title: Bayesian analysis on meta-analysis of case-control studies accounting for within-study correlation.
abstract: In retrospective studies, odds ratio is often used as the measure of association. Under independent beta prior assumption, the exact posterior distribution of odds ratio given a single 2 × 2 table has been derived in the literature. However, independence between risks within the same study may be an oversimplified assumption because cases and controls in the same study are likely to share some common factors and thus to be correlated. Furthermore, in a meta-analysis of case-control studies, investigators usually have multiple 2 × 2 tables. In this article, we first extend the published results on a single 2 × 2 table to allow within study prior correlation while retaining the advantage of closed-form posterior formula, and then extend the results to multiple 2 × 2 tables and regression setting. The hyperparameters, including within study correlation, are estimated via an empirical Bayes approach. The overall odds ratio and the exact posterior distribution of the study-specific odds ratio are inferred based on the estimated hyperparameters. We conduct simulation studies to verify our exact posterior distribution formulas and investigate the finite sample properties of the inference for the overall odds ratio. The results are illustrated through a twin study for genetic heritability and a meta-analysis for the association between the N-acetyltransferase 2 (NAT2) acetylation status and colorectal cancer.
authors.affiliation: Division of Biostatistics, The University of Texas Health Science Centre at Houston, Houston, TX, USA. yong.chen@uth.tmc.edu.
authors.forename: Yong
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN, USA.
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
authors.affiliation: Division of Biostatistics, The University of Texas Health Science Centre at Houston, Houston, TX, USA.
authors.forename: Sheng
authors.initials: S
authors.lastname: Luo
authors.affiliation: Division IV, Office of Biostatistics,/OTS/CDER/FDA, Spring, MD, USA.
authors.forename: Lei
authors.initials: L
authors.lastname: Nie
authors.affiliation: Department of Statistics & Learning, Bell Labs, Murray Hill, NJ, USA.
authors.forename: Sining
authors.initials: S
authors.lastname: Chen
mesh_terms: D001191:Arylamine N-Acetyltransferase / Q000235:genetics; D001499:Bayes Theorem; D016022:Case-Control Studies; D015179:Colorectal Neoplasms / Q000235:genetics; D020022:Genetic Predisposition to Disease / Q000235:genetics; D006801:Humans; D015201:Meta-Analysis as Topic; D016017:Odds Ratio; D012044:Regression Analysis; D018561:Space Simulation; D013223:Statistics as Topic / Q000379:methods*; D018433:Twin Studies as Topic / Q000379:methods
chemical_list: D001191:Arylamine N-Acetyltransferase; C478900:NAT2 protein, human