. Similar

results could have been obtained by adjusting the backward transition intensities or

a combination of forward and backward transition intensities.

The levels we have considered are based on standard categorisations and a similar

study can be carried out using different categorisations of the risk factors.

Our model for second and subsequent events is relatively crude and is based on

173

minimal data. The model can be improved by using a more detailed model for the

second and subsequent significant events.

Many new risk factors are associated with cardiovascular diseases, for example,

serum homocysteine. A model can be developed which includes such a risk fac-

tor. Thus the effects of intervention on serum homocysteine with medicines can be

determined.

We have not considered causes of death like cancers and they can be built into

the model. Such a model will also be useful in modelling insurance related items

like premiums and reserves.

Mortality has been decreasing at all ages over time and we can build the improve-

ments into our model as we have done for obesity. The decreasing trend is difficult

to quantify especially as there are causes of death that affect mortality in different

ways and to a different extent. Numerical estimates of improvements in mortality

by different causes of death will enable the modelling of a effect that changes over

calender time in the mortality model.

There are other diseases, for example, renal diseases that are multifactorial in

nature and can be modelled using a similar approach using possibly the same tran-

sition intensities for the risk factors where the risk factors are categorised into similar

categories.

The effect of statins, as a function of the duration of treatment is relatively crude,

as not all studies measuring the reduction in risk of IHD using treatment with statins

give the results by duration of treatment. If more data were made available so that

the effect of statins by duration of treatment could be modelled, the treated model

could be improved.

A cost-benefit analysis based on drug usage can be carried out by determining

the cost of drugs to treat a particular group of individuals against the benefit from

reduction in healthcare cost. This investigation of benefit from drug usage can use

a broader definition of healthy than has been used in this thesis, for example, we

can remove diabetics from the definition of healthy.

174

Appendix A

Table numbers describing the

parameters for the model

Table A.62: Summary of tables describing the transition intensities.

Factor Unadjusted transition Adjusted transitionintensities intensities

Body Mass Index 4.16 5.25Hypertension 4.17 5.26

Hypercholesterolaemia 4.18 5.27Diabetes 4.19 5.28

First Events 4.20 8.57Second and subsequent events 4.22 5.30

Long-term mortality 4.21 8.59Sudden death 4.23 5.31

175

Appendix B

Distribution of the English

population in 1994 and 2003

HSE (2003) gives the prevalence of different conditions like hypertension, hyper-

cholesterolamia, diabetes, body mass index IHd and stroke. Prevalence rates for

hypertension and hypercholesterolaemia are given two different definitions. Using

the data given in HSE (2003) we can calculate the distribution for some of the cate-

gories in our model. The categorisations match exactly for BMI, diabetes, IHD and

stroke.

Categories 3 for both hypertension and hypercholesterolamia match approxi-

mately. Categories 2 and 3 of hypertension combined match one definition of hyper-

tension approximately and Categories 1, 2 and 3 of hypercholesterolaemia combined

match one definition of hypercholesterolaemia approximately. We make sensible as-

sumptions about the distribution of the English population into different categories

of hypertension and hypercholesterolaemia based on the distribution in Framingham

data which are consistent with HSE (2003).

The distribution used in the calculations in this thesis is given in Tables B.63

and B.64.

176

Table B.63: Dynamic risk factor profile (percentages) in England in 1994.

Risk factor Category Male Female20 40 60 20 40 60

Diabetes 0 99.2 99.0 93.6 99.4 99.1 97.51 0.8 1.0 6.4 0.6 0.9 2.5

BMI 0 6.8 0.6 0.5 7.2 1.0 0.91 62.6 37.7 30.3 64.6 54.2 34.92 24.9 46.2 51.4 20.3 27.9 38.73 5.5 15.1 17.4 7.1 15.1 23.24 0.2 0.4 0.4 0.8 1.8 2.3

Hypertension 0 40.0 36.0 20.0 16.0 20.0 20.01 40.0 36.2 21.8 78.2 65.4 26.72 19.2 21.4 35.4 5.8 11.8 33.33 0.8 6.4 22.8 0.0 2.8 20.0

Hypercholesterolaemia 0 67.6 18.0 10.1 55.8 30.2 5.41 14.0 18.2 18.0 19.1 18.0 13.02 14.8 32.9 31.2 20.3 38.4 24.23 3.6 30.9 40.7 4.8 13.4 57.4

Significant Events “Event Free” 100.0 99.4 87.7 99.8 99.5 92.5MI 0.0 0.5 9.4 0.0 0.2 5.7HS 0.0 0.1 2.0 0.2 0.2 1.6

MI+HS 0.0 0.0 0.9 0.0 0.1 0.2

177

Table B.64: Dynamic risk factor profile (percentages) in England in 2003.

Risk factor Category Male Female20 40 50 60 20 40 50 60

Diabetes 0 99.6 97.2 96.4 91.9 99.1 98.5 97.4 95.31 0.4 2.8 3.6 8.1 0.9 1.5 2.6 4.7

BMI 0 6.4 0.5 0.4 0.6 7.4 1.0 1.0 0.71 62.4 27.3 23.7 22.4 61.2 43.5 39.8 32.32 22.6 46.9 47.7 50.3 18.3 33.4 32.8 39.03 8.2 24.0 26.8 25.6 11.1 18.6 22.4 25.54 0.4 1.3 1.4 1.1 2.0 3.5 4.0 2.5

Hypertension 0 44.0 40.0 33.0 25.0 45.0 45.0 40.0 30.01 45.4 40.3 36.2 32.1 53.7 46.0 40.5 32.42 10.4 16.9 23.7 32.4 1.3 7.0 15.3 30.23 0.2 2.8 7.1 10.5 0.0 2.0 4.2 7.4

Hypercholesterolaemia 0 73.6 23.1 19.0 20.3 69.3 30.7 20.7 16.31 11.0 16.0 16.0 17.0 13.0 15.0 16.0 15.02 11.5 36.4 37.0 35.6 14.4 35.6 37.3 34.23 3.9 24.5 28.0 27.1 3.3 18.7 26.0 34.5

Significant Events “Event Free” 99.9 98.7 95.8 87.3 99.5 99.1 97.3 92.3MI 0.0 1.0 3.0 10.5 0.3 0.3 1.8 5.2HS 0.1 0.3 0.8 1.6 0.2 0.4 0.8 1.9

MI+HS 0.0 0.0 0.4 0.6 0.0 0.2 0.1 0.6

178

Appendix C

Expected values and

variance-covariance matrices for

the parameters estimated from the

Framingham cohort data.

We will give the variance-covariance between the different parameters of the tran-

sition intensities for the transitions between different categories of different factors.

In the tables below the first column will give the expected values for the parameters

(we will label this column as E) and the remaining columns will give the variance-

covariance between parameters. The parameters are not same for all transitions and

we will use notation given in Table C.65 to label the parameters. An interaction

term will be denoted using the same notations with the components separated by a

colon(:). For example, an interaction term between age and sex will be denoted by

A1:S1.

179

Table C.65: Notation used in tables describing the expected values and variance-covariance between parameters.

Factor category NotationIntercept I0

Age A1Age2 A2

Sex Male S0Female S1

Obesity 0 M01 M12 M23 M34 M4

Hypertension 0 B01 B12 B23 B3

Hypercholesterolaemia 0 C01 C12 C23 C3

Diabetes 0 D01 D1

Cohort Original H0Offspring H1

Smoking Never smoked K0Current smoker K1

Given up K2

Prior MI No P0Yes P1

Prior HS No T0Yes T1

180

Table C.66: Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of BMI.

E I0I0 −2.0093 0.009433928

Table C.67: Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 2 of BMI for smoking: Current–ex.

E I0 A1 S1I0 −3.437322 0.1000403800 −0.0018526711 −0.0161471708A1 0.021774 −0.0018526711 0.0000386511 0.0001024603S1 −0.536672 −0.0161471708 0.0001024603 0.0216085306

Table C.68: Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 2 of BMI for smoking: Base case and ex–current.

E I0 A1 S1 A1:S1I0 −2.772462 0.0243633063 −0.0004966396 −0.0243633063 0.0004966396A1 −0.002208 −0.0004966396 0.0000109246 0.0004966396 −0.0000109246S1 −1.491325 −0.0243633063 0.0004966396 0.0456334811 −0.0009119809

A1:S1 0.023207 0.0004966396 −0.0000109246 −0.0009119809 0.0000195182

Table C.69: Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 3 of BMI for smoking: Current–ex.

E I0 S1I0 −3.261 0.01249987 −0.01249987S1 0.6245 −0.01249987 0.02837278

181

Table C.70: Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 3 of BMI for smoking: Base case and ex–current.

