MRC Biostatistics Unit, Cambridge, UK.
Stat Med. 2012 Dec 20;31(29):3805-20. doi: 10.1002/sim.5453. Epub 2012 Jul 4.
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.
目前已经很好地建立了用于量化单变量荟萃分析中异质性的措施，包括非常流行的 I(2)统计量。多变量荟萃分析，即研究提供多个可在单个分析中汇总的结果，也越来越常用。因此，提出了如何在多变量环境中量化异质性的问题。最自然地推广的是单变量 R(2)统计量，即随机和固定效应模型下估计治疗效果的方差比，因此该统计量是我们的基础。然后，我们使用该统计量推导出 I(2)的多变量类似物，我们称之为 I(R)(2)。我们还提供了一个多变量 H(2)统计量，即 Cochran 异质性统计量的推广及其相关自由度与通常的 I(2)统计量的伴随推广的比率，I(H)(2)。我们提出的异质统计量可与多变量荟萃分析中使用的所有常用估计和推断程序一起使用。我们将我们的方法应用于一些真实数据集，并展示了我们的统计量在多变量荟萃回归的背景下同样适用，其中在模型中包含了研究水平协变量的效果。当应用拟合多变量随机效应模型的任何程序时，都可以使用我们的异质统计量。
