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

Measures that quantify the impact of heterogeneity in univariate meta‐analysis, including the very popular I² 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 R² 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 I², which we call . We also provide a multivariate H² statistic, the ratio of a generalisation of Cochran's heterogeneity statistic and its associated degrees of freedom, with an accompanying generalisation of the usual I² 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.