Univariate meta-analysis concerns a single outcome of interest measured across a number of independent studies. However, many research studies will have also measured secondary outcomes. Multivariate meta-analysis allows us to take these secondary outcomes into account, and can also include studies where the primary outcome is missing. We define the efficiency (E) as the variance of the overall estimate from a multivariate meta-analysis relative to the variance of the overall estimate from a univariate meta-analysis. The extra information gained from a multivariate meta-analysis of n studies is then similar to the extra information gained if a univariate meta-analysis of the primary effect had a further n(1-E)/E studies. The variance contribution of a study's secondary outcomes (its borrowing of strength) can be thought of as a contrast between the variance matrix of the outcomes in that study and the set of variance matrices of all the studies in the meta-analysis. In the bivariate case this is given a simple graphical interpretation as the borrowing of strength plot. We discuss how these findings can also be used in the context of random effects meta-analysis. Our discussion is motivated by a published meta-analysis of ten anti-hypertension clinical trials.

中文翻译：

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次要结果在多元荟萃分析中的作用。

单变量荟萃分析涉及在多个独立研究中测得的单个目标结果。但是，许多研究也将测量次要结局。多元荟萃分析使我们能够考虑这些次要结果，也可以包括缺少主要结果的研究。我们将效率（E）定义为来自多元荟萃分析的总体估计的方差相对于来自单变量荟萃分析的总体估计的方差。然后，如果对n种研究的多元荟萃分析获得的额外信息类似于对主要作用的单变量荟萃分析还进行了进一步的n（1-E）/ E研究，则获得的额外信息将与之相似。研究的方差贡献 次要结果（其借用力）可以认为是该研究中结果的方差矩阵与荟萃分析中所有研究的方差矩阵集之间的对比。在双变量情况下，可以通过简单的图形解释将其作为强度图的借用。我们讨论了如何在随机效应荟萃分析的背景下使用这些发现。我们的讨论是基于已发表的十项抗高血压临床试验的荟萃分析得出的。