title: An Empirical Bayes Method for Multivariate Meta-analysis with an Application in Clinical Trials.
abstract: We propose an empirical Bayes method for evaluating overall and study-specific treatment effects in multivariate meta-analysis with binary outcome. Instead of modeling transformed proportions or risks via commonly used multivariate general or generalized linear models, we directly model the risks without any transformation. The exact posterior distribution of the study-specific relative risk is derived. The hyperparameters in the posterior distribution can be inferred through an empirical Bayes procedure. As our method does not rely on the choice of transformation, it provides a flexible alternative to the existing methods and in addition, the correlation parameter can be intuitively interpreted as the correlation coefficient between risks.
authors.forename: Yong
authors.initials: Y
authors.lastname: Chen
authors.forename: Sheng
authors.initials: S
authors.lastname: Luo
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
authors.forename: Xiao
authors.initials: X
authors.lastname: Su
authors.forename: Lei
authors.initials: L
authors.lastname: Nie
keywords: Bivariate beta-binomial model; Exact method; Hypergeometric function; Meta-analysis; Relative risk; Sarmanov family
references.citation: Control Clin Trials. 1986 Sep;7(3):177-88
references.pmid: 3802833
references.citation: Stat Med. 2011 Sep 10;30(20):2481-98
references.pmid: 21268052
references.citation: Stat Med. 1993 Dec 30;12(24):2273-84
references.pmid: 7907813
references.citation: Biostatistics. 2008 Jan;9(1):172-86
references.pmid: 17626226
references.citation: Diabetes Care. 1993 Sep;16(9):1231-5
references.pmid: 8404425
references.citation: J Clin Epidemiol. 2005 Oct;58(10):982-90
references.pmid: 16168343
references.citation: J Clin Epidemiol. 2006 Dec;59(12):1331-2; author reply 1332-3
references.pmid: 17098577
references.citation: Stat Med. 2007 Jan 15;26(1):78-97
references.pmid: 16526010
references.citation: Stat Med. 1997 Jun 30;16(12):1311-28
references.pmid: 9232755
references.citation: Diabetes Res Clin Pract. 2008 Jul;81(1):124-9
references.pmid: 18456364
references.citation: J Am Stat Assoc. 1981 Dec;76(376):782-801
references.pmid: 12312151
references.citation: CMAJ. 2008 Jul 29;179(3):229-34
references.pmid: 18663202
references.citation: Lancet. 2009 May 23;373(9677):1773-9
references.pmid: 19465232
references.citation: Diabetes. 2007 Dec;56(12):2990-6
references.pmid: 17898128
references.citation: Stat Med. 1995 Dec 30;14(24):2685-99
references.pmid: 8619108
references.citation: BMC Med Res Methodol. 2007 Jan 12;7:3
references.pmid: 17222330
references.citation: Am J Obstet Gynecol. 2010 Jun;202(6):654.e1-6
references.pmid: 20510967
references.citation: Med Decis Making. 2008 Sep-Oct;28(5):639-49
references.pmid: 18753684