Exploiting multivariate network meta-analysis: A calibrated Bayesian composite likelihood inference.

Multivariate network meta-analysis has emerged as a powerful tool in 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 potentially lead to misleading conclusions. In this paper, we proposed a calibrated Bayesian composite likelihood approach to overcome this limitation. The proposed method eliminated the need to specify a full 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 yielded unbiased estimates while maintaining coverage probabilities close to the nominal level. Furthermore, we implemented the proposed method on two real-world network meta-analysis datasets; one comparing treatment procedures for the root coverage and another comparing treatments for anaemia in chronic kidney disease patients.