Exploiting Multivariate Network Meta-Analysis: A Calibrated Bayesian Composite Likelihood Inference.

Multivariate network meta-analysis has emerged as a powerful tool for evidence synthesis by incorporating multiple outcomes and treatments. Despite its advantages, this method comes with methodological challenges, such as the issue of unreported within-study correlations among treatments and outcomes, which can lead to biased estimates and misleading conclusions. In this paper, we propose a calibrated Bayesian composite likelihood approach to overcome this limitation. The proposed method eliminates the need for a fully specified likelihood function while allowing for the unavailability of within-study correlations among treatments and outcomes. Additionally, we developed a hybrid Gibbs sampler algorithm along with the Open-Faced Sandwich post-sampling adjustment to enable robust posterior inference. Through comprehensive simulation studies, we demonstrated that the proposed approach yields unbiased estimates while maintaining coverage probabilities close to the nominal levels. We implemented the proposed method to two real-world network meta-analysis datasets: one comparing treatment procedures for root coverage and the other comparing treatments for anemia in patients with chronic kidney disease.