E I0 S1I0 −3.71876 0.002183405 −0.002183405S1 0.50956 −0.002183405 0.004343233


E I0 S1I0 −5.9188 0.04346362 −0.04346362S1 1.7403 −0.04346362 0.05410192


E I0I0 −3.035 0.01960746


E I0I0 −3.50362 0.002262433

Table C.74: Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 1 of BMI for smoking: Ex–current.

E I0I0 −3.323 0.03571379

182

Table C.75: Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 1 of BMI for smoking: Base case and current–ex.

E I0 S1I0 −3.94347 0.002531641 −0.002531641S1 0.27515 −0.002531641 0.005757444


E I0 S1I0 −7.5065 0.1666661 −0.1666661S1 1.5701 −0.1666661 0.1822911

183

Table C.77: Expected values and variance–covariances for parameters of transition intensity from category 0 to category 1 of hyper-tension.

E I0 A1 A2 S1 A1:S1I0 −4.13 0.1099409 −0.00342712 0.0000294768 −0.09573293 0.003460259A1 0.06934 −0.00342712 0.0001260597 −0.0000011078 0.003376615 −0.0001249414A2 −0.0005662 0.0000294768 −0.0000011078 0.0000000099 −0.0000291449 0.0000011005S1 −2.204 −0.09573293 0.003376615 −0.0000291449 0.1749632 −0.006275387

A1:S1 0.06351 0.003460259 −0.0001249414 0.0000011005 −0.006275387 0.0002304795A2:S1 −0.0004287 −0.0000299488 0.0000011016 −0.0000000099 0.0000539563 −0.0000020216

H1 −1.095 −0.001274792 0.0000327002 −0.0000001992 0.0002024078 −0.0000061204M1 0.2573 −0.01455831 0.0000068036 −0.000000057 0.00190522 −0.0000771451M2 0.6218 −0.01436442 −0.0000035284 0.000000032 0.00223496 −0.0000791349M3 0.8785 −0.01385553 −0.0000177377 0.0000001351 0.001962592 −0.0000709473M4 1.105 −0.01438133 0.000004775 −0.0000000385 0.002749146 −0.0001020141

A2:S1 H1 M1 M2 M3 M4I0 −0.0000299488 −0.001274792 −0.01455831 −0.01436442 −0.01385553 −0.01438133A1 0.0000011016 0.0000327002 0.0000068036 −0.0000035284 −0.0000177377 0.000004775A2 −0.0000000099 −0.0000001992 −0.000000057 0.000000032 0.0000001351 −0.0000000385S1 0.0000539563 0.0002024078 0.00190522 0.00223496 0.001962592 0.002749146

A1:S1 −0.0000020216 −0.0000061204 −0.0000771451 −0.0000791349 −0.0000709473 −0.0001020141A2:S1 0.0000000181 0.0000000453 0.0000007434 0.0000007214 0.0000006485 0.0000008759

H1 0.0000000453 0.0009237676 −0.0000841012 −0.0001285426 −0.0002490765 −0.0004909752M1 0.0000007434 −0.0000841012 0.01468002 0.01437584 0.01437937 0.01440241M2 0.0000007214 −0.0001285426 0.01437584 0.01480143 0.01441862 0.01440658M3 0.0000006485 −0.0002490765 0.01437937 0.01441862 0.01601178 0.01447267M4 0.0000008759 −0.0004909752 0.01440241 0.01440658 0.01447267 0.06727595

184


E I0 A1 A2 S1 A2:S1I0 −5.836 0.0821381 −0.00226034 0.0000183416 0.0009861149 −0.0000003111A1 0.1102 −0.00226034 0.0000804908 −0.0000006781 −0.0001277827 0.0000000324A2 −0.0008271 0.0000183416 −0.0000006781 0.0000000059 0.0000017337 −0.0000000005S1 −0.1456 0.0009861149 −0.0001277827 0.0000017337 0.00535546 −0.0000012657

A2:S1 0.00006362 −0.0000003111 0.0000000324 −0.0000000005 −0.0000012657 0.0000000003H1 −0.9199 −0.0009742087 0.0000185218 −0.0000000702 0.0001156763 −0.0000000178M1 0.0107 −0.01490801 −0.0000306989 0.0000002704 −0.0001936772 0.0000000667M2 0.2145 −0.01458802 −0.0000458328 0.0000004032 0.0000564424 0.0000000349M3 0.3865 −0.01432217 −0.0000534337 0.0000004682 0.0000262604 0.0000000261M4 0.6849 −0.01411496 −0.0000514572 0.0000004297 −0.0004607668 0.0000000874

H1 M1 M2 M3 M4I0 −0.0009742087 −0.01490801 −0.01458802 −0.01432217 −0.01411496A1 0.0000185218 −0.0000306989 −0.0000458328 −0.0000534337 −0.0000514572A2 −0.0000000702 0.0000002704 0.0000004032 0.0000004682 0.0000004297S1 0.0001156763 −0.0001936772 0.0000564424 0.0000262604 −0.0004607668

A2:S1 −0.0000000178 0.0000000667 0.0000000349 0.0000000261 0.0000000874H1 0.001165928 −0.000057814 −0.0000859326 −0.0001884119 −0.0003727817M1 −0.000057814 0.01614137 0.01571925 0.01572082 0.01573006M2 −0.0000859326 0.01571925 0.01609287 0.01575561 0.01571206M3 −0.0001884119 0.01572082 0.01575561 0.01660048 0.0157586M4 −0.0003727817 0.01573006 0.01571206 0.0157586 0.03151716

185

Table C.79: Expected values and variance–covariances for parameters of transitionintensity from category 2 to category 3 of hypertension.

E I0 A1I0 −5.1360706 0.1869959 −0.005993649A1 0.0900664 −0.005993649 0.0001957002A2 −0.0006924 0.0000467586 −0.0000015488S1 0.1203643 −0.0000764164 −0.0000135933H1 −0.9709361 −0.002165674 0.000037136

A2 S1 H1I0 0.0000467586 −0.0000764164 −0.002165674A1 −0.0000015488 −0.0000135933 0.000037136A2 0.0000000124 0.0000000429 −0.0000001503S1 0.0000000429 0.001282141 0.0001567999H1 −0.0000001503 0.0001567999 0.003311754

186


E I0 A1 H1I0 −1.1842643 0.0508537622 −0.0001997393 −0.001989802A1 −0.0075701 −0.0001997393 0.0000029093 0.0000202982H1 −0.266604 −0.0019898024 0.0000202982 0.003533M1 −0.0001575 −0.0377875153 0.0000101518 0.0003828242M2 −0.0276357 −0.0380964351 0.0000149685 0.0002925738M3 −0.119822 −0.0384668851 0.0000205015 0.0002775763M4 −0.5249702 −0.0386514908 0.000023089 0.0003352132

M1 M2 M3 M4I0 −0.03778752 −0.03809644 −0.03846689 −0.03865149A1 0.0000101518 0.0000149685 0.0000205015 0.000023089H1 0.0003828242 0.0002925738 0.0002775763 0.0003352132M1 0.03820601 0.03710523 0.0371196 0.03713227M2 0.03710523 0.03788942 0.03714863 0.03716414M3 0.0371196 0.03714863 0.03869607 0.0372053M4 0.03713227 0.03716414 0.0372053 0.05683518


E I0 A1 H1I0 −1.036503 0.005038201 −0.0000787409 −0.0008374909A1 −0.010882 −0.0000787409 0.0000012825 0.0000103226H1 −0.542841 −0.0008374909 0.0000103226 0.00122488

187


E I0 A1 A2 S1 A2:S1I0 −1.488 0.05287243 −0.001380233 0.0000116852 −0.001015143 0.0000002517A1 −0.009779 −0.001380233 0.0000529448 −0.0000004714 −0.0000418146 0.0000000102A2 −0.00002555 0.0000116852 −0.0000004714 0.0000000044 0.0000009196 −0.0000000003S1 0.3378 −0.001015143 −0.0000418146 0.0000009196 0.004012398 −0.0000010639

A2:S1 −0.00008308 0.0000002517 0.0000000102 −0.0000000003 −0.0000010639 0.0000000003H1 −0.5902 −0.001222485 0.0000299342 −0.000000176 0.0000786783 −0.0000000119M1 −0.002701 −0.0138739 −0.0000278487 0.0000002631 −0.0000784814 0.0000000447M2 −0.2324 −0.0135955 −0.0000427811 0.0000003966 0.0002028485 0.0000000086M3 −0.4527 −0.01337635 −0.00004869 0.0000004475 0.0001668086 0.0000000004M4 −0.706 −0.01308607 −0.0000476588 0.0000004129 −0.0003445093 0.0000000646

H1 M1 M2 M3 M4I0 −0.001222485 −0.0138739 −0.0135955 −0.01337635 −0.01308607A1 0.0000299342 −0.0000278487 −0.0000427811 −0.00004869 −0.0000476588A2 −0.000000176 0.0000002631 0.0000003966 0.0000004475 0.0000004129S1 0.0000786783 −0.0000784814 0.0002028485 0.0001668086 −0.0003445093

A2:S1 −0.0000000119 0.0000000447 0.0000000086 0.0000000004 0.0000000646H1 0.0009320046 −0.0000930166 −0.0001239266 −0.0002301313 −0.0004239788M1 −0.0000930166 0.0148818 0.01456737 0.01457444 0.01458425M2 −0.0001239266 0.01456737 0.01503418 0.01462872 0.01455988M3 −0.0002301313 0.01457444 0.01462872 0.01611216 0.0146212M4 −0.0004239788 0.01458425 0.01455988 0.0146212 0.05645253

188

Table C.83: Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of hypercholesterolaemia.

