Exploiting Gene-Environment Independence for Analysis of Case-Control Studies: An Empirical Bayes-Type Shrinkage Estimator to Trade-Off between Bias and Efficiency

• Published in: Biometrics Vol. 64; no. 3; pp. 685 - 694
• Main Authors: Mukherjee, Bhramar, Chatterjee, Nilanjan
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01-09-2008; Blackwell Publishing; Blackwell Publishing Ltd
• Subjects: Adenoma - etiology; Adenoma - genetics; Analytical estimating; Bayes Theorem; Bayesian analysis; Bias; Biomedical research; Biometric Methodology; Biometry; Case control studies; Case-only designs; Colorectal Neoplasms - etiology; Colorectal Neoplasms - genetics; Databases, Factual; Disease models; Environmental Exposure; Epidemiologic Methods; Estimating techniques; Estimation bias; Estimation methods; Estimators; Female; Gene-environment interaction; Genotype; Genotype & phenotype; Humans; Likelihood Functions; Logistic Models; Maximum likelihood estimation; Medical genetics; Odds Ratio; Ovarian Neoplasms - etiology; Ovarian Neoplasms - genetics; Parametric models; Profile likelihood; Regression analysis; Retrospective analysis; Retrospective Studies; Semiparametrics; Statistical variance; Stochastic Processes
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2007.00953.x

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.