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Analytical epidemiology Disease frequency Study design: cohorts & case control Choice of a reference group Biases
Alain Moren, 2006
Impact Causality Effect modification & confounding Stratification Significance testing Matching Multivariable analysis
Exposure Outcome
Third variable
Two main complications
(1) Effect modifier
(2) Confounding factor
- useful information
- bias
To analyse effect modification
To eliminate confounding
Solution = stratification stratified analysis
Create strata according to categories inside the range of values taken by third variable
Variation in the magnitude of measure of effect across levels of a third variable.
Effect modification is not a bias butuseful information
Effect modifier
Happens when RR or OR is different between strata (subgroups of population)
Effect modifier
• To identify a subgroup with a lower or higher risk
• To target public health action
• To study interaction between risk factors
AR NV - AR VVE = -----------------------------
AR NV
VE = 1 - RR
Vaccine efficacy
Vaccine efficacy
Status Pop. Cases Cases
per 1000 RR
V 301 545 150 0.49 0.28
NV 298 655 515 1.72 Ref.
Total 600 200 665 1.11
VE = 1 - RR = 1 - 0.28
VE = 72%
Vaccine efficacy by age group
Effect modification
Different effects (RR) in different strata (age groups)
VE is modified by age
Test for homogeneity among strata (Woolf test)
Oral contraceptives (OC) and myocardial infarction (MI)
Case-control study, unstratified data
OC MI Controls OR
Yes 693 320 4.8No 307 680 Ref.
Total 1000 1000
Physical activity and MI
*
*
*
**
40 50 60 70 80
1
2
3
4
5
6
Relative risk (RR) of dying from coronary heart disease for smoking physicians, by age groups, England & Wales,
RR
AgeDoll et Hill, 1966
302010
Effect (OR or RR) is a function of the effect modifier
Effect function
Any statistical test to help us?
• Breslow-Day
• Woolf test
• Test for trends: Chi square
Heterogeneity
Confounding
Distortion of measure of effect because of a third factor
Should be prevented
Needs to be controlled for
Simpson’s paradox
Hats Fit Do not fit % fit
Red 17 3 85%
Blue 9 1 90%
Hats Fit Do not fit % fit
Red 1 9 10%
Blue 3 17 15%
Second table
Hats Fit Do not fit % fit
Red 18 12 60%
Blue 12 18 40%
Day 2, one table only
Cases of Down syndroms by birth order
0
20
40
60
80
100
120
140
160
180
1 2 3 4 5
Birth order
Cases per 100 000 live births
Cases of Down Syndrom by age groups
0100200300400500600700800900
1000
< 20 20-24 25-29 30-34 35-39 40+
Age groups
Cases per 100000 live
births
0100200300400500600700800900
1000
Cases per 100000
1 2 3 4 5
Birth order
Cases of Down syndrom by birth order and mother's age
Confounding
Exposure Outcome
Third variable
To be a confounding factor, 2 conditions must be met:
Be associated with exposure - without being the consequence of exposure
Be associated with outcome - independently of exposure
To identify confounding
Compare crude measure of effect (RR or OR)
to
adjusted (weighted) measure of effect (Mantel Haenszel RR or OR)
Are Mercedes more dangerous than Porsches?
Type Total Accidents AR % RR
Porsche 1 000 300 30 1.5
Mercedes 1 000 200 20 Ref.
Total 2 000 500 25
95% CI = 1.3 - 1.8
Crude RR = 1.5Adjusted RR = 1.1 (0.94 - 1.27)
Car type Accidents
Confounding factor:Age of driver
Age Porsches Mercedes
< 25 years 550 (55%) 300 (30%)
>= 25 years 450 700
Chi2 = 127.9
Age Accidents No accidents< 25 years 370 (44%) 480
>= 25 years 130 (11%) 1020
Chi2 = 270.7
Exposure OutcomeHypercholesterolaemia Myocardial infarction
Third factorAtheroma
Any factor which is a necessary step in the causal chain is not a confounder
Salt Myocardial infarction
Hypertension
10 - 20 %
Any statistical test to help us?
When is ORMH different from crude OR ?
How to prevent/control confounding?
Prevention– Restriction to one stratum– Matching
Control– Stratified analysis– Multivariable analysis
Mantel-Haenszel summary measure
Adjusted or weighted RR or OR
Advantages of MH
• Zeroes allowed
OR MH = -------------------
kSUM (ai di / ni)
i=1
kSUM (bi cci / ni)
i=1
OR MH = -------------------
kSUM (ai di / ni)
i=1
kSUM (bi cci / ni)
i=1
Examples of stratified analysis
Effect modifierBelongs to natureDifferent effects in different strataSimpleUsefulIncreases knowledge of biological mechanismAllows targeting of PH action
Confounding factorBelongs to study
Weighted RR different from crude RRDistortion of effectCreates confusion in dataPrevent (protocol)
Control (analysis)
How to conduct a stratified analysis
Perform crude analysisMeasure the strength of association
List potential effect modifiers and confounders
Stratify data according topotential modifiers or confounders
Check for effect modification
If effect modification present, show the data by stratum
If no effect modification present, check for confoundingIf confounding, show adjusted dataIf no confounding, show crude data
How to define strata
In each stratum, third variable is no longer a confounder
Stratum of public health interest
If 2 risk factors, we stratify on the different levels of one of them to study the second
Residual confounding ?
Logical order of data analysis
How to deal with multiple risk factors:
Crude analysis
Multivariate analysis
1. stratified analysis
2. modelling
linear regression
logistic regression
A train can mask a second train
A variable can mask another variable
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