E I0 A1 A2I0 −5.2269056 0.08909502 −0.003438423 0.0000318029A1 0.1499105 −0.003438423 0.0001372999 −0.0000013029A2 −0.0016426 0.0000318029 −0.0000013029 0.0000000126S1 −3.2675613 −0.08786148 0.003416487 −0.0000317139

A1:S1 0.1147201 0.003424631 −0.0001370546 0.0000013019A2:S1 −0.0008875 −0.0000318166 0.0000013032 −0.0000000126

H1 −0.8872057 −0.001231024 0.0000218919 −0.0000000888

S1 A1:S1 A2:S1 H1I0 −0.08786148 0.003424631 −0.0000318166 −0.001231024A1 0.003416487 −0.0001370546 0.0000013032 0.0000218919A2 −0.0000317139 0.0000013019 −0.0000000126 −0.0000000888S1 0.1973033 −0.007649917 0.0000708585 0.0003930398

A1:S1 −0.007649917 0.0003036142 −0.0000028686 −0.0000125223A2:S1 0.0000708585 −0.0000028686 0.0000000276 0.0000000981

H1 0.0003930398 −0.0000125223 0.0000000981 0.0008362712

189


E I0 A1 A2I0 −4.2076029 0.1303879 −0.004869194 0.0000438529A1 0.1109442 −0.004869194 0.0001859283 −0.0000017056A2 −0.0012786 0.0000438529 −0.0000017056 0.0000000159S1 −3.0014722 −0.1296857 0.004854937 −0.0000437794

A1:S1 0.1119775 0.004863094 −0.0001858044 0.000001705A2:S1 −0.0009411 −0.0000438788 0.0000017062 −0.0000000159

H1 −0.7296496 −0.001093434 0.0000222007 −0.0000001144

S1 A1:S1 A2:S1 H1I0 −0.1296857 0.004863094 −0.0000438788 −0.001093434A1 0.004854937 −0.0001858044 0.0000017062 0.0000222007A2 −0.0000437794 0.000001705 −0.0000000159 −0.0000001144S1 0.2723079 −0.01008202 0.0000900474 0.0005645023

A1:S1 −0.01008202 0.0003801723 −0.0000034505 −0.0000176056A2:S1 0.0000900474 −0.0000034505 0.0000000318 0.0000001339

H1 0.0005645023 −0.0000176056 0.0000001339 0.0008236352


E I0 A1 A2I0 −5.482575 0.126806 −0.004494702 0.0000386495A1 0.155532 −0.004494702 0.0001657342 −0.0000014788A2 −0.00171 0.0000386495 −0.0000014788 0.0000000137S1 −0.594859 −0.003287488 −0.0002186636 0.0000049168

A1:S1 0.014914 0.0000617117 0.0000037287 −0.000000089H1 −0.77295 −0.00103399 0.0000145481 −0.0000000171

S1 A1:S1 H1I0 −0.003287488 0.0000617117 −0.00103399A1 −0.0002186636 0.0000037287 0.0000145481A2 0.0000049168 −0.000000089 −0.0000000171S1 0.03115602 −0.0005553824 0.0002164364

A1:S1 −0.0005553824 0.0000102079 −0.0000035631H1 0.0002164364 −0.0000035631 0.001513577

190


E I0 A1 A2 S1I0 −3.2804252 0.1184368 −0.004043614 0.0000333739 0.0006583392A1 0.0482805 −0.004043614 0.0001404788 −0.0000011762 −0.0000306195A2 −0.0004436 0.0000333739 −0.0000011762 0.00000001 0.0000001661S1 −0.4247719 0.0006583392 −0.0000306195 0.0000001661 0.0009699847


E I0 A1I0 −3.41 0.07114757 −0.00243102A1 0.05368 −0.00243102 0.0000851105A2 −0.0004721 0.0000201202 −0.0000007174S1 −0.2666 −0.0001139424 −0.000004386H1 −0.1472 −0.0008272622 0.000009892

A2 S1 H1I0 0.0000201202 −0.0001139424 −0.0008272622A1 −0.0000007174 −0.000004386 0.000009892A2 0.0000000062 0.0000000061 0.0000000005S1 0.0000000061 0.0006941191 0.0000108666H1 0.0000000005 0.0000108666 0.0009470285

191


E I0 A1 A2I0 −5.1154764 0.1372342 −0.004825084 0.0000409428A1 0.0914173 −0.004825084 0.0001740661 −0.0000015071A2 −0.0007403 0.0000409428 −0.0000015071 0.0000000133S1 2.9517965 −0.1360694 0.004812602 −0.0000409617

A1:S1 −0.1050866 0.004812363 −0.0001739298 0.0000015073A2:S1 0.0008393 −0.0000409515 0.0000015072 −0.0000000133

H1 −0.1105637 −0.001135009 0.0000121632 0.0000000184

S1 A1:S1 A2:S1 H1I0 −0.1360694 0.004812363 −0.0000409515 −0.001135009A1 0.004812602 −0.0001739298 0.0000015072 0.0000121632A2 −0.0000409617 0.0000015073 −0.0000000133 0.0000000184S1 0.2306148 −0.008152476 0.0000689757 0.0001092196

A1:S1 −0.008152476 0.0002950499 −0.0000025454 −0.0000009602A2:S1 0.0000689757 −0.0000025454 0.0000000224 −0.0000000107

H1 0.0001092196 −0.0000009602 −0.0000000107 0.000999542

192

Table C.89: Expected values and variance–covariances for parameters of transitionintensity from category 0 to category 1 of diabetes.

E I0 A1 A2 S1I0 −12.7 0.375079 −0.01181739 0.0000909846 −0.001658689A1 0.2251 −0.01181739 0.0003810729 −0.0000029792 0.0000183681A2 −0.00143 0.0000909846 −0.0000029792 0.0000000236 −0.0000002071S1 −0.3632 −0.001658689 0.0000183681 −0.0000002071 0.002321242H1 −0.4194 −0.004771272 0.0000873083 −0.000000363 0.0001721306M2 0.2369 0.0001273319 −0.0000658645 0.0000004876 0.0004319005M3 0.8942 0.00138868 −0.0001021031 0.0000007844 0.000153313M4 1.608 0.002288719 −0.0001194559 0.0000009312 −0.0005615972

H1 M2 M3 M4I0 −0.004771272 0.0001273319 0.00138868 0.002288719A1 0.0000873083 −0.0000658645 −0.0001021031 −0.0001194559A2 −0.000000363 0.0000004876 0.0000007844 0.0000009312S1 0.0001721306 0.0004319005 0.000153313 −0.0005615972H1 0.003824535 −0.0000847858 −0.0003073157 −0.0003117305M2 −0.0000847858 0.0032466 0.001846945 0.001714972M3 −0.0003073157 0.001846945 0.003963769 0.001805369M4 −0.0003117305 0.001714972 0.001805369 0.02420055

Table C.90: Expected values and variance–covariances for parameters of transitionintensity from category 1 to category 0 of diabetes.

E I0 A1 A2 H1I0 −4.1308061 0.7483285507 −0.02306671 0.0001740501 −0.01175224A1 0.0845094 −0.0230667116 0.0007217255 −0.0000055175 0.0002621207A2 −0.0007309 0.0001740501 −0.0000055175 0.0000000427 −0.0000014506H1 −1.6320013 −0.0117522416 0.0002621207 −0.0000014506 0.01030016

193

Table C.91: Expected values and variance–covariances for parameters of transition intensity to MI as the first event.

