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  1. Multiple papers have studied the use of gene‐environment (GE) independence to enhance power for testing gene‐environment interaction in case‐control studies. However, studies that evaluate the role ofGEindependence 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 ofGEindependence across studies. We use the retrospective likelihood framework to derive an adaptive combination of estimators obtained under the constrained model (assumingGEindependence) and unconstrained model (without assumptions ofGEindependence) with weights determined by measures ofGEassociation 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 relatedFTOgene and environmental factors body mass index and age.

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  2. Joint effects of genetic and environmental factors have been increasingly recognized in the development of many complex human diseases. Despite the popularity of case‐control and case‐only designs, longitudinal cohort studies that can capture time‐varying outcome and exposure information have long been recommended for gene–environment (G × E) interactions. To date, literature on sampling designs for longitudinal studies of G × E interaction is quite limited. We therefore consider designs that can prioritize a subsample of the existing cohort for retrospective genotyping on the basis of currently available outcome, exposure, and covariate data. In this work, we propose stratified sampling based on summaries of individual exposures and outcome trajectories and develop a full conditional likelihood approach for estimation that adjusts for the biased sample. We compare the performance of our proposed design and analysis with combinations of different sampling designs and estimation approaches via simulation. We observe that the full conditional likelihood provides improved estimates for the G × E interaction and joint exposure effects over uncorrected complete‐case analysis, and the exposure enriched outcome trajectory dependent design outperforms other designs in terms of estimation efficiency and power for detection of the G × E interaction. We also illustrate our design and analysis using data from the Normative Aging Study, an ongoing longitudinal cohort study initiated by the Veterans Administration in 1963. Copyright © 2017 John Wiley & Sons, Ltd.

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