Confounding and Effect Modification: Distribution and Measure

Abstract The paper considers the properties of and relations between confounding and effect modification from the perspective of causal inference and with a distinction drawn as to how each of these two epidemiologic concepts can be defined both with respect to a distribution of potential outcomes or with respect to a specific effect measure. Both concepts are conditional on other covariates but the form this conditionality takes differs. Both concepts are also properties of the population, and both are relative to the specific exposure and to the specific outcome. For a particular population, the presence of confounding depends on how the exposure was assigned; the presence of effect modification does not. The possibility of confounding without effect modification and vice versa is discussed both with respect to distribution and measure. Discussion is given as to how confounding and effect modification relate to statistical models and to the relevance of the points made in the paper to data analysis and interpretation.