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 -