Meta-analysis of mixed treatment comparisons at multiple follow-up times.

Mixed treatment comparisons (MTC) meta-analysis is a methodology for making inferences on relative treatment effects based on a synthesis of both direct and indirect evidence on multiple treatment contrasts. This is particularly useful in the context of cost-effectiveness analysis and medical decision making. Here, we extend these methods to a more complex situation where trials report results at one or more, different yet fixed, follow-up times. These methods are applied to an illustrative data set combining evidence on healing rates under six different treatments for gastro-esophageal reflux disease (GERD). A series of Bayesian hierarchical models based on piece-wise exponential hazards is developed that borrow strength across the MTC networks and also across time points. These include models for absolute and relative treatment effects, models with fixed or random effects over time, random walk models, and models with homogeneous or heterogeneous between-trials variation. The deviance information criterion (DIC) is used to guide model development and selection. Models for absolute treatment effects generate materially different rankings of the treatments than models that separate the trial-specific baselines from the relative treatment effects. The extent of between-trials heterogeneity in treatment effects depends on treatment contrast. In discussion we note that models of this type have a very wide potential application.