  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.