E I0 A1 S1 H1 B1 B2 B3I0 −10.372336 0.105241662 −0.001129207 −0.003310816 −0.0286422984 −0.008451659 −0.006571966 −0.00638537A1 0.061666 −0.001129207 0.0000174606 −0.0000390296 0.000213757 −0.0000486592 −0.000084205 −0.0000968107S1 −1.090692 −0.003310816 −0.0000390296 0.01037012 0.0010693533 0.0008192098 0.0009073377 0.0007191711H1 0.47499 −0.028642298 0.000213757 0.001069353 0.0464575686 0.0006180788 0.001101378 0.002175557B1 0.224828 −0.008451659 −0.0000486592 0.0008192098 0.0006180788 0.01697633 0.01193123 0.01211388B2 0.61329 −0.006571966 −0.000084205 0.0009073377 0.0011013782 0.01193123 0.01855958 0.01278343B3 0.695691 −0.00638537 −0.0000968107 0.0007191711 0.0021755574 0.01211388 0.01278343 0.02557979C1 0.215231 −0.008695888 −0.0000017878 −0.0004569939 0.0010623734 −0.0006473658 −0.0008295526 −0.000617542C2 0.399809 −0.009197168 0.0000055233 −0.001036416 0.0022080806 −0.000904417 −0.001314023 −0.00116611C3 0.791412 −0.010716158 0.0000290248 −0.00225589 0.00353562 −0.001175159 −0.0017719 −0.002122582D1 0.563511 0.002680061 −0.0000711317 0.0007692776 −0.0007987658 −0.0005781705 −0.001042566 −0.001560057K1 0.252527 −0.017522347 0.0000699108 0.003901166 0.0116710064 0.0002996411 0.0006742199 0.0005935046K2 0.212259 −0.013064957 0.0000060878 0.003613842 0.0109114817 0.0002659133 0.0005208366 0.0008598644

K1:H1 0.98183 0.013809742 −0.0000245478 −0.002120682 −0.0432220432 −0.0002192614 −0.0003908771 −0.0004178516K2:H1 −0.160044 0.016127148 −0.0000580887 −0.001100792 −0.0436294272 −0.0007422648 −0.001018504 −0.001148924

194

Table C.92: Expected values and variance–covariances for parameters of transition intensity to MI as the first event (contd.).

C1 C2 C3 D1 K1 K2 K1:H1 K2:H1I0 −0.008695888 −0.009197168 −0.01071616 0.002680061 −0.01752235 −0.01306496 0.01380974 0.01612715A1 −0.0000017878 0.0000055233 0.0000290248 −0.0000711317 0.0000699108 0.0000060878 −0.0000245478 −0.0000580887S1 −0.0004569939 −0.001036416 −0.00225589 0.0007692776 0.003901166 0.003613842 −0.002120682 −0.001100792H1 0.001062373 0.002208081 0.00353562 −0.0007987658 0.01167101 0.01091148 −0.04322204 −0.04362943B1 −0.0006473658 −0.000904417 −0.001175159 −0.0005781705 0.0002996411 0.0002659133 −0.0002192614 −0.0007422648B2 −0.0008295526 −0.001314023 −0.0017719 −0.001042566 0.0006742199 0.0005208366 −0.0003908771 −0.001018504B3 −0.000617542 −0.00116611 −0.002122582 −0.001560057 0.0005935046 0.0008598644 −0.0004178516 −0.001148924C1 0.01643673 0.009318168 0.009492455 0.0003809614 −0.0001181971 −0.0001905695 −0.0002047995 −0.0002162179C2 0.009318168 0.01738586 0.009934877 0.0004849014 −0.0002060469 0.000018595 −0.0006795763 −0.0006821643C3 0.009492455 0.009934877 0.01751694 0.0005234276 −0.0001793817 0.0002147392 −0.0009162769 −0.001104703D1 0.0003809614 0.0004849014 0.0005234276 0.01667428 0.0000047835 −0.0001378328 0.0000289351 0.0001716194K1 −0.0001181971 −0.0002060469 −0.0001793817 0.0000047835 0.0215695 0.01143971 −0.02065173 −0.01074582K2 −0.0001905695 0.000018595 0.0002147392 −0.0001378328 0.01143971 0.01971632 −0.01080407 −0.01890868

K1:H1 −0.0002047995 −0.0006795763 −0.0009162769 0.0000289351 −0.02065173 −0.01080407 0.06185938 0.04267262K2:H1 −0.0002162179 −0.0006821643 −0.001104703 0.0001716194 −0.01074582 −0.01890868 0.04267262 0.06753931

195

Table C.93: Expected values and variance–covariances for parameters of transitionintensity to AP as the first event.

E I0 A1 A2I0 −15.83 1.5484367356 −0.05139734 0.0004154788A1 0.3003 −0.0513973357 0.001741182 −0.0000142459A2 −0.002252 0.0004154788 −0.0000142459 0.0000001181S1 −0.4767 −0.0047346087 0.0000459647 −0.0000006791B1 0.382 0.0007399949 −0.0004087706 0.0000027243B2 0.6534 0.0063547418 −0.000544982 0.0000033597B3 0.8135 0.0078754184 −0.0005620673 0.0000032447

S1 B1 B2 B3I0 −0.004734609 0.0007399949 0.006354742 0.007875418A1 0.0000459647 −0.0004087706 −0.000544982 −0.0005620673A2 −0.0000006791 0.0000027243 0.0000033597 0.0000032447S1 0.008875153 0.0007638706 0.0007282078 0.0003682267B1 0.0007638706 0.01896234 0.01358705 0.01366093B2 0.0007282078 0.01358705 0.02147522 0.01411485B3 0.0003682267 0.01366093 0.01411485 0.02822245

196

Table C.94: Expected values and variance–covariances for parameters of transitionintensity to CI as the first event.

E I0 A1 S1 H1I0 −9.94479 0.233001356 −0.002781132 0.0014111077 −0.0437679285A1 0.04473 −0.002781132 0.0000433027 −0.0001336456 0.0004576575S1 −0.71547 0.001411108 −0.0001336456 0.0234543123 −0.0002709974H1 −1.02807 −0.043767929 0.0004576575 −0.0002709974 0.0685808141C1 0.34986 −0.049104685 0.0000086875 −0.0013283537 0.0051062503C2 0.88983 −0.050684193 0.0000305391 −0.0031806047 0.0082177334C3 1.35656 −0.053774491 0.0000836888 −0.0064655379 0.0112466876D1 0.80995 0.006940811 −0.00023956 0.0017786614 −0.0016476186

C1 C2 C3 D1I0 −0.04910468 −0.05068419 −0.05377449 0.006940811A1 0.0000086875 0.0000305391 0.0000836888 −0.00023956S1 −0.001328354 −0.003180605 −0.006465538 0.001778661H1 0.00510625 0.008217733 0.01124669 −0.001647619C1 0.07669922 0.0484823 0.04888906 0.001158058C2 0.0484823 0.06835839 0.04992933 0.001423589C3 0.04888906 0.04992933 0.06466329 0.001412594D1 0.001158058 0.001423589 0.001412594 0.044900523

197

Table C.95: Expected values and variance–covariances for parameters of transitionintensity to TIA as the first event.

E I0 A1 A2I0 −21.18 7.445228815 −0.2156215 0.001532994A1 0.3201 −0.215621497 0.006365507 −0.0000456782A2 −0.001708 0.001532994 −0.0000456782 0.0000003309B1 0.9223 −0.016807059 −0.001640642 0.0000107702B2 1.129 0.003366577 −0.002125641 0.000013421B3 1.434 0.004611114 −0.002092346 0.0000126566

B1 B2 B3I0 −0.01680706 0.003366577 0.004611114A1 −0.001640642 −0.002125641 −0.002092346A2 0.0000107702 0.000013421 0.0000126566B1 0.09279986 0.07803751 0.0781955B2 0.07803751 0.09622291 0.07897316B3 0.0781955 0.07897316 0.1037432

198

Table C.96: Expected values and variance–covariances for parameters of transitionintensity to HS as the first event.

E I0 A1 H1 B1I0 −13.844725 0.230365671 −0.002686199 −0.0386218844 −0.0209044A1 0.099791 −0.002686199 0.0000375975 0.0004287557 −0.0000930812H1 0.715844 −0.038621884 0.0004287557 0.0269559914 0.001382242B1 0.171366 −0.020904403 −0.0000930812 0.0013822415 0.03934174B2 0.402586 −0.017861161 −0.0001568008 0.0026145728 0.02725376B3 1.190671 −0.017173992 −0.0001848266 0.0045414381 0.02757598K1 0.769259 −0.027351577 0.0002090775 0.0010279271 0.000062737K2 0.205008 −0.013726839 0.000033561 −0.0027149063 −0.0002298659

B2 B3 K1 K2I0 −0.0178611608 −0.0171739924 −0.02735158 −0.01372684A1 −0.0001568008 −0.0001848266 0.0002090775 0.000033561H1 0.0026145728 0.0045414381 0.001027927 −0.002714906B1 0.0272537557 0.0275759847 0.000062737 −0.0002298659B2 0.04317236 0.0286245735 0.0008436548 0.0003517183B3 0.0286245735 0.0430389785 0.0009351089 0.00106394K1 0.0008436548 0.0009351089 0.02417397 0.0119228K2 0.0003517183 0.0010639398 0.0119228 0.02421168

Table C.97: Expected values and variance–covariances for parameters of transitionintensity to HS following a MI.

E I0I0 −4.867 0.03999552

Table C.98: Expected values and variance–covariances for parameters of transitionintensity to MI following an AP.

