Effect Modification and Interaction

Abstract

This article discusses definitions and concepts of effect modification, interaction, synergism, and related concepts and terms. The term effect modification has been applied to two distinct phenomena. For the first phenomenon, effect modification simply means that some chosen measure of effect varies across levels of background variables. This phenomenon is thus more precisely termed effect-measure modification, and in the statistics literature is more often termed heterogeneity or interaction [1]. For the second phenomenon, effect modification means that the mechanism of effect differs with background variables, which is known in the biomedical literature as dependent action or (again) interaction. The two phenomena are often confused, as reflected by the use of the same terms (effect modification and interaction) for both. In fact they have only limited points of contact. 1 Effect-Measure Modification (Heterogeneity of Effect) To make the concepts and distinctions precise, suppose we are studying the effects that change in a variable X will have on a subsequent variable Y, in the presence of a background variable Z that precedes X and Y. For example, X might be treatment level such as dose or treatment arm, Y might be a health outcome variable such as life expectancy following treatment, and Z might be sex (1 = female, 0 = male). To measure effects, write Y x for the outcome one would have if administered treatment level x of X; for example, if X = 1 for active treatment, X = 0 for placebo, then Y 1 is the outcome a subject will have if X = 1 is administered, and Y 0 is the outcome a subject will have if X = 0 is administered. The Y x are often called potential outcomes (see Causality/Causation). One measure of the effect of changing X from 0 to 1 on the outcome is the difference Y 1 − Y 0 ; for example, if Y were life expectancy, Y 1 − Y 0 would be the change in life expectancy. If this difference varied with sex in a systematic fashion, one could say that the difference was modified by sex, or that there was