A note on the empirical Bayes heterogeneity variance estimator in meta-analysis

This paper focuses on the empirical Bayes (EB) or Mandel-Paule estimator of the heterogeneity variance in meta-analysis, which was discussed by Morris and proposed in earlier publications by Mandel and Paule in an inter-laboratory context. The relationship of the EB estimator to other heterogeneity variance estimators typically used in meta-analysis is explored, and approximate variance estimators for the EB estimate of the heterogeneity variance are proposed based on the M-estimation method. Statistical inference for the overall treatment effect using the EB estimator and the proposed standard errors is discussed using two example data sets from meta-analysis applications.