Combination of direct and indirect evidence in mixed treatment comparisons

TLDR

Mixed treatment comparison meta‑analysis extends pairwise meta‑analysis to networks of trials (e.g., A vs B, B vs C, A vs C) and serves to strengthen inference on relative efficacy by combining direct and indirect evidence and to enable simultaneous comparison of all treatments for optimal selection. The authors develop a suite of Bayesian hierarchical models implemented in WinBUGS to analyze mixed treatment comparison data. They employ multivariate random‑effects Bayesian models that allow treatment‑specific between‑trial variance to be either homogeneous or heterogeneous and compare fixed baseline effects with random baselines drawn from a common distribution. Applied to an illustrative data set, the models were compared via posterior distributions, and the authors evaluated model fit and selection using Bayesian deviance and node‑based criticism while discussing the underlying assumptions and parameterization of MTC models. © 2004 John Wiley & Sons, Ltd.

Abstract

Abstract Mixed treatment comparison (MTC) meta‐analysis is a generalization of standard pairwise meta‐analysis for A vs B trials, to data structures that include, for example, A vs B, B vs C, and A vs C trials. There are two roles for MTC: one is to strengthen inference concerning the relative efficacy of two treatments, by including both ‘direct’ and ‘indirect’ comparisons. The other is to facilitate simultaneous inference regarding all treatments, in order for example to select the best treatment. In this paper, we present a range of Bayesian hierarchical models using the Markov chain Monte Carlo software WinBUGS. These are multivariate random effects models that allow for variation in true treatment effects across trials. We consider models where the between‐trials variance is homogeneous across treatment comparisons as well as heterogeneous variance models. We also compare models with fixed (unconstrained) baseline study effects with models with random baselines drawn from a common distribution. These models are applied to an illustrative data set and posterior parameter distributions are compared. We discuss model critique and model selection, illustrating the role of Bayesian deviance analysis, and node‐based model criticism. The assumptions underlying the MTC models and their parameterization are also discussed. Copyright © 2004 John Wiley & Sons, Ltd.