Understanding interactions between risk factors, and assessing the utility of the additive and multiplicative models through simulations

Abstract

Interaction analysis is used to investigate the magnitude of an effect which two risk factors have on disease risk, and on each other. To study interactions, both additive and multiplicative models have been used, although their interpretations are not universally understood. In this study, we set out to investigate the resulting interactions of several risk factors relationships in additive or multiplicative scenarios using simulations, in the context of case-control studies. Our simulation set up showed that independent risk factors approach additive relative risk at low disease prevalence. However, risk factors that contribute to the same chain of events (i.e. have synergy) lead to multiplicative relative risk. Additionally, thresholds on the number of required risk factors for a disease (the multifactorial threshold model) lead to intermediaries between additive and multiplicative risks. We proposed a novel measure of interaction consistent with additive, multiplicative and multifactorial threshold models. Finally, we demonstrate the utility of the simulation strategy and discovered relationships on real data by analyzing and interpreting gene-gene odds ratios from a case-control rheumatoid arthritis study.