• Between-study covariance matrix;
  • Heterogeneity;
  • Method of moments estimator;
  • Multivariate meta-analysis;
  • Random effect model

Summary Meta-analysis is a powerful approach to combine evidence from multiple studies to make inference about one or more parameters of interest, such as regression coefficients. The validity of the fixed effect model meta-analysis depends on the underlying assumption that all studies in the meta-analysis share the same effect size. In the presence of heterogeneity, the fixed effect model incorrectly ignores the between-study variance and may yield false positive results. The random effect model takes into account both within-study and between-study variances. It is more conservative than the fixed effect model and should be favored in the presence of heterogeneity. In this paper, we develop a noniterative method of moments estimator for the between-study covariance matrix in the random effect model multivariate meta-analysis. To our knowledge, it is the first such method of moments estimator in the matrix form. We show that our estimator is a multivariate extension of DerSimonian and Laird’s univariate method of moments estimator, and it is invariant to linear transformations. In the simulation study, our method performs well when compared to existing random effect model multivariate meta-analysis approaches. We also apply our method in the analysis of a real data example.