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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 references18

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          Applied multivariate statistical analysis

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            Cochrane Handbook for Systematic Reviews of Interventions

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              Undue reliance on I2 in assessing heterogeneity may mislead

              Background The heterogeneity statistic I 2, interpreted as the percentage of variability due to heterogeneity between studies rather than sampling error, depends on precision, that is, the size of the studies included. Methods Based on a real meta-analysis, we simulate artificially 'inflating' the sample size under the random effects model. For a given inflation factor M = 1, 2, 3,... and for each trial i, we create a M-inflated trial by drawing a treatment effect estimate from the random effects model, using s i 2 /M as within-trial sampling variance. Results As precision increases, while estimates of the heterogeneity variance τ 2 remain unchanged on average, estimates of I 2 increase rapidly to nearly 100%. A similar phenomenon is apparent in a sample of 157 meta-analyses. Conclusion When deciding whether or not to pool treatment estimates in a meta-analysis, the yard-stick should be the clinical relevance of any heterogeneity present. τ 2, rather than I 2, is the appropriate measure for this purpose.
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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
                70ce908c-886a-43f2-8844-bf4d39731cec
                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.

                History
                : 20 June 2011
                : 07 May 2012
                Categories
                Research Articles

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

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