Diagnostics for generalized linear hierarchical models in network meta-analysis

Hong Zhao, James S Hodges, Brad Carlin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Network meta-analysis (NMA) combines direct and indirect evidence comparing more than 2 treatments. Inconsistency arises when these 2 information sources differ. Previous work focuses on inconsistency detection, but little has been done on how to proceed after identifying inconsistency. The key issue is whether inconsistency changes an NMA's substantive conclusions. In this paper, we examine such discrepancies from a diagnostic point of view. Our methods seek to detect influential and outlying observations in NMA at a trial-by-arm level. These observations may have a large effect on the parameter estimates in NMA, or they may deviate markedly from other observations. We develop formal diagnostics for a Bayesian hierarchical model to check the effect of deleting any observation. Diagnostics are specified for generalized linear hierarchical NMA models and investigated for both published and simulated datasets. Results from our example dataset using either contrast- or arm-based models and from the simulated datasets indicate that the sources of inconsistency in NMA tend not to be influential, though results from the example dataset suggest that they are likely to be outliers. This mimics a familiar result from linear model theory, in which outliers with low leverage are not influential. Future extensions include incorporating baseline covariates and individual-level patient data.

Original languageEnglish (US)
Pages (from-to)333-342
Number of pages10
JournalResearch Synthesis Methods
Issue number3
StatePublished - Sep 2017

Bibliographical note

Funding Information:
This work formed part of the first author's PhD dissertation in the Division of Biostatistics at the University of Minnesota.

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.


  • Bayesian analysis
  • diagnostics in NMA
  • inconsistency
  • multiple treatment comparisons


Dive into the research topics of 'Diagnostics for generalized linear hierarchical models in network meta-analysis'. Together they form a unique fingerprint.

Cite this