Abstract
Multiple papers have studied the use of gene-environment (G-E) independence to enhance power for testing gene-environment interaction in case-control studies. However, studies that evaluate the role of G-E independence in a meta-analysis framework are limited. In this paper, we extend the single-study empirical Bayes type shrinkage estimators proposed by Mukherjee and Chatterjee (2008) to a meta-analysis setting that adjusts for uncertainty regarding the assumption of G-E independence across studies. We use the retrospective likelihood framework to derive an adaptive combination of estimators obtained under the constrained model (assuming G-E independence) and unconstrained model (without assumptions of G-E independence) with weights determined by measures of G-E association derived from multiple studies. Our simulation studies indicate that this newly proposed estimator has improved average performance across different simulation scenarios than the standard alternative of using inverse variance (covariance) weighted estimators that combines study-specific constrained, unconstrained, or empirical Bayes estimators. The results are illustrated by meta-analyzing 6 different studies of type 2 diabetes investigating interactions between genetic markers on the obesity related FTO gene and environmental factors body mass index and age.