E I0I0 −4.273 0.01612899

199

Table C.99: Expected values and variance–covariances for parameters of transitionintensity to HS following an AP.

E I0I0 −5.6925 0.06666568

Table C.100: Expected values and variance–covariances for parameters of transitionintensity to MI following a CI.

E I0I0 −4.0841 0.04545442

Table C.101: Expected values and variance–covariances for parameters of transitionintensity to MI following a TIA.

E I0I0 −4.6734 0.0999937

Table C.102: Expected values and variance–covariances for parameters of transitionintensity to HS following a TIA.

E I0I0 −4.0856 0.05555547

Table C.103: Expected values and variance–covariances for parameters of transitionintensity to MI following a HS.

E I0I0 −4.4166 0.07692061

200

Table C.104: Expected values and variance–covariances for parameters of probabil-ity of sudden death following an MI.

E I0 A1I0 −5.925423 0.471213198 −0.006754687A1 0.052901 −0.006754687 0.0000993252

Table C.105: Expected values and variance–covariances for parameters of probabil-ity of sudden death following an HS.

E I0I0 −1.9394 0.01733004

201

Table C.106: Expected values and variance–covariances for parameters of long–termmortality transition intensity.

E I0 A1 A2 S1I0 −5.408 0.3901787 −0.007674236 0.00003366 −0.002244126A1 −0.01475 −0.007674236 0.0001837365 −0.0000010461 0.0000271818A2 0.000746 0.00003366 −0.0000010461 0.0000000076 −0.0000001618S1 −0.4099 −0.002244126 0.0000271818 −0.0000001618 0.001492361H1 −0.5201 −0.004142726 0.0000778557 −0.0000003578 −0.0000476286M1 −1.776 −0.2264808 0.003035789 −0.0000019028 0.0000625121M2 −2.503 −0.2217841 0.00293116 −0.0000014295 0.0008099575M3 −3.313 −0.2223333 0.003011524 −0.0000024264 0.0008341164M4 −3.564 −0.2268893 0.0032176 −0.0000040762 −0.0009048428B1 0.2891 −0.01748629 0.0000723523 0.0000022172 0.0005217273B2 1.074 −0.006257379 −0.000254421 0.0000044496 0.000848612B3 2.78 −0.007985966 −0.0002069676 0.0000040924 0.0008121338

A1:B1 −0.004866 0.000254 −0.0000017482 −0.0000000264 −0.0000074735A1:B2 −0.01443 0.000102246 0.0000026368 −0.000000056 −0.0000125249A1:B3 −0.03381 0.0001260708 0.0000019404 −0.0000000505 −0.0000122014

C1 −0.2117 0.0003406512 −0.0000359136 0.0000002595 −0.0001436421C2 −0.2564 0.0003439696 −0.0000323768 0.0000002283 −0.0002464289C3 −0.1145 0.001265285 −0.000054097 0.0000003791 −0.0004512184D1 0.2824 0.0003972621 −0.0000126834 0.0000000564 0.0000592774K1 0.5689 −0.001591465 −0.0000196561 0.0000002835 0.0005357142K2 0.1455 −0.000831562 −0.0000248642 0.0000002549 0.0005026465P1 3.234 0.006271605 −0.0002305686 0.0000018392 0.0003413111

A1:P1 −0.03133 −0.0000694015 0.0000025443 −0.0000000208 −0.0000009894T1 4.2 0.006813728 −0.000345124 0.0000038492 −0.00021791

A1:T1 −0.04398 −0.0000717706 0.0000043736 −0.0000000525 0.0000024775A1:M1 0.01585 0.002913007 −0.0000406242 0.00000003 0.0000027078A1:M2 0.02248 0.002857258 −0.0000394187 0.0000000249 −0.0000053801A1:M3 0.03635 0.002877419 −0.0000408755 0.0000000414 −0.0000077096A1:M4 0.04252 0.002954248 −0.0000441679 0.0000000677 0.000012563

202

Table C.107: Expected values and variance–covariances for parameters of long–termmortality transition intensity (contd.).

H1 M1 M2 M3 M4I0 −0.004142726 −0.2264808 −0.2217841 −0.2223333 −0.2268893A1 0.0000778557 0.003035789 0.00293116 0.003011524 0.0032176A2 −0.0000003578 −0.0000019028 −0.0000014295 −0.0000024264 −0.0000040762S1 −0.0000476286 0.0000625121 0.0008099575 0.0008341164 −0.0009048428H1 0.0033617 −0.0004427155 −0.001045726 −0.001786309 −0.002171891M1 −0.0004427155 0.2437593 0.2242039 0.2253563 0.2257824M2 −0.001045726 0.2242039 0.2556844 0.2291743 0.2295459M3 −0.001786309 0.2253563 0.2291743 0.3171842 0.2356762M4 −0.002171891 0.2257824 0.2295459 0.2356762 1.732657B1 0.0005529927 −0.006961515 −0.01231618 −0.01615187 −0.01552471B2 0.001099377 −0.008894279 −0.01551693 −0.02476641 −0.02598103B3 0.001883575 −0.008681516 −0.01690227 −0.02800414 −0.04465685

A1:B1 −0.0000063273 0.0001013318 0.0001698273 0.0002236798 0.000208681A1:B2 −0.0000128251 0.000129885 0.0002134731 0.0003420767 0.0003514628A1:B3 −0.0000224509 0.0001289586 0.0002345033 0.0003846164 0.0006060322

C1 0.0001631126 −0.000195146 −0.0004008041 −0.0000007281 0.0009810158C2 0.0002607555 −0.0002105775 −0.0004209722 −0.0000102984 −0.0001116791C3 0.0003908151 −0.0005514461 −0.0009257386 −0.000444616 0.0004191611D1 −0.0000610528 0.0002112599 0.0001740494 0.0000598774 −0.0005411896K1 0.0000406585 0.0002834771 0.0008819364 0.0007373812 0.0001871184K2 −0.0001715485 0.0003530134 0.0006263274 0.0003512851 −0.0004481773P1 −0.002892854 −0.002525115 −0.003844286 −0.00727967 −0.004818319

A1:P1 0.0000336218 0.0000374517 0.0000602827 0.0001022419 0.000101714T1 −0.001334664 0.005205958 0.005622667 −0.000271019 −0.01723704

A1:T1 0.0000140909 −0.0000796277 −0.0000930224 −0.0000168901 0.0002064005A1:M1 0.0000053506 −0.003132 −0.002865458 −0.002881884 −0.002892684A1:M2 0.000012195 −0.002868895 −0.003292247 −0.002930839 −0.002941725A1:M3 0.0000208066 −0.002885671 −0.002931918 −0.004148086 −0.003023097A1:M4 0.0000273478 −0.002892751 −0.002938838 −0.003023475 −0.02399278

203


B1 B2 B3 A1:B1 A1:B2I0 −0.01748629 −0.006257379 −0.007985966 0.000254 0.000102246A1 0.0000723523 −0.000254421 −0.0002069676 −0.0000017482 0.0000026368A2 0.0000022172 0.0000044496 0.0000040924 −0.0000000264 −0.000000056S1 0.0005217273 0.000848612 0.0008121338 −0.0000074735 −0.0000125249H1 0.0005529927 0.001099377 0.001883575 −0.0000063273 −0.0000128251M1 −0.006961515 −0.008894279 −0.008681516 0.0001013318 0.000129885M2 −0.01231618 −0.01551693 −0.01690227 0.0001698273 0.0002134731M3 −0.01615187 −0.02476641 −0.02800414 0.0002236798 0.0003420767M4 −0.01552471 −0.02598103 −0.04465685 0.000208681 0.0003514628B1 0.06606099 0.03871503 0.03922931 −0.000901485 −0.0005295172B2 0.03871503 0.08743145 0.04284408 −0.0005283891 −0.001180989B3 0.03922931 0.04284408 0.1079267 −0.0005348412 −0.0005827752

A1:B1 −0.000901485 −0.0005283891 −0.0005348412 0.0000127615 0.0000075351A1:B2 −0.0005295172 −0.001180989 −0.0005827752 0.0000075351 0.0000164604A1:B3 −0.0005358725 −0.0005823584 −0.001463498 0.0000076175 0.000008242

C1 −0.0001672349 −0.000059244 −0.0000276606 0.0000016496 −0.0000001606C2 −0.0003224679 −0.0002980388 −0.0004475935 0.0000036909 0.0000027253C3 −0.0004332263 −0.0005632935 −0.000742279 0.0000049712 0.0000058317D1 0.0000930598 −0.0002216426 −0.0002022178 −0.0000023369 0.0000022837K1 0.0001015908 −0.000001296 −0.0000273767 −0.0000012462 0.000000746K2 0.0001867409 0.0001562764 0.0000754998 −0.00000235 −0.0000013719P1 −0.001427185 −0.003982871 −0.00436422 0.0000211473 0.0000590563

