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      Quantifying the impact of between-study heterogeneity in multivariate meta-analyses

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          Abstract

          Measures that quantify the impact of heterogeneity in univariate meta-analysis, including the very popular I 2 statistic, are now well established. Multivariate meta-analysis, where studies provide multiple outcomes that are pooled in a single analysis, is also becoming more commonly used. The question of how to quantify heterogeneity in the multivariate setting is therefore raised. It is the univariate R 2 statistic, the ratio of the variance of the estimated treatment effect under the random and fixed effects models, that generalises most naturally, so this statistic provides our basis. This statistic is then used to derive a multivariate analogue of I 2, which we call . We also provide a multivariate H 2 statistic, the ratio of a generalisation of Cochran's heterogeneity statistic and its associated degrees of freedom, with an accompanying generalisation of the usual I 2 statistic, . Our proposed heterogeneity statistics can be used alongside all the usual estimates and inferential procedures used in multivariate meta-analysis. We apply our methods to some real datasets and show how our statistics are equally appropriate in the context of multivariate meta-regression, where study level covariate effects are included in the model. Our heterogeneity statistics may be used when applying any procedure for fitting the multivariate random effects model. Copyright © 2012 John Wiley & Sons, Ltd.

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          Most cited references 18

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          Applied multivariate statistical analysis

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            Cochrane Handbook for Systematic Reviews of Interventions

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              Advanced methods in meta-analysis: multivariate approach and meta-regression.

              This tutorial on advanced statistical methods for meta-analysis can be seen as a sequel to the recent Tutorial in Biostatistics on meta-analysis by Normand, which focused on elementary methods. Within the framework of the general linear mixed model using approximate likelihood, we discuss methods to analyse univariate as well as bivariate treatment effects in meta-analyses as well as meta-regression methods. Several extensions of the models are discussed, like exact likelihood, non-normal mixtures and multiple endpoints. We end with a discussion about the use of Bayesian methods in meta-analysis. All methods are illustrated by a meta-analysis concerning the efficacy of BCG vaccine against tuberculosis. All analyses that use approximate likelihood can be carried out by standard software. We demonstrate how the models can be fitted using SAS Proc Mixed. Copyright 2002 John Wiley & Sons, Ltd.
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                Author and article information

                Journal
                Stat Med
                Stat Med
                sim
                Statistics in Medicine
                Blackwell Publishing Ltd
                0277-6715
                1097-0258
                20 December 2012
                04 July 2012
                : 31
                : 29
                : 3805-3820
                Affiliations
                [a ]MRC Biostatistics Unit Cambridge, U.K.
                [b ]School of Health and Population Sciences, University of Birmingham Birminghan, U.K.
                Author notes
                *Correspondence to: Dan Jackson, MRC Biostatistics Unit, Cambridge, U.K.
                Article
                10.1002/sim.5453
                3546377
                22763950
                Copyright © 2012 John Wiley & Sons, Ltd.

                Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.

                Categories
                Research Articles

                Biostatistics

                generalised variance, meta-regression, multivariate methods, random effects models

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