Goldsmith’s teachers lecture 2011

Medical statisticsJoan Morris

Professor of Medical Statistics

Aims

• To describe medical statistics• To give examples of where medical

statistics has contributed to society• Use of statistics in screening• To mention some novel statistical

methods

Statistics - definition

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and

presentation of data.

Data Collection

Data Collection

• Florence Nightingale

– She realised that soldiers were dying from malnutrition, poor sanitation, and lack of activity.

– She kept meticulous records of the death toll in the hospitals as evidence of the importance of patient welfare.

Polar Area Diagrams

National Data Collection

• National Mortality Statistics• Health survey for England and Wales• Population statistics …..

• Large amounts of data are available on the web

Standardised mortality ratios: Mortality from skin cancer

0

50

100

150

200

All

birth

s (in

thou

sand

s)

15 20 25 30 35 40 45 50Maternal age at birth (years)

All births in England and Wales according to maternal age :1989-91 compared with 2005-2007

1989-91 : 2090,000 births

2005-07 : 1991,000 births

Comparisons of individuals

Observationalcross-sectionalcase-control studiescohort studies

InterventionalRandomised controlled trials

Comparisons of populations

Time trends

Ecological studies:Geographical variationsAge/sex patternsSocial variations

EpidemiologyEpidemiology

Comparison of Individuals

• Study Design– Ensure “valid” data is collected – Ensure enough data is collected

• Main designs– Case control studies– Cohort studies– Clinical trials

Richard Doll (doctor) and Austin Bradford Hill (statistician)

Is there a relationship between smoking and lung cancer?

British Doctors Cohort Study(BMJ 1994;309:901-911)

34,000 British male doctors who replied to a postal questionnaire in 1951 and further questionnaires in 1957, 66, 72, 78, 90, …

Flagged the doctors at NHSCR and obtained their death certificates as they died. Compared death rates in smokers and non-smokers..

Number of cigarettes smoked per day

Risk of dying from lung cancer compared to non smokers

None 1.0

1 to 9 4.1

10 to 19 10.5

20 to 30 23.6

More than 30 41.9

Is there a relationship between smoking and lung cancer?

What causes Sudden Infant Death Syndrome ?

• Sudden Infant Death Syndrome Case Control Study

• Methods– Collected information about infants that were potential

“SIDS”– Identified “similar” children who had not died – Compared the differences

• Results– Children who died were much more likely to have

been put on their fronts to sleep than children who did not die

Randomised Controlled Trial

• A clinical trial is an experiment in which a treatment is administered to humans in order to evaluate its efficacy and safety

• Randomised = allocated to groups on basis of chance e.g. tossing a coin (ensures fair comparison)

• Controlled = a comparison group

Can folic acid reduce neural tube defects (e.g. spina bifida)?

• MRC Vitamin trial - randomised controlled trial

• Large: 1817 women who had had a previous NTD, 33 centres, 7 countries

Can folic acid reduce neural tube defects (e.g. spina bifida)?

• Results : Women who did not receive folic acid were 3 times more likely to have a second NTD pregnancy

• Impact : Women are advised to take folic acid prior to becoming pregnant

• Majority of countries around the world fortify flour with folic acid

Collection of Data

• Study Design– Cohort– Case Control– Clinical Trial

Analysis

• Could the observed results have arisen by chance ?

• Given that we have a sample what can we say about the population from which the sample comes

Folic Acid vs Placebo forNeural Tube Defects 

 

  

 

    Neural Tube Defects

    Yes No Total

Folic Acid

Yes 6 587 593

No 21 581 602

Risk of NTD in treated group =Risk of NTD in control group =

Relative Risk of NTD in treated group compared to control group =

P values

• P is the probability of the observed event or one more extreme occurring if the null hypothesis is true

• Null hypothesis : No difference in treatments

• P = probability out of 27 babies with an NTD what is the chance that 6 or less are in the FA group and 21 in placebo group IF FA has no effect

No. treated No. died A 20 4 B 20 2

A 100 20 B 100 10

A 200 40 B 200 20

RR death in A vs B = 2.0Is it due to chance or not ?

Interpreting the results of a trial

P values

• P < 0.05 is taken to mean statistical significance

• This means if there is no difference between treatments, and you do 20 trials one will be statistically significant

Folic Acid vs Placebo forNeural Tube Defects

RR = 0.29

P = 0.008

Therefore we assume there is a real difference between the folic acid group and the placebo group

But how big is the reduction ?

