Applicability of the simple independent action model to epidemiologic studies involving two factors and a dichotomous outcome.

In epidemiologic case-control studies and occupational cohort studies involving more than one exposure, it is sometimes of interest to investigate the possibility that two exposures or factors have an effect that is mutually enhancing. This paper begins with a simple classic model for independence of effect and describes how this model can be applied to cohort and case-control studies. A ratio index, borrowed from the toxicologic literature, can be used to quantify departures from this null model for prospective cohort studies. Models additive in log nonresponse are appropriate in this context. Proper stratification will remove confounding effects, although the possibility that covarying susceptibilities among individuals in the population are masking or producing the appearance of synergy remains. However, under a generalized null model that requires simple independent action for each individual, but allows the response probabilities to vary among individuals, the population-based ratio parameter may not be one but should lie in a specified interval. In a case-control setting, the simple independent action model implies that the ratio of the bivariate exposure distribution for cases, divided by that for controls, should be additive in functions of the exposure levels, generalizing an earlier result. The index takes a different form when one of the factors is preventive rather than causal, and in this context, models additive in log risk become appropriate. An example is provided, and difficulties in interpretation are discussed.