Bayesian mixed treatment comparisons meta‐analysis for correlated outcomes subject to reporting bias

Many randomized controlled trials report more than one primary outcome. As a result, multivariate meta‐analytic methods for the assimilation of treatment effects in systematic reviews of randomized controlled trials have received increasing attention in the literature. These methods show promise with respect to bias reduction and efficiency gain compared with univariate meta‐analysis. However, most methods for multivariate meta‐analysis have focused on pairwise treatment comparisons (i.e. when the number of treatments is 2). Current methods for mixed treatment comparisons meta‐analysis (i.e. when the number of treatments is more than 2) have focused on univariate or, very recently, bivariate outcomes. To broaden their application, we propose a framework for mixed treatment comparisons meta‐analysis of multivariate (two or more) outcomes where the correlations between multivariate outcomes within and between studies are accounted for through copulas, and the joint modelling of multivariate random effects respectively. We consider a Bayesian hierarchical model using Markov chain Monte Carlo methods for estimation. An important feature of the framework proposed is that it allows for borrowing of information across correlated outcomes. We show via simulation that our approach reduces the effect of outcome reporting bias in a variety of missing outcome scenarios. We apply the method to a systematic review of randomized controlled trials of pharmacological treatments for alcohol dependence, which tends to report multiple outcomes potentially subject to outcome reporting bias.