Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: Methods for the absolute risk difference and relative risk

Multivariate meta-analysis is increasingly utilised in biomedical research to combine data of multiple comparative clinical studies for evaluating drug efficacy and safety profile. When the probability of the event of interest is rare, or when the individual study sample sizes are small, a substantial proportion of studies may not have any event of interest. Conventional meta-analysis methods either exclude such studies or include them through ad hoc continuality correction by adding an arbitrary positive value to each cell of the corresponding 2 x 2 tables, which may result in less accurate conclusions. Furthermore, different continuity corrections may result in inconsistent conclusions. In this article, we discuss a bivariate Beta-binomial model derived from Sarmanov family of bivariate distributions and a bivariate generalised linear mixed effects model for binary clustered data to make valid inferences. These bivariate random effects models use all available data without ad hoc continuity corrections, and accounts for the potential correlation between treatment (or exposure) and control groups within studies naturally. We then utilise the bivariate random effects models to reanalyse two recent meta-analysis data sets.