Bayesian estimation and prediction for network meta-analysis with contrast-based approach

Network meta-analysis is gaining prominence in clinical epidemiology and health technology assessments that enable comprehensive assessment of comparative effectiveness for multiple available treatments. In network meta-analysis, Bayesian methods have been one of the standard approaches for the arm-based approach and are widely applied in practical data analyses. Also, for most cases in these applications, proper noninformative priors are adopted, which does not incorporate subjective prior knowledge into the analyses, and reference Bayesian analyses are major choices. In this article, we provide generic Bayesian analysis methods for the contrast-based approach of network meta-analysis, where the generic Bayesian methods can treat proper and improper prior distributions. The proposed methods enable direct sampling from the posterior and posterior predictive distributions without formal iterative computations such as Markov chain Monte Carlo, and technical convergence checks are not required. In addition, representative noninformative priors that can be treated in the proposed framework involving the Jeffreys prior are provided. We also provide an easy-to-handle R statistical package, BANMA, to implement these Bayesian analyses via simple commands. The proposed Bayesian methods are illustrated using various noninformative priors through applications to two real network meta-analyses.