Producing treatment hierarchies in network meta-analysis using probabilistic models and treatment-choice criteria

A key output of network meta-analysis (NMA) is the relative ranking of the treatments; nevertheless, it has attracted a lot of criticism. This is mainly due to the fact that ranking is an influential output and prone to over-interpretations even when relative effects imply small differences between treatments. To date, common ranking methods rely on metrics that lack a straightforward interpretation, while it is still unclear how to measure their uncertainty. We introduce a novel framework for estimating treatment hierarchies in NMA. At first, we formulate a mathematical expression that defines a treatment choice criterion (TCC) based on clinically important values. This TCC is applied to the study treatment effects to generate paired data indicating treatment preferences or ties. Then, we synthesize the paired data across studies using an extension of the so-called "Bradley-Terry" model. We assign to each treatment a latent variable interpreted as the treatment "ability" and we estimate the ability parameters within a regression model. Higher ability estimates correspond to higher positions in the final ranking. We further extend our model to adjust for covariates that may affect treatment selection. We illustrate the proposed approach and compare it with alternatives in two datasets: a network comparing 18 antidepressants for major depression and a network comparing 6 antihypertensives for the incidence of diabetes. Our approach provides a robust and interpretable treatment hierarchy which accounts for clinically important values and is presented alongside with uncertainty measures. Overall, the proposed framework offers a novel approach for ranking in NMA based on concrete criteria and preserves from over-interpretation of unimportant differences between treatments.