Multilevel Network Meta-Regression for population-adjusted treatment comparisons

David M Phillippo*, Sofia Dias, A E Ades, Mark Belger, Alan Brnabic, Alexander Schacht, Daniel Saure, Zbigniew Kadziola, Nicky J Welton

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

50 Citations (Scopus)
102 Downloads (Pure)


Standard network meta-analysis (NMA) and indirect comparisons combine aggregate data from multiple studies on treatments of interest, assuming that any effect modifiers are balanced across populations. Population adjustment methods relax this assumption using individual patient data from one or more studies. However, current Matching Adjusted Indirect Comparison and Simulated Treatment Comparison methods are limited to pairwise indirect comparisons and cannot predict into a specified target population. Existing meta-regression approaches incur aggregation bias.

We propose a new method extending the standard NMA framework. An individual-level regression model is defined, and aggregate data are fitted by integrating over the covariate distribution to form the likelihood. Motivated by the complexity of the closed-form integration, we propose a general numerical approach using Quasi-Monte Carlo integration. Covariate correlation structures are accounted for using copulae. Crucially for decision making, comparisons may be provided in any target population with a given covariate distribution.

We illustrate the method with a network of plaque psoriasis treatments. Estimated population-average treatment effects are similar across study populations, as differences in the distributions of effect modifiers are small. Better fit is achieved than a random effects NMA, uncertainty is substantially reduced by explaining within- and between-study variation, and estimates are more interpretable.
Original languageEnglish
Pages (from-to)1189-1210
Number of pages22
JournalJournal of the Royal Statistical Society: Series A
Issue number3
Early online date7 Jun 2020
Publication statusPublished - 18 Jun 2020


  • effect modification
  • indirect comparison
  • individual patient data
  • network meta-analysis


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