Abstract
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 10 antihypertension clinical trials.
