Effect modification and
stratification
Last session - confounding
 Situation when a third factor is associated
with both exposure and disease
 Association between exposure and
disease may not be causal; instead, it is
due to a third factor which is associated
with both exposure and disease.
Confounding
Exposure Disease
Confounding
factor
Confounding
Alcohol Lung cancer
Smoking
Effect modification (interaction)
 the effect of exposure on disease is
dependent on the level of a third factor
Effect modification
Exposure Disease
Effect modifier
Biological Interaction
Last’s Dictionary of Epidemiology (4th Ed)
Biological interaction is the interdependent
operation of two or more causes to produce,
prevent or control disease
Factor 1
+ Factor 2 Outcome
7
Examples of biological interaction
1. Antibiotic tetracycline and tooth
discolouration
• Tetracycline is associated with discoloration of
teeth but mainly among children <8 years
• effect of antibiotic (exposure) on tooth colour
(outcome) is modified by age (effect modifier)
8
Examples of biological interaction
2. Measles and vaccination
• Exposure to measles virus is
associated with measles infection if
not vaccinated or has not had
measles
• Here immune status = effect
modifier
9
Statistical interaction
when the association between exposure and
outcome of interest varies according to the
level of a third factor (the effect modifier)
Exposure Outcome
10
Effect modifier (the 3rd factor)
Examples of statistical interaction
1. Energy from total fat and coronary heart disease
(CHD)
Energy from total fat is associated with CHD among younger women (HR=2.68,
95%CI 1.40,5.12) but not among older women (HR=1.22, 95%CI 0.86,1.71)
(Source: Jakobsen et al.Am J Epidemiol. 2004)
11
2. Effort Reward Imbalance (ERI)
and depressive symptoms among
children (China)
School-related stress (ERI school questionnaire)
is associated with depressive symptoms among
low SES children compared to high SES children
(Source: Guo et al. Int J Environ Res Public Health.
2014)
CHD, smoking and age in British
doctors study (rates per 100,000)
Non-smokers Heavy smokers
Rate Rate RR
<45 7 104 14.9
45-54 118 393 3.3
55-64 531 1025 1.9
Positive and negative effect
modification
 Positive:
◦ “susceptibility factor” or “vulnerability factor”,
◦ its presence (or higher values) strengthens the
association between exposure and disease.
 Negative:
◦ “resiliency factor” or “buffering factor”
◦ its presence (or higher values) weakens the
association between exposure and disease
CHD, smoking and age in British
doctors study (rates per 100,000)
Non-smokers Heavy smokers
Rate Rate RR
<45 7 104 14.9
45-54 118 393 3.3
55-64 531 1025 1.9
Reciprocal nature of effect
modification
• For any given outcome and two predictor variables, it is a purely
arbitrary decision which predictor variable will be the exposure,
and which the potential effect modifier.
• Effect modification is reciprocal. In any of examples, the
exposure and other factor (or variable) could have be labelled
the other way round, and the same effect would still have been
seen.
15
CHD, smoking and age in British
doctors study (rates per 100,000)
Non-smokers Heavy smokers
Rate Rate RR
<45 7 104 14.9
45-54 118 393 3.3
55-64 531 1025 1.9
CHD, smoking and age in British
doctors study (rates per 100,000)
Non-smokers Heavy smokers
Rate Rate
<45 7 104
45-54 118 393
55-64 531 1025
RR 75.9 9.9
Identification of effect modification
 Stratified analysis
 Compare effect estimates in strata
 Assess differences in effects by significance
tests (p-value for heterogeneity)
 Pooled estimates (e.g. standardised) not
appropriate when there is an interaction
Confounding vs. interaction
Confounding
 Alternative explanation
 Distorts the “truth”
 Efforts to remove it to get
nearer to the “truth”
 When present, stratum
specific effects are similar to
each other but different from
the overall crude effect.
Effect modification
 One factor modifies effect of
another factor
 It is genuine, not artefact
 Property of the relationship
between factors
 We should detect and
describe it but not remove it.
Example: Height and IQ – real
association or not?
