Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales.

When conducting a meta-analysis of clinical trials with binary outcomes, a normal approximation for the summary treatment effect measure in each trial is inappropriate in the common situation where some of the trials in the meta-analysis are small, or the observed risks are close to 0 or 1. This problem can be avoided by making direct use of the binomial distribution within trials. A fully Bayesian method has already been developed for random effects meta-analysis on the log-odds scale using the BUGS implementation of Gibbs sampling. In this paper we demonstrate how this method can be extended to perform analyses on both the absolute and relative risk scales. Within each approach we exemplify how trial-level covariates, including underlying risk, can be considered. Data from 46 trials of the effect of single-dose ibuprofen on post-operative pain are analysed and the results contrasted with those derived from classical and Bayesian summary statistic methods. The clinical interpretation of the odds ratio scale is not straightforward. The advantages and flexibility of a fully Bayesian approach to meta-analysis of binary outcome data, considered on an absolute risk or relative risk scale, are now available.