Non-parametric Bayesian approach to multiple treatment comparisons in network meta-analysis with application to comparisons of anti-depressants

Network meta-analysis is a powerful tool to synthesize evidence from independent studies and compare multiple treatments simultaneously. A critical task of performing a network meta-analysis is to offer ranks of all available treatment options for a specific disease outcome. Frequently, the estimated treatment rankings are accompanied by a large amount of uncertainty, suffer from multiplicity issues, and rarely permit possible ties of treatments with similar performance. These issues make interpreting rankings problematic as they are often treated as absolute metrics. To address these shortcomings, we formulate a ranking strategy that adapts to scenarios with high-order uncertainty by producing more conservative results. This improves the interpretability while simultaneously accounting for multiple comparisons. To admit ties between treatment effects in cases where differences between treatment effects are negligible, we also develop a Bayesian non-parametric approach for network meta-analysis. The approach capitalizes on the induced clustering mechanism of Bayesian non-parametric methods, producing a positive probability that two treatment effects are equal. We demonstrate the utility of the procedure through numerical experiments and a network meta-analysis designed to study antidepressant treatments.