A general approach to detect gene (G)-environment (E) additive interaction leveraging G-E independence in case-control studies

It is increasingly of interest in statistical genetics to test for the presence of a mechanistic interaction between genetic (G) and environmental (E) risk factors by testing for the presence of an additive GxE interaction. In case-control studies involving a rare disease, a statistical test of no additive interaction typically entails a test of no relative excess risk due to interaction (RERI). It is also well known that a test of multiplicative interaction exploiting G-E independence can be dramatically more powerful than standard logistic regression for case-control data. Likewise, it has recently been shown that a likelihood ratio test of a null RERI incorporating the G-E independence assumption (RERI-LRT) outperforms the standard RERI approach. In this paper, the authors describe a general, yet relatively straightforward approach to test for GxE additive interaction exploiting G-E independence. The approach which relies on regression models for G and E is particularly attractive because, unlike the RERI-LRT, it allows the regression model for the binary outcome to remain unrestricted. Therefore, the new methodology is completely robust to possible mis-specification in the outcome regression. This is particularly important for settings not easily handled by RERI-LRT, such as when E is a count or a continuous exposure with multiple components, or when there are several auxiliary covariates in the regression model. While the proposed approach avoids fitting an outcome regression, it nonetheless still allows for straightforward covariate adjustment. The methods are illustrated through an extensive simulation study and an ovarian cancer empirical application.