Dr. Adam Hafdahl

Department of Mathematics, Washington University

Title: Random-effects meta-analysis of correlation matrices: Refinements and evaluation

ABSTRACT: I will discuss the multivariate meta-analysis problem of combining heterogeneous correlation matrices across independent studies. A conventional fixed-effects approach, via generalized least squares, improves appreciably with two refinements: using initial estimates of the common correlations in the conditional covariance matrices used as (inverse) weight matrices, and analyzing Fisher z-transformed correlations. The present work extends these refinements to the random-effects case where both the between-studies mean and covariance-component matrix of correlation parameters are estimated. Complications include what to substitute for each study's correlation parameters in its conditional covariance matrix, and how to express Fisher-z results in the Pearson-r metric. Proposed strategies were evaluated in a Monte Carlo study. In terms of elementwise estimation and inference, all five refined methods outperformed the conventional approach - analyze Pearson-r correlations with conditional covariances based on observed correlations -- especially with many small studies. The best method depended on whether mean correlations or variance components were the focal parameter.