Folic Acid vs Placebo forNeural Tube DefectsRR = 0.29

95% Confidence Interval : 0.10 to 0.76

P = 0.008

95% confidence intervals means that 95% of the time this interval contains the true reduction

Therefore it gives an indication of the likely size of the reduction

01

23

45

67

8N

TD p

reva

lenc

e pe

r 100

0 bi

rths

0 2 4 6 8 10Plasma folate (ng/ml)

Folic Acid and NTD Dose Response

Folic Acid and NTD Dose Response01

23

45

67

8N

TD p

reva

lenc

e pe

r 100

0 bi

rths

0 2 4 6 8 10Plasma folate (ng/ml)

Interpretation

• The same proportional increase in serum folate has the same proportional reduction in NTD

• All women benefit from taking folic acid. There is not a threshold effect

So far….

• Collection– Nightingale– National statistics– Study design

• Presentation – Estimates and confidence intervals

• Analysis – Vital to interpretation

Use of Statistics in Screening

Screening is the identification, among apparently healthy individuals, of those who are sufficiently at risk from a specific disorder to benefit from a subsequent diagnostic test, procedure or direct preventive action.

Screening for Heart Disease

Relative odds of major IHD event by fifths of the distribution of haemostatic and lipid markers for all men (•——•) and for men free of IHD at baseline examination ( ––– ).∘ ∘

Yarnell J et al. Eur Heart J 2004;25:1049-1056

The European Society of Cardiology

AffectedUnaffected

Biomarker : ZZ

AffectedUnaffected

Screen negative Screen positiveBiomarker : ZZ

Affected

FPR=5%

Unaffected

Screen negative Screen positiveBiomarker : ZZ

False positives

False negatives

Risk Factor

Unaffected Affected

Good test

Screening for a medical disorder

Risk Factor

Unaffected Affected

Poor test

Screening for a medical disorder

Is Cholesterol any good for screening ?

2

4

6

8

.2 .4 .6 .8fol

AffectedUnaffected

Risk screen converter

www.wolfson.qmul.ac.uk/rsc/

Detection Rate

False Positive Rate

4.2mm Hg

7.5mm Hg

• Are there any good screening tests ?

Antenatal screening for Down’s syndrome

Quadruple test markers

0.25 0.5 1 2 4 8 16

Maternal serum total hCG (MoM)

0.25 0.5 1 2 4 8 16

Maternal serum inhibin-A (MoM)

Total hCG Inhibin-A

0.25 0.5 1 2 4 8 16

Maternal serum AFP (MoM)

0.25 0.5 1 2 4 8 16

Maternal serum uE3 (MoM)

AFP uE3

Down’s syndrome

Unaffected Down’s syndrome

Unaffected

Down’s syndrome

Down’s syndrome

Unaffected Unaffected

01:108 1:106 1:104 1:102 1:1 102:1 104:1

Down’s syndrome

Unaffected

Distribution of risk in Down’s syndrome and unaffected pregnancies using AFP, uE3, total hCG and inhibin-A

measured at 14-20 weeks (+ maternal age)

Risk of a Down’s syndrome pregnancy at term

Recent Developments

• Collection• Analysis• Interpretation or explanation• Presentation

Collection

• Danish mother and child study – Recruiting people on the internet

• Linking data sets– Probability linking eg

• Date of mother’s birth fairly accurate• Gestational age of baby often wrong• Weight of baby –REALLY ACCURATE !!!

Analysis

• Meta-analysis• Monte-carlo simulations• Bayesian analysis• Analysis of micro-arrays

Several studies looking at the same thing

• Each study may be relatively inconclusive because of too much uncertainty (too small)

• Statistical (mathematical) method of combining and presenting results from several studies

• Can indicate more robust results

Overall (I-squared = 35.2%, p = 0.159 for heterogeneity)

Phibbs 1991

Corbet 1991

Halliday 1984

Study

Stevenson 1992

Ten Centre 1987

Bose 1990

Wilkinson 1985

3/36

27/208

6/49

Treat

55/109

23/159

11/176

0/16

7/38

44/202

6/51

Cont

56/106

40/149

20/185

2/16

0.70 (0.58, 0.85)

0.45 (0.13, 1.62)

0.60 (0.38, 0.92)

1.04 (0.36, 3.01)

RR (95% CI)

0.96 (0.74, 1.24)

0.54 (0.34, 0.85)

0.58 (0.29, 1.17)

0.20 (0.01, 3.86)

0.70 (0.58, 0.85)

0.45 (0.13, 1.62)

0.60 (0.38, 0.92)

1.04 (0.36, 3.01)

RR (95% CI)

0.96 (0.74, 1.24)

0.54 (0.34, 0.85)

0.58 (0.29, 1.17)

0.20 (0.01, 3.86)

Favours treatment Favours control 1.1 .2 .5 1 2 5 10

Prophylactic synthetic surfactant for preventing mortality in preterm infants

Comparing institutions, individual doctors and identifying outliers

• What’s the problem?– Lots of variables important– Random variation– Random variation greater for smaller units or

institutions

• Way of presenting the values for units so that this is taken into account

Funnel plot

Conclusion

• As much about collection, interpretation and presentation as calculation

• Making sense out of uncertainty