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Meta‐analysis of studies with bivariate binary outcomes: a marginal beta‐binomial model approach
Author(s) -
Chen Yong,
Hong Chuan,
Ning Yang,
Su Xiao
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6620
Subject(s) - bivariate analysis , binomial (polynomial) , marginal model , statistics , binary data , beta binomial distribution , beta (programming language) , econometrics , mathematics , binomial distribution , beta distribution , binary number , binomial proportion confidence interval , negative binomial distribution , computer science , regression analysis , poisson distribution , arithmetic , programming language
When conducting a meta‐analysis of studies with bivariate binary outcomes, challenges arise when the within‐study correlation and between‐study heterogeneity should be taken into account. In this paper, we propose a marginal beta‐binomial model for the meta‐analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta‐binomial model (Chen et al. , 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed‐form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta‐binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study‐specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta‐binomial model with the bivariate generalized linear mixed model and the Sarmanov beta‐binomial model by simulation studies. Interestingly, the results show that the marginal beta‐binomial model performs better than the Sarmanov beta‐binomial model, whether or not the true model is Sarmanov beta‐binomial, and the marginal beta‐binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta‐analyses of diagnostic accuracy studies and a meta‐analysis of case–control studies are conducted for illustration. Copyright © 2015 John Wiley & Sons, Ltd.