A1:P1 0.0000200353 0.0000589918 0.0000663533 −0.0000002947 −0.0000008852T1 −0.0007174523 −0.00110658 −0.003716004 0.0000044887 0.0000066813

A1:T1 0.0000066982 0.0000099901 0.00004067 −0.0000000227 −0.0000000389A1:M1 0.000096208 0.0001260763 0.000126673 −0.0000014198 −0.0000018631A1:M2 0.0001661793 0.0002111512 0.0002337113 −0.0000023364 −0.0000029621A1:M3 0.0002195491 0.0003404813 0.0003842441 −0.0000031007 −0.0000047866A1:M4 0.0002071991 0.0003493839 0.0006066692 −0.0000028239 −0.0000048072

204


A1:B3 C1 C2 C3 D1I0 0.0001260708 0.0003406512 0.0003439696 0.001265285 0.0003972621A1 0.0000019404 −0.0000359136 −0.0000323768 −0.000054097 −0.0000126834A2 −0.0000000505 0.0000002595 0.0000002283 0.0000003791 0.0000000564S1 −0.0000122014 −0.0001436421 −0.0002464289 −0.0004512184 0.0000592774H1 −0.0000224509 0.0001631126 0.0002607555 0.0003908151 −0.0000610528M1 0.0001289586 −0.000195146 −0.0002105775 −0.0005514461 0.0002112599M2 0.0002345033 −0.0004008041 −0.0004209722 −0.0009257386 0.0001740494M3 0.0003846164 −0.0000007281 −0.0000102984 −0.000444616 0.0000598774M4 0.0006060322 0.0009810158 −0.0001116791 0.0004191611 −0.0005411896B1 −0.0005358725 −0.0001672349 −0.0003224679 −0.0004332263 0.0000930598B2 −0.0005823584 −0.000059244 −0.0002980388 −0.0005632935 −0.0002216426B3 −0.001463498 −0.0000276606 −0.0004475935 −0.000742279 −0.0002022178

A1:B1 0.0000076175 0.0000016496 0.0000036909 0.0000049712 −0.0000023369A1:B2 0.000008242 −0.0000001606 0.0000027253 0.0000058317 0.0000022837A1:B3 0.0000204411 −0.0000004145 0.0000051179 0.0000076892 0.0000011987

C1 −0.0000004145 0.00207869 0.001026674 0.001063727 0.0000682373C2 0.0000051179 0.001026674 0.00235803 0.001121498 0.0000789914C3 0.0000076892 0.001063727 0.001121498 0.002465429 0.000077477D1 0.0000011987 0.0000682373 0.0000789914 0.000077477 0.002495486K1 0.000000787 −0.0000206906 −0.0000389427 −0.0000292502 −0.0000244134K2 0.000000238 0.0000083415 0.0000311168 0.0000254746 −0.0000285033P1 0.000067192 −0.0002698132 −0.0002463159 −0.0001632373 −0.0002349508

A1:P1 −0.0000010206 0.0000043585 0.0000034718 0.0000009645 0.0000009893T1 0.00003796 −0.0006444833 −0.0006850586 −0.0003219848 −0.000404696

A1:T1 −0.0000004083 0.0000090974 0.000011164 0.0000060154 0.0000047268A1:M1 −0.0000019029 0.0000020316 0.0000014299 0.0000049101 −0.0000036118A1:M2 −0.0000033094 0.000004543 0.0000034951 0.0000094059 −0.000003913A1:M3 −0.0000053799 −0.0000013229 −0.00000227 0.0000027865 −0.0000041168A1:M4 −0.0000083842 −0.0000159507 −0.0000004476 −0.0000073866 0.0000008213

205


K1 K2 P1 A1:P1 T1I0 −0.001591465 −0.000831562 0.006271605 −0.0000694015 0.006813728A1 −0.0000196561 −0.0000248642 −0.0002305686 0.0000025443 −0.000345124A2 0.0000002835 0.0000002549 0.0000018392 −0.0000000208 0.0000038492S1 0.0005357142 0.0005026465 0.0003413111 −0.0000009894 −0.00021791H1 0.0000406585 −0.0001715485 −0.002892854 0.0000336218 −0.001334664M1 0.0002834771 0.0003530134 −0.002525115 0.0000374517 0.005205958M2 0.0008819364 0.0006263274 −0.003844286 0.0000602827 0.005622667M3 0.0007373812 0.0003512851 −0.00727967 0.0001022419 −0.000271019M4 0.0001871184 −0.0004481773 −0.004818319 0.000101714 −0.01723704B1 0.0001015908 0.0001867409 −0.001427185 0.0000200353 −0.0007174523B2 −0.000001296 0.0001562764 −0.003982871 0.0000589918 −0.00110658B3 −0.0000273767 0.0000754998 −0.00436422 0.0000663533 −0.003716004

A1:B1 −0.0000012462 −0.00000235 0.0000211473 −0.0000002947 0.0000044887A1:B2 0.000000746 −0.0000013719 0.0000590563 −0.0000008852 0.0000066813A1:B3 0.000000787 0.000000238 0.000067192 −0.0000010206 0.00003796

C1 −0.0000206906 0.0000083415 −0.0002698132 0.0000043585 −0.0006444833C2 −0.0000389427 0.0000311168 −0.0002463159 0.0000034718 −0.0006850586C3 −0.0000292502 0.0000254746 −0.0001632373 0.0000009645 −0.0003219848D1 −0.0000244134 −0.0000285033 −0.0002349508 0.0000009893 −0.000404696K1 0.002058291 0.001098887 −0.0004020367 0.0000050697 0.0001700734K2 0.001098887 0.001926529 0.0001375042 −0.0000031987 0.0000104802P1 −0.0004020367 0.0001375042 0.1709851 −0.002338854 −0.02351156

A1:P1 0.0000050697 −0.0000031987 −0.002338854 0.0000326792 0.0002961877T1 0.0001700734 0.0000104802 −0.02351156 0.0002961877 0.3137101

A1:T1 −0.0000036492 −0.0000014303 0.0002901488 −0.0000036666 −0.004069411A1:M1 −0.0000020241 −0.0000050049 0.0000413481 −0.0000006051 −0.0000867234A1:M2 −0.0000088719 −0.0000087834 0.0000634037 −0.0000009664 −0.000101503A1:M3 −0.0000051072 −0.0000043031 0.0001027283 −0.0000014368 −0.0000242155A1:M4 0.000006167 0.0000099057 0.0001013699 −0.0000019371 0.0002159077

206


A1:T1 A1:M1 A1:M2 A1:M3 A1:M4I0 −0.0000717706 0.002913007 0.002857258 0.002877419 0.002954248A1 0.0000043736 −0.0000406242 −0.0000394187 −0.0000408755 −0.0000441679A2 −0.0000000525 0.00000003 0.0000000249 0.0000000414 0.0000000677S1 0.0000024775 0.0000027078 −0.0000053801 −0.0000077096 0.000012563H1 0.0000140909 0.0000053506 0.000012195 0.0000208066 0.0000273478M1 −0.0000796277 −0.003132 −0.002868895 −0.002885671 −0.002892751M2 −0.0000930224 −0.002865458 −0.003292247 −0.002931918 −0.002938838M3 −0.0000168901 −0.002881884 −0.002930839 −0.004148086 −0.003023475M4 0.0002064005 −0.002892684 −0.002941725 −0.003023097 −0.02399278B1 0.0000066982 0.000096208 0.0001661793 0.0002195491 0.0002071991B2 0.0000099901 0.0001260763 0.0002111512 0.0003404813 0.0003493839B3 0.00004067 0.000126673 0.0002337113 0.0003842441 0.0006066692

A1:B1 −0.0000000227 −0.0000014198 −0.0000023364 −0.0000031007 −0.0000028239A1:B2 −0.0000000389 −0.0000018631 −0.0000029621 −0.0000047866 −0.0000048072A1:B3 −0.0000004083 −0.0000019029 −0.0000033094 −0.0000053799 −0.0000083842

C1 0.0000090974 0.0000020316 0.000004543 −0.0000013229 −0.0000159507C2 0.000011164 0.0000014299 0.0000034951 −0.00000227 −0.0000004476C3 0.0000060154 0.0000049101 0.0000094059 0.0000027865 −0.0000073866D1 0.0000047268 −0.0000036118 −0.000003913 −0.0000041168 0.0000008213K1 −0.0000036492 −0.0000020241 −0.0000088719 −0.0000051072 0.000006167K2 −0.0000014303 −0.0000050049 −0.0000087834 −0.0000043031 0.0000099057P1 0.0002901488 0.0000413481 0.0000634037 0.0001027283 0.0001013699

A1:P1 −0.0000036666 −0.0000006051 −0.0000009664 −0.0000014368 −0.0000019371T1 −0.004069411 −0.0000867234 −0.000101503 −0.0000242155 0.0002159077

A1:T1 0.0000539275 0.000001312 0.0000016308 0.0000006158 −0.0000025561A1:M1 0.000001312 0.0000415266 0.000037831 0.0000380702 0.0000382316A1:M2 0.0000016308 0.000037831 0.0000437362 0.0000386807 0.0000388508A1:M3 0.0000006158 0.0000380702 0.0000386807 0.0000559017 0.0000400066A1:M4 −0.0000025561 0.0000382316 0.0000388508 0.0000400066 0.0003398793

207

Bibliography

Adams, K. F., Schatzkin, A., Harris, T. B., Kipnis, V., Mouw, T.,

Ballard-Barbash, R., Hollenbeck, A. and Leitzmann, M. F. (2006).

