Bias, Confounding, and Effect Modification within a Causal Framework

This chapter introduces the major sources of systematic error in epidemiological research and explains how they affect the validity of statistical estimates and causal conclusions. Students learn to distinguish bias from random error and explore three principal sources of distortion: confounding, selection bias, and information bias. Confounding occurs when another variable associated with both the exposure and the outcome distorts the observed association; selection bias arises when participant selection or retention depends on exposure or outcome status; and information bias results from systematic errors in measuring exposures, outcomes, or covariates. Using epidemiological examples, such as the relationship between coffee consumption and lung cancer confounded by smoking, the chapter demonstrates how these biases can produce misleading associations. It also introduces modern causal inference through the counterfactual framework, Y(a), which conceptualizes the potential outcome under a specified exposure condition, and explains causal estimands such as the Average Treatment Effect (ATE) and Average Treatment Effect on the Treated (ATT).

The second major focus is causal identification and the use of Directed Acyclic Graphs (DAGs) to formulate and evaluate causal relationships before conducting statistical analyses. Students examine the three fundamental identification assumptions: exchangeability, which requires comparability between exposure groups conditional on relevant covariates; positivity, which requires a positive probability of receiving each exposure level within relevant covariate strata; and consistency, which links observed outcomes to the corresponding potential outcomes under clearly defined exposure conditions. The chapter explains how DAGs represent causal pathways and help identify backdoor paths, confounders, mediators, and colliders. Students learn why controlling for appropriate confounders can reduce bias, whereas adjusting for mediators when estimating total effects may cause overadjustment, and conditioning on colliders may introduce spurious associations. The material further distinguishes confounding from mediation and effect modification, emphasizing that effect modification represents genuine heterogeneity in the exposure effect across population subgroups rather than a form of bias. It also discusses interaction on additive and multiplicative scales and introduces measures such as the Relative Excess Risk due to Interaction (RERI), Attributable Proportion due to Interaction (AP), and Synergy Index (S).

The final component addresses strategies for preventing, controlling, and evaluating bias through study design and statistical analysis. Students explore design-based approaches, including randomization, restriction, matching, standardized measurement procedures, blinding, instrument calibration, and participant-retention strategies. Analytical methods include stratification, the Mantel–Haenszel estimator, direct and indirect standardization, multivariable regression, propensity scores, and inverse probability weighting (IPW). The chapter also introduces instrumental variable methods, multiple imputation for missing data under the Missing at Random (MAR) assumption, quantitative bias analysis, and the E-value for evaluating the potential influence of unmeasured confounding. Particular emphasis is placed on selecting adjustment variables according to the underlying causal structure rather than relying solely on statistical significance. Through these concepts, Statistics students develop the ability to critically assess epidemiological evidence, construct and interpret causal diagrams, distinguish confounding from mediation and effect modification, and select appropriate methods for estimating causal effects. Overall, the chapter establishes that credible causal inference depends on clearly defined research questions, defensible causal assumptions, appropriate study designs, valid measurements, and statistically sound analytical strategies.