Multivariate meta-analysis on correlation coefficients

Abstract

In this paper a large sample test is derived for testing the homogeneity of correlation matrices based on Fisher’s z-transformation, and it is demonstrated that the test maintains the type I error rate satisfactorily. Towards this, the asymptotic joint distribution of the sample correlations is derived when the samples come from a multivariate population that could be non-normal. Assuming that the homogeneity hypothesis holds, methodology is provided to perform a meta-analysis of the common correlation matrix. An application to the correlations among the three cholesterol related variables: low-density lipoprotein (LDL), non-high density lipoprotein (NHDL) and Apolipoprotein B (APOB), in an investigation of the efficacy of cholesterol lowering drug, Ezetimibe, in combination with statins in patients with hypercholesterolemia, is provided.