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.
Highlights
Network meta-analysis (NMA) has become increasingly popular in the past decade for comparing the efficacy and/or safety of several medical interventions (Zarin et al, 2017)
While meta-analysis only allows for the comparison of two treatments, network meta-analysis allows for the comparison of all relevant treatments in a single analysis in order to support policies and costs pertaining to newly developed treatments as well as guidelines for health practitioners
In cases where we find that the posterior variance of djj does not differ significantly from the prior variance, for any disconnected treatments j and j, we would have demonstrated theoretically that the Bayesian contrast-based approach lacks utility in those cases
Summary
Network meta-analysis (NMA) has become increasingly popular in the past decade for comparing the efficacy and/or safety of several medical interventions (Zarin et al, 2017). We introduce for the first time a theoretical framework to understand how evidence flows in Bayesian models of disconnected networks with respect to estimating the relative effect of disconnected treatments. We achieve this by considering the standard contrast-based NMA model (Dias et al, 2013) and evaluating theoretically, in disconnected networks, the ratio of posterior to prior variance between all pairs of disconnected treatments. The standard contrast-based NMA model is not useful to analyze disconnected networks (even when the number of studies, treatments or patients is large) when using uninformative priors. This would involve adapting the normal approximation and delta-method presented at the beginning of Section 4 to accommodate different distributions and link functions
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