HPG 6104 • Epidemiological Methods II

Confounding & Effect Modification

Week 3 Student Companion Guide

What Is Confounding?

A confounder is a variable that distorts (inflates or deflates) the true association between an exposure and an outcome. To be a confounder, a variable must simultaneously satisfy three criteria:

Associated with Exposure

The confounder is distributed unequally between exposed and unexposed groups.

Independent Risk Factor

Affects the risk of the outcome over and above the effect of the exposure.

Not on Causal Pathway

It is not an intermediary step. The exposure does not cause the confounder.

The 10% Rule (Detecting Confounding)

A heuristic used to determine if a variable is a meaningful confounder:

| (Crude OR - Adjusted OR) | / Crude OR > 0.10

Example: If Crude OR = 5.09 and Adjusted OR = 5.42. The change is |5.09 - 5.42| / 5.09 = 6.5%. Because 6.5% < 10%, it is only mild confounding.

Confounding vs. Effect Modification

This is the most commonly confused point in epidemiology. One is a bias to be removed; the other is a biological/social reality to be reported.

Feature	Confounding (Bias)	Effect Modification (Finding)
What it is	A bias—the true association is distorted.	A real phenomenon—the effect genuinely differs between groups.
What to do	Adjust for it (regression or pool via M-H).	Report it! Present stratum-specific estimates.
OR across strata	Similar within strata (homogeneous).	Differs significantly across strata (heterogeneous).
Statistical Test	Compare crude vs. adjusted OR (10% rule).	Interaction term p-value (e.g., p < 0.05).

Controlling for Confounding

Study Design Approaches

Randomization: The gold standard (RCTs). Balances both measured and unmeasured confounders.
Restriction: Limit the study to one stratum (e.g., only non-smokers). Simple, but reduces generalisability.
Matching: Pair cases and controls on confounder values. Controls it, but requires complex matched analysis (and prevents studying the matched variable).

Data Analysis Approaches

Stratification: Compute stratum-specific estimates (Mantel-Haenszel pooling). Best for 1 or 2 categorical confounders.
Multivariable Regression: Include confounders as covariates. Can handle many simultaneously.
Propensity Scores: Model probability of exposure. Used in large observational studies. Cannot fix unmeasured confounding.

R Code Quick Reference

# 1. Crude OR (No adjustment)
m_crude <- glm(LungCa ~ Smoking, data=df, family=binomial)
exp(coef(m_crude))

# 2. Adjusted OR (Controlling for Confounder 'OccExp')
m_adj <- glm(LungCa ~ Smoking + OccExp, data=df, family=binomial)
exp(coef(m_adj))

# 3. Testing Effect Modification (Interaction Term)
m_int <- glm(LungCa ~ Smoking * AgeGrp, data=df, family=binomial)
summary(m_int) # Look at the 'Smoking:AgeGrp' p-value row