A competing risks approach to “biologic” interaction

In epidemiology, the concepts of “biologic” and “statistical” interactions have been the subject of extensive debate. We present a new approach to biologic interaction based on Rothman’s original (Am J Epidemiol, 104:587–592, 1976) discussion of sufficient causes. We do this in a probabilistic framework using competing risks and argue that sufficient cause interaction between two factors can be evaluated via the parameters in a particular statistical model, the additive hazard rate model. We present empirical conditions for presence of sufficient cause interaction and an example based on data from a liver cirrhosis trial illustrates the ideas.