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
Case-control study of alcohol and
lung cancer
Alcohol No alcohol
Cases 450 300
Controls 200 250
Estimated odds ratio =1.9
The same data stratified by smoking:
Non-smokers Smokers
Alcohol No alcohol Alcohol No
alcohol
Cases 50 100 400 200
Controls 100 200 100 50
Estimated odds ratio 1.0 1.0
Alcohol and smoking in controls
Alcohol No alcohol
Smokers 100 50
Non-smokers 100 200
Non-drinkers: 1 in 5 were smokers,
Drinkers: 1 in 2 were smokers.
Confounding
Alcohol Lung cancer
Smoking
Most common confounders:
 Gender (men have higher mortality and more
risk factors)
 Age (risk of most diseases increases with age)
 Socioeconomic status (risk of most diseases
higher in lower SE groups)
 Ethnic group
 Smoking
 Alcohol
 etc...
Control of confounding
Design
 Randomisation
 Restriction
 Matching
Analysis (if data collected)
 Stratification
 Regression modelling
Residual confounding
 Unmeasured confounding factors or
measurement error in confounding
factors may lead to residual confounding.
 The possibility of residual confounding
cannot be completely eliminated in
observational studies.
Effect modification (interaction)
 the effect of exposure on disease is
dependent on the level of a third factor
Effect modification
Exposure Disease
Effect modifier
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
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)
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
Mantel-Haenszel pooled X2 and OR
 
 

iii
iii
ncb
nda
OR
/
/
. 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
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
Interpretation of results
 There is still an association between
smoking and cancer but less strong than
originally showed (in crude analysis)
 The confounding variable (drinking) made
the association between smoking and
cancer look stronger that it is.
 There is NO STATISTICAL TEST to help
you decide whether change in odds ratios
(1.63 to 1.43 in our example) is large
enough to say that variable is confounder.
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
Effect modification
 Third variable can be called EFFECT
MODIFIER
 Effect modification = interaction =
heterogeneity between strata
 Testing for effect modification – Kirkwood
and Sterne, 186-187
 We will look back to STATA output
. 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
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