There have been recent proposals advocating the use of additive gene-environment interaction instead of the widely used multiplicative scale, as a more relevant public health measure. Using gene-environment independence enhances the power for testing multiplicative interaction in case-control studies. However, under departure from this assumption, substantial bias in the estimates and inflated Type I error in the corresponding tests can occur. This paper extends the empirical Bayes (EB) approach previously developed for multiplicative interaction that trades off between bias and efficiency in a data-adaptive way, to the additive scale. An EB estimator of Relative Excess Risk due to Interaction is derived and the corresponding Wald test is proposed with general regression setting under a retrospective likelihood framework. We study the impact of gene-environment association on the resultant test with case-control data. Our simulation studies suggest that the EB approach uses the gene-environment independence assumption in a data-adaptive way and provides power gain compared to the standard logistic regression analysis and better control of Type I error when compared to the analysis assuming gene-environment independence. We illustrate the methods with data from the Ovarian Cancer Association Consortium.
