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.
Bibliographical noteFunding Information:
Yong Chen was supported by grant number R03HS022900 from the Agency for Healthcare Research and Quality. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Agency for Healthcare Research and Quality. Sheng Luo’s research was supported in part by National Institutes of Health/National Center for Advancing Translational Sciences grant KL2 TR000370. 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 from the U.S. National Cancer Institute”.
- Bivariate beta-binomial model
- Exact method
- Hypergeometric function
- Relative risk
- Sarmanov family