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Exploiting gene-environment independence for analysis of case-control studies: an empirical Bayes-type shrinkage estimator to trade-off between bias and efficiency.
Pubmed ID
18162111 (View this publication on the PubMed website)
Biometrics. 2008 Sep; Volume 64 (Issue 3): Pages 685-94
Mukherjee B, Chatterjee N
  • Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. email:
  • Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Department of Health and Human Services, Rockville, Maryland 20852, U.S.A. email:

Standard prospective logistic regression analysis of case-control data often leads to very imprecise estimates of gene-environment interactions due to small numbers of cases or controls in cells of crossing genotype and exposure. In contrast, under the assumption of gene-environment independence, modern "retrospective" methods, including the "case-only" approach, can estimate the interaction parameters much more precisely, but they can be seriously biased when the underlying assumption of gene-environment independence is violated. In this article, we propose a novel empirical Bayes-type shrinkage estimator to analyze case-control data that can relax the gene-environment independence assumption in a data-adaptive fashion. In the special case, involving a binary gene and a binary exposure, the method leads to an estimator of the interaction log odds ratio parameter in a simple closed form that corresponds to an weighted average of the standard case-only and case-control estimators. We also describe a general approach for deriving the new shrinkage estimator and its variance within the retrospective maximum-likelihood framework developed by Chatterjee and Carroll (2005, Biometrika92, 399-418). Both simulated and real data examples suggest that the proposed estimator strikes a balance between bias and efficiency depending on the true nature of the gene-environment association and the sample size for a given study.

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