A variance shrinkage method improves arm-based Bayesian network meta-analysis

Zhenxun Wang, Lifeng Lin, James S. Hodges, Richard MacLehose, Haitao Chu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Network meta-analysis is a commonly used tool to combine direct and indirect evidence in systematic reviews of multiple treatments to improve estimation compared to traditional pairwise meta-analysis. Unlike the contrast-based network meta-analysis approach, which focuses on estimating relative effects such as odds ratios, the arm-based network meta-analysis approach can estimate absolute risks and other effects, which are arguably more informative in medicine and public health. However, the number of clinical studies involving each treatment is often small in a network meta-analysis, leading to unstable treatment-specific variance estimates in the arm-based network meta-analysis approach when using non- or weakly informative priors under an unequal variance assumption. Additional assumptions, such as equal (i.e. homogeneous) variances for all treatments, may be used to remedy this problem, but such assumptions may be inappropriately strong. This article introduces a variance shrinkage method for an arm-based network meta-analysis. Specifically, we assume different treatment variances share a common prior with unknown hyperparameters. This assumption is weaker than the homogeneous variance assumption and improves estimation by shrinking the variances in a data-dependent way. We illustrate the advantages of the variance shrinkage method by reanalyzing a network meta-analysis of organized inpatient care interventions for stroke. Finally, comprehensive simulations investigate the impact of different variance assumptions on statistical inference, and simulation results show that the variance shrinkage method provides better estimation for log odds ratios and absolute risks.

Original languageEnglish (US)
Pages (from-to)151-165
Number of pages15
JournalStatistical methods in medical research
Issue number1
Early online dateAug 5 2020
StatePublished - Jan 2021

Bibliographical note

Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported in part by NIH NLM R01LM012982.

Publisher Copyright:
© The Author(s) 2020.


  • Bayesian inference
  • network meta-analysis
  • variance prior
  • variance shrinkage method


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