1. Analytical epidemiology
Disease frequency
Study design: cohorts & case control
Choice of a reference group
Biases
Impact
Causal inference
Stratification
- Effect modification - Confounding
Matching
Significance testing
Multivariable analysis
Alain Moren, 2006

2. Exposure Outcome
Third variable

3. Two main complications
(1) Effect modifier
(2) Confounding factor
- useful information
- bias

4. 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

5. Effect modifier
Variation in the magnitude of measure of effect across levels of a third variable.
Effect modification is not a bias but useful information
Happens when RR or OR is different between strata (subgroups of population)

6. Effect modifier To identify a subgroup with a lower or higher risk
To target public health action
To study interaction between risk factors

7. Vaccine efficacy AR NV - AR V VE = ----------------------------- AR NV
VE = RR

8. Vaccine efficacy
VE = RR =
VE = 72%

9. Vaccine efficacy by age group

10. Effect modification
Different effects (RR) in different strata (age groups)
VE is modified by age
Test for homogeneity among strata (Woolf test)

11. Oral contraceptives (OC) and myocardial infarction (MI)
Case-control study, unstratified data
OC MI Controls OR
Yes
No Ref.
Total

13. Physical activity and MI

15. Effect function Effect (OR or RR) is a function of the effect modifier
Relative risk (RR) of dying from coronary heart disease
for smoking physicians, by age groups, England & Wales, RR 6 * 5 4 3 * 2 * * 1 * 10 20 30 40 50 60 70 80
Age
Doll et Hill, 1966

16. Any statistical test to help us?
Breslow-Day
Woolf test
Test for trends: Chi square
Heterogeneity

17. Confounding Distortion of measure of effect because of a third factor
Should be prevented
Needs to be controlled for

18. Simpson’s paradox

19. Second table

20. Day 2, one table only

23. Birth
order
Down
syndrom
Age or
mother

25. Confounding Exposure Outcome Third variable
To be a confounding factor, 2 conditions must be met:
Exposure
Outcome
Third variable
Be associated with exposure
- without being the consequence of exposure
Be associated with outcome
- independently of exposure

26. To identify confounding
Compare crude measure of effect (RR or OR) to
adjusted (weighted) measure of effect
(Mantel Haenszel RR or OR)

27. Are Mercedes more dangerous than Porsches?
95% CI =

28. Crude RR = 1.5
Adjusted RR = 1.1 ( )

29. Car type Accidents
Confounding factor:
Age of driver

30. Age Porsches Mercedes
< 25 years 550 (55%) 300 (30%)
>= 25 years
Chi2 = 127.9
Age Accidents No accidents
< 25 years 370 (44%) 480
>= 25 years 130 (11%) 1020
Chi2 = 270.7

31. Exposure Outcome Third factor
Hypercholesterolaemia Myocardial infarction
Third factor
Atheroma
Any factor which is a necessary step in the causal chain is not a confounder

32. Salt Myocardial infarction
Hypertension

33. Any statistical test to help us?
When is ORMH different from crude OR ? %

34. How to prevent/control confounding?
Prevention
Restriction to one stratum
Matching
Control
Stratified analysis
Multivariable analysis

35. Mantel-Haenszel summary measure
Adjusted or weighted RR or OR
Advantages of MH
Zeroes allowed
OR MH = k
SUM (ai di / ni)
i=1
SUM (bi cci / ni)

36. OR MH = -------------------k
SUM (ai di / ni)
i=1
SUM (bi cci / ni)

37. Examples of stratified analysis

38. Weighted RR different from crude RR
Effect modifier
Belongs to nature
Different effects in different strata
Simple
Useful
Increases knowledge of biological mechanism
Allows targeting of PH action
Confounding factor
Belongs to study
Weighted RR different from crude RR
Distortion of effect
Creates confusion in data
Prevent (protocol)
Control (analysis)

39. How to conduct a stratified analysis
Perform crude analysis Measure the strength of association
List potential effect modifiers and confounders
Stratify data according to potential modifiers or confounders
Check for effect modification
If effect modification present, show the data by stratum
If no effect modification present, check for confounding If confounding, show adjusted data If no confounding, show crude data

40. 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 ?

41. 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

42. A train can mask a second train
A variable can mask another variable

44. What happened? Hat % Fitting Colour
Blue and red hats not evenly distributed between the 2 tables table I, 33 % blue table II, 66 % blue
Hat fitting higher in Table I (83%) vs table II (13%)
Tables