Height
Gender
IQ
• High negative association between height and IQ
Height and IQ
Height
Gender
IQ
• Find out that Gender is related to Height and that Gender
is related to IQ
• Therefore, Gender is a potential confounder
Women are
Shorter
Women have
higher IQ’s
Height and IQ
Height
Gender
IQ
• If after adjustment for Gender there is NO association
between height and IQ, then Gender was a confounder
Women are
Shorter
Women have
higher IQ’s
Height and IQ
Height
Gender
IQ
• If after adjustment for Gender there is still a strong
negative association between Height and IQ, then
Gender is not a confounder
Women are
Shorter
Women have
higher IQ’s
Height and IQ
Height
Gender
IQ
• If after adjustment for Gender there is still an association
between Height and IQ, but the nature and/or strength of
the association changes with Gender, then Gender is an
Effect Modifier.
Women are
Shorter
Women have
higher IQ’s
Height and IQ
Height
Gender
IQ
• If there is no association between Gender and IQ, then
Gender cannot be a confounder
• Likewise, if gender is not associated with height, then
Gender cannot be a confounder
• The confounder must be related to both the cause and
the effect
Women are
Shorter
Women have
higher IQ’s
Step-by-step guide to the stratified
analysis
Example
 A study was undertaken to assess whether
smokingh increased risk of stomach cancer.
Data were collected from 36,000 individuals
Stomach cancer
Yes No Total
Smokers 800 (4.0%) 19200 20000
Non-smokers 400 (2.5%) 15600 16000
Total 1200 34800 36000
Example
 X2=62.07 p<0.001
Odds(low) 800/19200
OR = ----------- = ------------ = 1.63
Odds(high) 400/15600
 95% CI = 1.44-1.84 (Stata)
 The study found a significantly higher odds
of cancer in smokers
But is it real association?
 Smokers are more likely to be drinkers
 Drinking doubles the risk of stomach
cancer
 THEREFORE some of the higher risk in
smokers could be because they tend to
drink more frequently (and have higher risk
because of drinking).
?
Smoking Stomach cancer
Alcohol
?
Confounding
 We say that alcohol is a confounding
variable because it is related both to the
outcome variable and to exposure
(smoking)
 Ignoring alcohol in the analysis leads to
misleading results
INDIVIDUALS
Drinkers
Non-drinkers
Test association between
smoking and cancer
X2 and OR
Test association between
smoking and cancer
X2 and OR
Pool these if OR similar across strata
= Mantel-Haenszel pooled X2 and OR
Example
DRINKERS Stomach cancer
Yes No Total
Smokers 140 6000 6140
Non-smokers 130 7800 7930
Total 270 13800 14070
DRINKERS Stomach cancer
Yes No Total
Smokers 660 13200 13860
Non-smokers 270 7800 8070
Total 930 21000 21930
Example
NON-DRINKERS Stomach cancer
Yes No Total
Smokers 140 (2.28%) 6000 6140
Non-smokers 130 (1.64%) 7800 7930
Total 270 13800 14070
DRINKERS Stomach cancer
Yes No Total
Smokers 660 (4.76%) 13200 13860
Non-smokers 270 (3.35%) 7800 8070
Total 930 21000 21930
Stratum specific calculations
NON-DRINKERS
X2=7.55 p=0.006
OR (95% CI) = 1.40 (1.09-1.79)
DRINKERS:
X2=25.19 p<0.001
OR (95% CI) = 1.44 (1.25-1.67)
 Stratum specific OR are lower than the
crude OR (1.44 and 1.40 vs 1.63)
 Stratum specif OR are similar to each other
 This means that it is logical and sensible to
pool them
 If they are different (very different) – we
should consider drinking to be an EFFECT
MODIFIER (the effect of smoking on cancer
is modified by drinking status)
Effect modification
 We still need to check one important aspect of M-H
analysis – we make the assumption that the
association between exposure and the outcome is
the same in each level of confounding factor
 If this is NOT true, then you cannot combine stratum
specific ORs into one pooled estimate
 If the exposure-outcome association varies in
different levels of third variable we say that such third
variable modifies the effect of exp on outcome
Steps for dealing with possible
confounders
1. Calculate crude X2 and OR – DONE (X2
signif. and OR calculated)
