Bayesian Inference on Risk Differences: An Application to Multivariate Meta-Analysis of Adverse Events in Clinical Trials

Yong Chen, Sheng Luo, Haitao Chu, Peng Wei

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1 Scopus citations


Multivariate meta-analysis is useful in combining evidence from independent studies that involve several comparisons among groups based on a single outcome. For binary outcomes, the commonly used statistical models for multivariate meta-analysis are multivariate generalized linear mixed effects models which assume risks, after some transformation, follow a multivariate normal distribution with possible correlations. In this article, we consider an alternative model for multivariate meta-analysis where the risks are modeled by the multivariate beta distribution proposed by Sarmanov. This model has several attractive features compared to the conventional multivariate generalized linear mixed effects models, including simplicity of likelihood function, no need to specify a link function, and a closed-form expression of distribution functions for study-specific risk differences. We investigate the finite sample performance of this model through simulation studies and illustrate its use with an application to multivariate meta-analysis of adverse events of tricyclic antidepressant treatment in clinical trials.

Original languageEnglish (US)
Pages (from-to)142-155
Number of pages14
JournalStatistics in Biopharmaceutical Research
Issue number2
StatePublished - Apr 2013

Bibliographical note

Funding Information:
The authors are grateful to Dr. Steven Snapinn, the Associate Editor, and two anonymous reviewers for the helpful comments that have greatly improved this article. Yong Chen’s research was partially supported by a start-up fund and the PRIME award from the University of Texas School of Public Health. Sheng Luo’s research is partially supported by two NIH/NINDS grants U01NS043127 and U01NS43128. Haitao Chu was supported in part by the U.S. Department of Health and Human Services Agency for Healthcare Research and Quality grant R03HS020666, and P01CA142538 P30CA077598 from the U.S. National Cancer Institute. Peng Wei was supported in part by the National Institutes of Health grant HL095511.


  • Bivariate beta-binomial model
  • Exact method
  • Hypergeometric function
  • Relative risk
  • Sarmanov family


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