On evidence cycles in network meta-analysis

Lifeng Lin, Haitao Chu, James S. Hodges

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)425-436
Number of pages12
JournalStatistics and its Interface
Issue number4
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 International Press of Boston, Inc.


  • Bayesian hierarchical model
  • Evidence cycle
  • Indirect evidence
  • Network meta-analysis
  • Relative effect
  • Treatment network


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