Testing for Sufficient-Cause Interactions in Case-Control Studies of Non-Rare Diseases

Sufficient-cause interaction (also called mechanistic interaction or causal co-action) has received considerable attention recently. Two statistical tests, the 'relative excess risk due to interaction' (RERI) test and the 'peril ratio index of synergy based on multiplicativity' (PRISM) test, were developed specifically to test such an interaction in cohort studies. In addition, these two tests can be applied in case-control studies for rare diseases but are not valid for non-rare diseases. In this study, we proposed a method to incorporate the information of disease prevalence to estimate the perils of particular diseases. Moreover, we adopted the PRISM test to assess the sufficient-cause interaction in case-control studies for non-rare diseases. The Monte Carlo simulation showed that our proposed method can maintain reasonably accurate type I error rates in all situations. Its powers are comparable to the odds-scale PRISM test and far greater than the risk-scale RERI test and the odds-scale RERI test. In light of its desirable statistical properties, we recommend using the proposed method to test for sufficient-cause interactions between two binary exposures in case-control studies.