Article type
Year
Abstract
Background: Treatment effects for multiple outcomes can be meta-analyzed separately or jointly, but no systematic empirical comparison of the two approaches exists.
Objectives: To compare separate (univariate) and joint (multivariate) meta-analysis of categorical outcomes that have known within-study correlation structure.
Methods: From the Cochrane Library of Systematic Reviews (2012, first quarter), we identified 45 reviews, including 1473 trials and 258 675 patients, that contained 2 or 3 univariate meta-analyses of categorical outcomes for the same interventions that could also be analyzed jointly. All meta-analyses had at least seven trials from which the cross-classification tables for all outcomes were exactly recoverable [e.g., outcomes were mutually exclusive (5 reviews), or one was a subset of the other (40 reviews)]. This ensured known correlation structures. We analyzed these data with univariate and multivariate models based on discrete and approximate likelihoods. For computational convenience, the discrete models were fit in the Bayesian framework using slightly informative prior distributions.
Results: Overall, the summary effects for each outcome and the accompanying confidence/credible intervals were similar with univariate and multivariate meta-analysis (both using the approximate and the discrete likelihood). However, the multivariate model gave smaller between-study variance estimates. The two models differed much more when estimating the relative treatment effects of the outcomes than when estimating the effect of each outcome alone. Multivariate models gave similar summary odds ratio estimates, but slightly shorter uncertainty intervals for each outcome individually, compared with univariate models. Positive (negative) correlations between outcomes led to considerably longer (shorter) uncertainty intervals with multivariate models.
Conclusions: It is likely that in all 45 topics conclusions about summary effect estimates would remain qualitatively similar with either approach, but predictive intervals for new studies would be shorter with the multivariate model.
Objectives: To compare separate (univariate) and joint (multivariate) meta-analysis of categorical outcomes that have known within-study correlation structure.
Methods: From the Cochrane Library of Systematic Reviews (2012, first quarter), we identified 45 reviews, including 1473 trials and 258 675 patients, that contained 2 or 3 univariate meta-analyses of categorical outcomes for the same interventions that could also be analyzed jointly. All meta-analyses had at least seven trials from which the cross-classification tables for all outcomes were exactly recoverable [e.g., outcomes were mutually exclusive (5 reviews), or one was a subset of the other (40 reviews)]. This ensured known correlation structures. We analyzed these data with univariate and multivariate models based on discrete and approximate likelihoods. For computational convenience, the discrete models were fit in the Bayesian framework using slightly informative prior distributions.
Results: Overall, the summary effects for each outcome and the accompanying confidence/credible intervals were similar with univariate and multivariate meta-analysis (both using the approximate and the discrete likelihood). However, the multivariate model gave smaller between-study variance estimates. The two models differed much more when estimating the relative treatment effects of the outcomes than when estimating the effect of each outcome alone. Multivariate models gave similar summary odds ratio estimates, but slightly shorter uncertainty intervals for each outcome individually, compared with univariate models. Positive (negative) correlations between outcomes led to considerably longer (shorter) uncertainty intervals with multivariate models.
Conclusions: It is likely that in all 45 topics conclusions about summary effect estimates would remain qualitatively similar with either approach, but predictive intervals for new studies would be shorter with the multivariate model.