An empirical comparison of univariate and multivariate meta-analyses for categorical outcomes

Stat Med. 2014 Apr 30;33(9):1441-59. doi: 10.1002/sim.6044. Epub 2013 Nov 28.


Treatment effects for multiple outcomes can be meta-analyzed separately or jointly, but no systematic empirical comparison of the two approaches exists. From the Cochrane Library of Systematic Reviews, we identified 45 reviews, including 1473 trials and 258,675 patients, that contained two or three univariate meta-analyses of categorical outcomes for the same interventions that could also be analyzed jointly. Eligible were meta-analyses with at least seven trials reporting all outcomes for which the cross-classification tables were exactly recoverable (e.g., outcomes were mutually exclusive, or one was a subset of the other). This ensured known correlation structures. Outcomes in 40 reviews had an is-subset-of relationship, and those in 5 were mutually exclusive. We analyzed these data with univariate and multivariate models based on discrete and approximate likelihoods. Discrete models were fit in the Bayesian framework using slightly informative priors. The summary effects for each outcome were similar with univariate and multivariate meta-analyses (both using the approximate and discrete likelihoods); however, the multivariate model with the discrete likelihood gave smaller between-study variance estimates, and narrower predictive intervals for new studies. When differences in the summary treatment effects were examined, the multivariate models gave similar summary estimates but considerably longer (shorter) uncertainty intervals because of positive (negative) correlation between outcome treatment effects. It is unclear whether any of the examined reviews would change their overall conclusions based on multivariate versus univariate meta-analyses, because extra-analytical and context-specific considerations contribute to conclusions and, secondarily, because numerical differences were often modest.

Keywords: Bayesian analysis; joint meta-analysis; multinomial likelihood; multivariate normal; regularized regression; restricted maximum likelihood.

Publication types

  • Comparative Study
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Analysis of Variance
  • Datasets as Topic
  • Empirical Research*
  • Meta-Analysis as Topic*
  • Multivariate Analysis*
  • Review Literature as Topic
  • Statistics as Topic / methods*