Exploiting gene-environment independence for analysis of case-control studies: an empirical Bayes-type shrinkage estimator to trade-off between bias and efficiency.
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.
Mukherjee
Bhramar
B
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. email: bhramar@umich.edu.
Chatterjee
Nilanjan
N
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: chattern@mail.nih.gov.
D000236:Adenoma / Q000209:etiology / Q000235:genetics; D001499:Bayes Theorem; D015982:Bias; D001699:Biometry; D016022:Case-Control Studies; D015179:Colorectal Neoplasms / Q000209:etiology / Q000235:genetics; D016208:Databases, Factual; D004781:Environmental Exposure; D004812:Epidemiologic Methods; D005260:Female; D005838:Genotype; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D016017:Odds Ratio; D010051:Ovarian Neoplasms / Q000209:etiology / Q000235:genetics; D012189:Retrospective Studies; D013269:Stochastic Processes