Confounding
&
Effect modification
E2040: Introduction to Epidemiology and Environmental Health
2024
Three major issues in alternative
interpretation of observed association:
• Chance (random variation)
• Bias
• Confounding
What is confounding?
• Another factor (alternative explanation) might be causing an observed
association: confounding
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
Alcohol No alcohol
Cases 50 100
Controls 100 200
Estimated odds ratio 1.0
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
More explanations of confounding
• Confounding refers to a situation in which a non-causal association
between a given exposure and outcome is observed due to the
influence of a third variable, usually referred to as a confounder.
“Confounding is confusion, or mixing, of effects; the effect of the
exposure is mixed together with the effect of another variable, leading
to bias”
-Rothman, 2002
Common
confounders
• Sex (men have higher mortality and more risk
factors)
• Age (risk of most chronic diseases increases
with age)
• Socioeconomic status (more lifestyle and
behavioral risk factors, poorer healthcare access
at lower SES)
• Ethnic group (less healthcare access, higher
environmental exposures, more discrimination
among under-represented groups)
• Smoking
• Alcohol consumption
• Etc.
Another example – birth order and Down Syndrome
Maternal age confounds the relationship between birth order and Down Syndrome
Stark CR & Mantel N. Effects of maternal age and birth order on the risk of mongolism and leukemia. J Natl Cancer Inst. 1966; 37: 687-98.
A variable must meet three criteria to be a confounder
1. Must be associated with the exposure
• Maternal age is associated with birth order
2. Must be associated with the outcome
• Maternal age is a known risk factor for Down Syndrome
3. Must not be on the causal pathway between exposure and outcome
• Birth order does not cause maternal age
Down Syndrome
Down Syndrome
x
Solving problems at different stages
• At the stage of design
• Randomization in RCTs helps reduce confounding by observed and
unobserved factors
• Restriction
• Matching
• At the analysis stage
• Stratification
• Adjustment – add potential confounders to statistical models to control their
influence on outcome
Design stage
Randomization helps distribute confounders
among experimental groups
Condition A Condition B
• If there are enough participants, we hope that randomization will increase the likelihood that the groups will be
comparable on characteristics about which we may be concerned (such as sex, age, race, and severity of disease).
Restriction
• Restricting entry into the study to individuals who have the same value for a
particular variable
• E.g., Restricting study entry to non-smokers
• E.g., Restricting study entry to women only
• Very effective method for preventing confounding in any type of study design,
though has important implications for generalizability of results.
Eligibility criterion
Matching
Select variables that could
act as confounders
1
Create matched pairs or groups
of participants (cases & controls)
similar on those variables
2
Conduct study/analysis on
pairs/groups
3
25-30 31-35 36-40 41-45
Down Syndrome
Analysis stage
First, detect if confounding is present
Crude effect estimate
Does not account for any confounding variable(s)
Adjusted effect estimate
Accounts for confounding variable(s)/potentially confounding
variables
Empirical assessment of confounding:
Crude effect estimate ≠ Adjusted effect estimate
Stratification
The objective of stratified analysis is to set the level of the confounding
variable and produce groups within which the confounder does not vary
Then, we evaluate the exposure-disease relationship within each stratum of
the confounder
? ?
Yes No
There are limits to stratification
• Can only stratify on categorical variables
• Numerous strata can be problematic
• Sparse data and imprecise estimates
• Impractical to adjust for multiple confounding variables
• Controlling for age and gender, if gender is measured with 2 categories
and age is measured with 5, end up with 10 strata
Standardization
• A statistical approach to remove confounding by a common
characteristic
• Age
• Sex
• Marital status
• Education
• The most common standardization is carried out for mortality or
disease incidence rates for age & sex
• Over time
• Across countries/geographical areas
What do you
observe about
crude and agestandardized
rates
of DM in China?
Another example—compare all-cause mortality between
Sweden & Panama
Another example—compare all-cause mortality between
Sweden & Panama
How can this be?
Another example—compare all-cause mortality between
Sweden & Panama
How can this be?
Sweden has an older population (17% vs. 5% of people older than 60 years) and mortality
increases with age.
Adjustment
• If the number of potential confounders is
large, multivariate analyses (regression
analysis) offer the only real solution
• Can handle several confounders
simultaneously
• Uses statistical regression models
• Always done with statistical software (SAS,
Stata, R)
Residual confounding
• Unmeasured confounders or error in the measurement of observed
confounders may lead to “residual” confounding
• Confounding remains or is imperfectly accounted for
• Possibility of residual confounding cannot be completely eliminated in
observational studies
Effect modification
When are we concerned with an interaction?
• When we have TWO exposures we are interested in and want to see if the
joint effect of these two exposures on the outcome differs from the effect
of either exposure independently
• E.g., Drinking and driving are independent causes for injury, but together
they increase the risk more than either exposure independently
• Synergistic – effect of the two is more potent than either one alone
• Antagonistic – effect of one is diminished by the other
Factor 1
Factor 2
Identifying interactions – what is the combined effect
of factors A & Z on outcome Y?
