Grouped random effects models for Bayesian meta-analysis

Meta-analysis refers to quantitative methods to combine results from independent studies so as to draw overall conclusions. Frequently, results from dissimilar studies are inappropriately combined, resulting in suspect inferential synthesis. We present a straightforward method to identify and address this problem through the development of grouped random effect models for meta-analysis. We examine 15 comparative studies that investigate the efficacy of a new anti-epileptic drug, progabide. The flexibility of this modelling scheme is exemplified by the result that the open studies support the efficacy of progabide while the closed studies support the reverse hypothesis. Bayesian approaches for meta-analysis are preferable because of the small number of studies prevalent in meta-analysis. We specify diffuse proper prior and hyperprior distributions to assure posterior propriety. We investigate sensitivity of the posterior to choice of prior. We use Gibbs sampling and the Metropolis algorithm to generate samples from the relevant posteriors. We analyse posterior summaries and plots of model parameters to suggest solutions to questions of interest.