TY - JOUR

T1 - Quantifying the impact of between-study heterogeneity in multivariate meta-analyses

AU - Jackson, Dan

AU - White, Ian R

AU - Riley, Richard D

N1 - Copyright © 2012 John Wiley & Sons, Ltd.

PY - 2012

Y1 - 2012

N2 - 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 I(R)(2). 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, I(H)(2). 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.

AB - 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 I(R)(2). 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, I(H)(2). 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.

U2 - 10.1002/sim.5453

DO - 10.1002/sim.5453

M3 - Article

C2 - 22763950

SN - 1097-0258

VL - 31

SP - 3805

EP - 3820

JO - Statistics in Medicine

JF - Statistics in Medicine

IS - 29

ER -