Statistics and Its Interface

Volume 13 (2020)

Number 4

On evidence cycles in network meta-analysis

Pages: 425 – 436



Lifeng Lin (Department of Statistics, Florida State University, Tallahassee, Fl., U.S.A.)

Haitao Chu (Division of Biostatistics, University of Minnesota, Minneapolis, Mn, U.S.A.)

James S. Hodges (Division of Biostatistics, University of Minnesota, Minneapolis, Mn, U.S.A.)


As an extension of pairwise meta-analysis of two treatments, network meta-analysis has recently attracted many researchers in evidence-based medicine because it simultaneously synthesizes both direct and indirect evidence from multiple treatments and thus facilitates better decision making. The Bayesian hierarchical model is a popular method to implement network meta-analysis, and it is generally considered more powerful than conventional pairwise metaanalysis, leading to more precise effect estimates with narrower credible intervals. However, the improvement of effect estimates produced by Bayesian network meta-analysis has never been studied theoretically. This article shows that such improvement depends highly on evidence cycles in the treatment network. When all treatment comparisons are assumed to have different heterogeneity variances, a network meta-analysis produces posterior distributions identical to separate pairwise meta-analyses for treatment comparisons that are not contained in any evidence cycles. However, this equivalence does not hold under the commonly-used assumption of a common heterogeneity variance for all comparisons. Simulations and a case study are used to illustrate the equivalence of the Bayesian network and pairwise metaanalyses in certain networks.


Bayesian hierarchical model, evidence cycle, indirect evidence, network meta-analysis, relative effect, treatment network

This research was supported in part by the U.S. National Institutes of Health NLM R21 012197 (HC, LL) and NLM R21 012744 (HC, JH). The first-named author was also supported by the Doctoral Dissertation Fellowship from the University of Minnesota Graduate School.

The content is solely the responsibility of the authors and does not necessarily represent official views of the National Institutes of Health.

Received 2 November 2018

Accepted 17 May 2019

Published 31 July 2020