• Interaction = joint effect of two exposures
• When the rate of disease in the presence of two or more risk factors
differs from the rate expected to result from their individual effects.
• Positive interaction: The effect of two risk factors combined is greater
than what we would expect (also called synergism)
• Negative interaction: The effect of two risk factors combined is less
than what we would expect from either risk factor independently (also
called antagonism).
Effect measure modification (EMM) is a similar concept
• We are concerned with EMM when we have an exposure and
outcome and wish to examine whether the relationship between the
two differs by levels (strata) of a third variable
• Effect modification occurs when the effect of a risk factor (X) on an
outcome (Y) differs in strata formed by a third variable (Z)
• Effect of exposure on disease is modified depending on the value of a
third variable called an “effect modifier”
• Effect measure (e.g., risk difference, risk ratio) differs across different
levels/strata of the third variable
Effect measure modification (EMM)
+ Predisposing gene
- Predisposing gene
Example of EMM
Women Men
1.0
1.5
2.0
2.5
0.5 <60 y ⩾60 y <60 y ⩾60 y
Jakobsen MU et al. Dietary fat and risk of coronary heart disease: possible effect modification by gender and age. American Journal of Epidemiology 2004; 160: 141-9.
HazardRatio(HR)ofcoronaryheart
diseaserelatedtototalfatintake
Other examples of effect modification
• Example 2
• Exposure to the antibiotic tetracycline
is related to the discoloration of teeth
• This discoloration occurs when
children up to 8 years of age take
tetracycline
• Discoloration is not observed when
adults take tetracycline
• Example 3
• Individuals exposed to the measles
virus will develop measles
infection
• Unless they have prior history of
measles
• Unless they have been vaccinated
Notation in epidemiology to represent EMM
Exposure Disease Exposure Disease
Going back to our examples
• Example 1
• Age is the effect-modifier
Antibiotic Tooth color
Age
• Example 2
• Immune status is the effect-modifier
Virus Measles
Immune protection
Stratification aids
in understanding
interaction/ EMM
• Stratification is essential to
understanding interaction and
EMM
• Creating 2x2 tables (“crosstabulating”)
for the exposuredisease
relationship by
categories of another variable
• E.g., young/old, smokers/nonsmokers
Yes No
Yes No
Yes No
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.
42
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
How does interaction/EMM differ from confounding?
• Confounding
• An alternative explanation for
observed relationship
• Distorts the “truth”
• Epi attempts to remove it to get
nearer to the truth
• When it is present, stratumspecific
effects are similar to each
other but different from overall
crude effect
• Interaction / EMM
• One effect modifies the effect of
another factor
• It is genuine, not an artefact
• Property of the relationship
between factors
• We should detect and describe it
but not remove it.
Interaction vs. confounding
Let’s work through an example
Question: Does fat consumption modify the association between smoking and
the risk of myocardial infarction (heart attack)?
Smoking status Heart Attack No Heart Attack Total
Smokers 42 158 200
Non-Smokers 21 175 196
Total 63 333 396
Calculate the Odds Ratio (OR), what is it?
Step 1: calculate crude measure of association
Let’s work through an example
Smoking status Heart Attack No Heart Attack Total
Smokers a=42 b=158 200
Non-Smokers c=21 d=175 196
Total 63 333 396
𝑂𝑅 =
𝑎𝑑
𝑏𝑐
𝑂𝑅 = 2.22 [95% 𝐶𝐼: 1.26, 3.91]
Let’s work through an example
Question: Does fat consumption modify the association between smoking and
the risk of myocardial infarction (heart attack)?
Smoking + Heart
Attack
- Heart
Attack
Total
Smokers 12 133 145
Non-Smokers 11 123 134
Total 23 256 279
Step 2: calculate associations within strata
1: Dietary fat intake <30% of calories 2: Dietary fat intake >30% of calories
Smoking + Heart
Attack
- Heart
Attack
Total
Smokers 30 25 55
Non-Smokers 10 52 62
Total 40 77 117
1.01 [95% 𝐶𝐼: 0.43, 2.37] 6.29 [95% 𝐶𝐼: 2.64, 14.75]
What does this mean?
Crude OR = 2.22
Stratum specific ORs
Dietary fat <30% = 1.01 (0.43, 2.37)
Dietary fat >30% = 6.29 (2.64, 14.75)
Is there effect measure modification? Is there confounding?
https://sph.unc.edu/wp-content/uploads/sites/112/2015/07/nciph_ERIC12.pdf
Heterogeneity vs. homogeneity of effects
When effect estimates are different in strata of the potential effect
modifier → heterogeneity is present
Strata 1: OR=1.8
Strata 2: OR=5.7
When effect estimates are similar in strata of the potential effect modifier
→ homogenous effect estimates
Strata 1: OR=2.3
Strata 2: OR=2.5
What have we learnt today?
• Principle of confounding
• Principles of effect modification
• Step-by-step method of tidentifying confounding and effect
modification by stratification
• Interpretation of results involving confounding and effect
modification