2. List possible confounders – we have chosen
alcohol in our example
3. Determine whether they are possible
confounders
a. Association with exposure
b. Association with outcome
c. Not on causal pathway
4. Do stratified analysis by possible
confounder
5. Calculate pooled X2 and OR (= look at
the association that is adjusted for
confounder)
6. If crude OR and pooled OR different –
conclude that variable is a confounder
Steps for dealing with possible
confounders
. mhodds cancer smok, by(drink)
Maximum likelihood estimate of the odds ratio
Comparing smok==2 vs. smok==1
by drink
-------------------------------------------------------------------------
drink | Odds Ratio chi2(1) P>chi2 [95% Conf. Interval]
----------+--------------------------------------------------------------
1 | 1.444444 25.19 0.0000 1.25020 1.66886
2 | 1.400000 7.55 0.0060 1.10001 1.78181
-------------------------------------------------------------------------
Mantel-Haenszel estimate controlling for drink
----------------------------------------------------------------
Odds Ratio chi2(1) P>chi2 [95% Conf. Interval]
----------------------------------------------------------------
1.433140 32.73 0.0000 1.266074 1.622251
----------------------------------------------------------------
Test of homogeneity of ORs (approx): chi2(1) = 0.05
Pr>chi2 = 0.8274
. mhodds cancer smok, by(drink)
Maximum likelihood estimate of the odds ratio
Comparing smok==2 vs. smok==1
by drink
-------------------------------------------------------------------------
drink | Odds Ratio chi2(1) P>chi2 [95% Conf. Interval]
----------+--------------------------------------------------------------
1 | 1.444444 25.19 0.0000 1.25020 1.66886
2 | 1.400000 7.55 0.0060 1.10001 1.78181
-------------------------------------------------------------------------
Mantel-Haenszel estimate controlling for drink
----------------------------------------------------------------
Odds Ratio chi2(1) P>chi2 [95% Conf. Interval]
----------------------------------------------------------------
1.433140 32.73 0.0000 1.266074 1.622251
----------------------------------------------------------------
Test of homogeneity of ORs (approx): chi2(1) = 0.05
Pr>chi2 = 0.8274
Example
 STATA = test of homogeneity (NULL
hypothesis is that stratum specific ORs are
homogenous)
 Our example – test of homogeneity: p=0.83
 We can assume that stratum specific
estimates are same or similar and we can
use pooled estimate
Summary of results
 Results are best summarized in the table
Association
between smoking
and cancer
OR P-value Conclusion
Crude assoc. 1.63 <0.001 Odds of cancer 1.63 times higher
if smoker
Stratified anal.
Drinkers 1.44 <0.001 Odds of cancer 1.44 times higher
if smoker
Non-drinkers 1.40 0.006 Odds of cancer 1.40 times higher
if smoker
Adjusted for
drinking
1.43 <0.001 Confounded. Odds of cancer 1.43
times higher rather than 1.63
times higher if smoker
When is effect modification important?
 If we find that stratum specific odds ratios are
not homogenous (p-value for test of
homogeneity <0.05) we cannot report pooled
estiamte
 We need to report stratum specific results!
 Test for homogeneity has low power; → a
large p-value does not establish the absence of
effect modification. Small p-value however
suggest that effect modification is substantial
How to examine effect modification
 Always examine stratum specific odds ratios
– how different do they look?
 If there is clear evidence of effect
modification, report the exp-outcome
association separately for each stratum
 If there is moderate evidence of effect
modification, report both M-H OR and
stratum specific OR
 If no evidence of effect modification, use MH
OR
Stratification on more than one
confounding variable
 Possible
 Combine categories of confounding variables
and create strata from all possible
combinations
 Problem – number of strata increases fast (for
example 3 dichotomous variables = 2x2x2=8
strata)
 We may use other techniques, such as logistic
regression