A Theoretical Investigation of How Evidence Flows in Bayesian Network Meta-Analysis of Disconnected Networks

Abstract

Network meta-analysis has gained popularity in the last decade as a method for comparing the efficacy/safety of multiple medical interventions by synthesizing data across clinical studies. Bayesian methods for network meta-analysis have undergone further development than frequentist methods and are more convenient to use. Most of the current literature pertains to connected networks but disconnected networks commonly arise. There is not at the moment a trusted gold-standard approach to analyze disconnected networks. Intuitively, the standard method for analyzing connected networks, which is contrast-based, does not seem useful in disconnected networks, but this has not been explained rigorously. Our work is the first to provide the theoretical groundwork for understanding how evidence flows within Bayesian contrast-based models of disconnected networks. We achieve this by quantifying the ratio of posterior to prior variance of disconnected treatment contrasts. We show that when using an uninformative prior on the treatment contrasts, the standard approach is not useful to analyze disconnected networks (even when the number of studies, treatments or patients is large); however, it can be useful under moderately informative priors, which can be informed from additional observational data when available. A simulation study provides a demonstration of the theoretical results and explores non-asymptotic cases. An illustration on a real-world dataset is provided.