Overweight, obesity and mortality in a large prospective cohort of persons 50 to

71 years old. The New England Journal of Medicine, 355(8), 763–778.

Agresti, A. (1990). Categorical data analysis. John Wiley & Sons.

Anderson, K. M., Odell, P. M., Wilson, P. W. and Kannel, W. B. (1991).

Cardiovascular disease risk profiles. American Heart Journal, 121(1), 293–298.

Bender, R., Jockel, K.-H., Trautner, C., Spraul, M. and Berger, M.

(1999). Effect of age on excess mortality in obesity. The Journal of the American

Medical Association, 281(16), 1498–1504.

Berger, B., Stenstrom, G. and Sundkvist, G. (1999). Incidence, preva-

lence and mortality of diabetes in a large population. A report from the

Skaraborg Diabetes Registry. Diabetes Care, 22(5), 773–778.

Burden, R. L. and Fiares, J. (2001). Numerical Analysis. Brooks/Cole, Pacific

Grove, USA, 7th edition.

Burke, A. P., Farb, A., Malcom, G. T., Liang, Y.-H., Smialek, J. and

Virmani, R. (1997). Coronary risk factors and plaque morphology in men with

coronary disease who died suddenly. The New England Journal of Medicine,

336(18), 1276–1282.

Butland, B., Jebb, S., Kopelman, P., McPherson, K., Thomas, S.,

Mardell, J. and Parry, V. (2007). Tackling obesities: future choices - project

report. Government Office for Science.

208

Calle, E. E., Thun, M. J., Petrelli, J. M., Rodriguez, C. and Heath Jr.,

C. W. (1999). Body-mass index and mortality in a prospective cohort of U.S.

adults. The New England Journal of Medicine, 341(15), 1097–1105.

Capewell, S., Livingston, B. M., MacIntyre, K., Chalmers, J. W. T.,

Boyd, J., Finlayson, A., Redpath, A., Pell, J. P., Evans, C. J. and

McMurray, J. J. V. (2000). Trends in case-fatality in 117718 patients admitted

with acute myocardial infarction in Scotland. European Heart Journal, 21, 1833–

1840.

Caro, J., Migliaccio-Walle, K., Ishak, K. J. and Proskorovsky, I. (2005).

The morbidity and mortality following a diagnosis of peripheral arterial disease:

Long-term follow-up of a large database. BMC Cardiovascular Disorders, 5(14).

Cook, D. G., Shaper, A. G., Pocock, S. J. and Kussick, S. J.

(1986). Giving up smoking and the risk of heart attacks: A report from the

Britisk Regional Heart Study. The Lancet, pages 1376–1380.

Critchley, J. A. and Capewell, S. (2003). Mortality risk reduction associated

with smoking cessation in patients with coronary heart disease: A systematic

review. The Journal of the American Medical Association, 290(1), 86–97.

Curtis, P. (2007). All men over 50 should take drug to lower cholesterol, says

heart expert. The Guardian dated 28 July.

Dawber, T. R., Meadors, G. F. and Moore, F. E. (1951). Epidemiological

approaches to heart disease: The Framingham Study. American Journal of Public

Health, 41(3), 279–286.

De Backer, G., Ambrosioni, E., Borch-Johnsen, K., Brotons, C.,

Cifkova, R., Dallongeville, J., Ebrahim, S., Faergeman, O., Graham,

I., Mancia, G., Cats, V. M., Orth-Gomer, K., Perk, J., Pyorala, K.,

Rodicio, J. L., Sans, S., Sansoy, V., Sechtem, U., Silber, S., Thom-

sen, T. and Wood, D. (2004). European guidelines on cardiovascular disease

prevention in clinical practice: Third joint task force of European and other so-

cieties on cardiovascular disease prevention in clinical practice (constituted by

209

representatives of eight societies and by invited experts ). Atherosclerosis, 173,

381–391.

Dobson, A. J., Alexander, H. M., Heller, R. F. and Lloyd, D. M. (1991).

How soon after quitting smoking does risk of heart attack decline? Journal of

Clinical Epidemiology, 44(11), 1247–1253.

Doll, R., Peto, R., Boreham, J. and Sutherland, I. (2004). Mortality

in relation to smoking: 50 years’ observations on male British doctors. British

Medical Journal, 328, 1519–1527.

Flegal, K. M., Graubard, B. I., Williamson, D. F. and Gail, M. H.

(2007). Cause - specific excess deaths associated with underweight, overweight

and obesity. The Journal of the American Medical Association, 298(17), 2028–

2037.

Fontaine, K. R., Redden, D. T., Wang, C., Westfall, A. O. and Allison,

D. B. (2003). Years o life lost due to obesity. The Journal of the American

Medical Association, 289(2), 187–193.

Gallop, A. and Baker, A. (2006). Life expectancy at age 65 continues to rise.

News Release: Office of National Statistics.

Godtfredsen, N. S., Holst, C., Prescott, E., Vestbo, J. and

Osler, M. (2002). Smoking reduction, smoking cessation and mor-

tality: A 16 year follow-up of 19,732 men and women from the

Copenhagen Centre for Prospective Population Studies. American Journal of

Epidemiology, 156(11), 994–1001.

Gu, K., Cowie, C. C. and Harris, M. I. (1998). Mortality in adults with and

without diabetes in a national cohort of the U.S. population, 1971-1993. Diabetes

Care, 21(7), 1138–1145.

Hardie, K., Jamrozik, K., Hankey, G. J., Broadhurst, R. J. and An-

derson, C. (2005). Trends in five-year survival and risk of recurrent stroke after

210

first-ever stroke in the Perth Community Stroke study. Cerebrovascular Diseases,

19, 179–185.

Hart, C. L., Hole, D. J. and Smith, G. D. (1999). Risk factors and 20-year

stroke mortality in men and women in the Renfrew/Paisely Study in Scotland.

Stroke, 30, 1999–2007.

Hart, C. L., Hole, D. J. and Smith, G. D. (2000). Comparison of risk factors

for stroke incidence and stroke mortality in 20 years of follow-up in men and

women in the Renfrew/Paisely study in Scotland. Stroke, 31, 1893–1896.

Hoem, J. M. (1988). The versatility of the Markov chain as a tool in the math-

ematics of life insurance. International Congress of Actuaries. Series R., pages

171–202.

Humphries, S. E., Talmud, P. J., Hawe, E., Bolla, M., Day, I. N. M.

and Miller, G. J. (2001). Apolipoprotein E4 and coronary heart disease in

middle-aged men who smoke: A prospective study. The Lancet, 358, 115–119.

Hunt, D., Blakely, T., Woodward, A. and Wilson, N. (2005). The smoking-

mortality association varies over time and by ethnicity in New Zealand. Interna-

tional Journal of Epidemiology, 34(5), 1020–1028.

Jee, S. H., Sull, J. W., Park, J., Lee, S.-Y., Ohrr, H., Guallar, E. and

Samet, J. M. (2006). Body-mass index and mortality in Korean men and women.

The New England Journal of Medicine, 355(8), 779–787.

Kawachi, I., Colditz, G. A., Stampfer, M. J., Willett, W. C., Man-

son, J. E., Rosner, B., Hunter, D. J., Hennekens, C. H. and Speizer,

F. E. (1993). Smoking cessation in relation to total mortality rates in women: A

prospective cohort study. Annals of Internal Medicine, 119(10), 992–1000.

Khachigian, L. M. (ed.) (2005). High-risk atherosclerotic plaques: mechanisms,

imaging, models and therapy. CRC Press.

211

Lam, T. H., Ho, S. Y., Hedley, A. J., Mak, K. H. and Peto, R. (2001).

Mortality and smoking in Hong Kong: Case-control study of all adult deaths in

1998. British Medical Journal, 323, 361–366.

Law, M. R., Wald, N. J. and Rudnicka, A. R. (2003). Quantifying effect of

statins on low density lipoprotein cholesterol, ischaemic heart disease, and stroke:

Systematic review and meta-analysis. British Medical Journal, 326, 1423–1429.

