Estimation of a Matrix of Heterogeneity Parameters in Multivariate Meta-Analysis of Random-Effects Models

Multivariate meta-analysis has potential over its univariate counterpart. The most common challenge in univariate or multivariate meta-analysis is estimating heterogeneity parameters in non-negative domains under the random-effects model assumption. In this context, two new multivariate estimation methods are demonstrated; first, by extending the Sidik and Jonkman (2005) univariate estimates to a multivariate setting, and second, by considering an iterative version of the Sidik and Jonkman method, namely, a method developed in Wouhib (2013). These two methods are compared with extended DerSimonian and Laird methods (Jackson et al. 2009; Chen et al. 2012) by using an example and simulation in random-effects multivariate meta-analysis. Finally, the benefits of the proposed estimates are evaluated in terms of precision in estimating vectors of effect sizes and associated covariance matrices via simulation. Also, some limitations and remedies resulting from negative definite matrix in estimating heterogeneity parameters will be discussed.