Extending DerSimonian and Laird's methodology to perform multivariate random effects meta-analyses

Multivariate meta-analysis is increasingly used in medical statistics. In the univariate setting, the non-iterative method proposed by DerSimonian and Laird is a simple and now standard way of performing random effects meta-analyses. We propose a natural and easily implemented multivariate extension of this procedure which is accessible to applied researchers and provides a much less computationally intensive alternative to existing methods. In a simulation study, the proposed procedure performs similarly in almost all ways to the more established iterative restricted maximum likelihood approach. The method is applied to some real data sets and an extension to multivariate meta-regression is described.