Law, M. R., Wald, N. J. and Thompson, S. G. (1994). By how much and how

quickly does reduction in serum cholesterol concentration lower risk of ischaemic

heart disease? British Medical Journal, 308, 367–372.

Lee, A. H., Somerford, P. J. and Yau, K. K. W. (2003). Factors influencing

survival after stroke in Western Australia. Medical Journal of Australia, 179,

289–293.

Lightwood, J. M. and Glantz, S. A. (1997). Short-term economic and health

benefits of smoking cessation. Circulation, 96, 1089–1096.

Macdonald, A. S., Waters, H. R. and Wekwete, C. T. (2005a). A model

for coronary heart disease and stroke with applications to critical illness insurance

underwriting I: The model. North American Actuarial Journal, 9(1), 13–40.

Macdonald, A. S., Waters, H. R. and Wekwete, C. T. (2005b). A model

for coronary heart disease and stroke with applications to critical illness insurance

underwriting II: Applications. North American Actuarial Journal, 9(1), 41–56.

Mathers, C. D. and Loncar, D. (2005). Updated projections of global mortality

and burden of disease, 2002-2030: Data sources, methods and results. Technical

report, World Health Organisation.

NCEP Expert Panel (2001). Executive summary of the third report

of the National Cholesterol Education Program (NCEP) expert panel on de-

tection, evaluation and treatment of high blood cholesterol in adults

(Adult Treatment Panel III). The Journal of the American Medical Association,

285(19), 2486–2497.

212

Office of National Statistics (2006). Mortality statistics: Cause.

Review of the Registrar General on deaths by cause, sex and age, in

England and Wales, 2005. DH2 32, Office of National Statistics.

The SPARCL Investigators (2006). High-dose atorvastatin after stroke or tran-

sient ischemic attack. The New England Journal of Medicine, 355(6), 549–559.

Well-Connected Reports (2006). Diabetes: Type 2. Technical Report 60,

A.D.A.M.’s, www.well-connected.com.

Well-Connected Reports (2007a). High blood pressure. Technical Report 14,


Well-Connected Reports (2007b). Cholesterol. Technical Report 23,


Well-Connected Reports (2007c). Weight control and diet. Technical Re-

port 53, A.D.A.M.’s, www.well-connected.com.

McElduff, P., Jaefarnezhad, M. and Durrington, P. N. (2006).

American, British and European recommendations for statins in the primary pre-

vention of cardiovascular disease applied to British men studied prospectively.

Heart, 92, 1213–1218.

Morgan, C. L., Currie, C. J. and Peters, J. R. (2000). Relationship between

diabetes and mortality. A population study using record linkage. Diabetes Care,

23(8), 1103–1107.

Negri, E., La Vecchia, C., D’Avanzo, B., Nobili, A. and La Malfa, R. G.

(1994). Acute myocardial infarction: Association with time since stopping smok-

ing in Italy. Journal of Epidemiology and Community Health, 48, 129–133.

Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models.

Journal of the Royal Statistical Society. Series A (General), 135(3), 370–384.

Palinski, W. (2001). New evidence for beneficial effects of statins unrelated to

lipid lowering. Arteriosclerosis, Thrombosis and Vascular Biology, 21, 3–5.

213

Pekkanen, J., Nissinen, A., Punsar, S. and Karvonen, M. J. (1992). Short-

and long-term association of serum cholesterol with mortality. The 25-year follow-

up of the Finnish cohorts of the Seven Countries Study. American Journal of

Epidemiology, 135(11), 1251–1258.

Prescott, E., Scharling, H., Osler, M. and Schnohr, P. (2002). Im-

portance of light smoking and inhalation habits on risk of myocardial infarc-

tion and all cause mortality. A 22 year follow up of 12149 men and women in

The Copenhagen City Heart Study. Journal of Epidemiology and Community

Health, 56, 702–706.

Qiao, Q., Tervahauta, M., Nissinen, A. and Tuomilehto, J. (2000). Mor-

tality from all causes and from coronary heart disease related to smoking and

changes in smoking during a 35-year follow-up of middle-aged Finnish men. Eu-

ropean Heart Journal, 21, 1621–1626.

Rastenyte, D., Tuomilehto, J., Domarkiene, S., Cepaitis, Z. and Reklai-

tiene, R. (1996). Risk factors for death from stroke in middle-aged Lithuanian

men. Stroke, 27, 672–676.

Rickards, L., Fox, K., Roberts, C., Fletcher, L. and Goddard, E. (2004).

Living in britain: Results from the 2002 general household survey. Technical

Report 31, Office of National Statistics, UK.

Rogers, R. G., Hummer, R. A. and Krueger, P. M. (2003). The effect of

obesity on overall, circulatory disease- and diabetes-specific mortality. Journal of

Biosocial Sciences, 35, 107–129.

Smith, G. D., Shipley, M. J., Marmot, M. G. and Rose, G. (1992). Plasma

cholesterol concentration and mortality. The Whitehall Study. The Journal of the

American Medical Association, 267(1).

Solomon, C. G. and Manson, J. E. (1997). Obesity and mortality: A review

of the epidemiologic data. American Journal of Clinical Nutrition, 66(suppl),

1044S–1050S.

214

Sproston, K. and Primatesta, P. (eds.) (2004a). Health Survey for England

2003. Volume 1: Cardiovascular disease. The Stationary Office, London.

Sproston, K. and Primatesta, P. (eds.) (2004b). Health Survey for England

2003. Volume 2: Risk factors for cardiovascular diseases. The Stationary Office,

London.

Sproston, K. and Primatesta, P. (eds.) (2004c). Health Survey for England

2003. Volume 3: Methodology and documentation. The Stationary Office, London.

Stamler, J., Daviglus, M. L., Garside, D. B., Dyer, A. R., Greenland, P.

and Neaton, J. D. (2000). Relationship of baseline serum cholesterol levels in 3

large cohorts of younger men to long-term coronary, cardiovascular, and all-cause

mortality and to longevity. The Journal of the American Medical Association,

284(3), 311–318.

Stanner, S. (ed.) (2005). Cardiovascular disease; diet, nutrition and emerging risk

factors. Blackwell Publishing for British Nutrition Foundation.

Van Den Hoogen, P. C. W., Feskens, E. J. M., Nagelkerke, N. J. D.,

Menotti, A., Nissinen, A. and Kromhout, D. (2000). The relation between

blood pressure and mortality due to coronary heart disease among men in different

parts of the world. The New England Journal of Medicine, 342(1), 1–8.

Vaughan, C. J., Murphy, M. B. and Buckley, B. M. (1996). Statins do more

than just lower cholesterol. The Lancet, 348, 1079–1082.

Wadsworth, M., Kuh, D., Richards, M. and Hardy,

R. (2006). Cohort profile: The 1946 national birth cohort

(MRC National Survey of Health and Development). International Journal

of Epidemiology, 35, 49–54.

Wald, N. J. and Law, M. R. (2003). A strategy to reduce cardiovascular disease

by more than 80%. British Medical Journal, 326, 1419–1424.

Walley, T., Folino-Gallo, P., Stephens, P. and Van Ganse, E. (2005).

Trends in prescribing and utilization of statins and other lipid lowering drugs

215

across Europ 1997-2003. British Journal of Clinical Pharmacology, 60(5), 543–

551.

Wannamethee, G. S., Shaper, G. A. and Ebrahim, S. (2000). HDL-

cholesterol, total cholesterol, and the risk of stroke in middle-aged British men.

Stroke, 31, 1882–1888.

Wekwete, C. T. (2002). Genetics and critical illness insurance underwriting:

models for breast cancer and ovarian cancer and for coronary heart disease and

stroke. Ph.D. thesis, Heriot-Watt University, www.ma.hw.ac.uk/ams.html.

Williams, B., Poulter, N. R., Brown, M. J., Davis, M., McInnes,

G. T., Potter, J. F., sever, P. S. and McGThom, S. (2004). Guide-

lines for management of hypertension: Report of the fourth working party of

the British Hypertension Society, 2004-BHS IV. Journal of Human Hypertension,

18(3), 139–185.

Wood, D., Wray, R., Poulter, N., Williams, B., Kirby, M., Patel, V.,

Durrington, P., Reckless, J., Davis, M., Sivers, F. and Potter, J.

(2005). JBS2: Joint British Societies’ guidelines on prevention of cardiovascular

disease in clinical practice. Heart, 91(Suppl V), v1–v52.

Zaninotto, P., Wardle, H., Stamatakis, E., Mindell, J. and Head, J.

(2006). Forecasting obesity to 2010. Technical report, Department of Health,

UK.

216

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AN INDIVIDUAL LIFE HISTORY MODEL FOR HEART DISEASE, …andrewc/actuarial/chatterjee_thesis.pdf · DISEASE, STROKE AND DEATH: STRUCTURE, PARAMETERISATION AND APPLICATIONS. By Tushar