An evaluation of bivariate random‐effects meta‐analysis for the joint synthesis of two correlated outcomes

Often multiple outcomes are of interest in each study identified by a systematic review, and in this situation a separate univariate meta-analysis is usually applied to synthesize the evidence for each outcome independently; an alternative approach is a single multivariate meta-analysis model that utilizes any correlation between outcomes and obtains all the pooled estimates jointly. Surprisingly, multivariate meta-analysis is rarely considered in practice, so in this paper we illustrate the benefits and limitations of the approach to provide helpful insight for practitioners. We compare a bivariate random-effects meta-analysis (BRMA) to two independent univariate random-effects meta-analyses (URMA), and show how and why a BRMA is able to 'borrow strength' across outcomes. Then, on application to two examples in healthcare, we show: (i) given complete data for both outcomes in each study, BRMA is likely to produce individual pooled estimates with very similar standard errors to those from URMA; (ii) given some studies where one of the outcomes is missing at random, the 'borrowing of strength' is likely to allow BRMA to produce individual pooled estimates with noticeably smaller standard errors than those from URMA; (iii) for either complete data or missing data, BRMA will produce a more appropriate standard error of the pooled difference between outcomes as it incorporates their correlation, which is not possible using URMA; and (iv) despite its advantages, BRMA may often not be possible due to the difficulty in obtaining the within-study correlations required to fit the model. Bivariate meta-regression and further research priorities are also discussed.