Attributing Effects to Interactions

A framework is presented that allows an investigator to estimate the portion of the effect of one exposure that is attributable to an interaction with a second exposure. We show that when the 2 exposures are statistically independent in distribution, the total effect of one exposure can be decomposed into a conditional effect of that exposure when the second is absent and also a component due to interaction. The decomposition applies on difference or ratio scales. We discuss how the components can be estimated using standard regression models, and how these components can be used to evaluate the proportion of the total effect of the primary exposure attributable to the interaction with the second exposure. In the setting in which one of the exposures affects the other, so that the 2 are no longer statistically independent in distribution, alternative decompositions are discussed. The various decompositions are illustrated with an example in genetic epidemiology. If it is not possible to intervene on the primary exposure of interest, the methods described in this article can help investigators to identify other variables that, if intervened upon, would eliminate the largest proportion of the effect of the primary exposure.