Bayesian estimation in random effects meta‐analysis using a non‐informative prior

Pooling information from multiple, independent studies (meta-analysis) adds great value to medical research. Random effects models are widely used for this purpose. However, there are many different ways of estimating model parameters, and the choice of estimation procedure may be influential upon the conclusions of the meta-analysis. In this paper, we describe a recently proposed Bayesian estimation procedure and compare it with a profile likelihood method and with the DerSimonian-Laird and Mandel-Paule estimators including the Knapp-Hartung correction. The Bayesian procedure uses a non-informative prior for the overall mean and the between-study standard deviation that is determined by the Berger and Bernardo reference prior principle. The comparison of these procedures focuses on the frequentist properties of interval estimates for the overall mean. The results of our simulation study reveal that the Bayesian approach is a promising alternative producing more accurate interval estimates than those three conventional procedures for meta-analysis. The Bayesian procedure is also illustrated using three examples of meta-analysis involving real data. Copyright © 2016 John Wiley & Sons, Ltd.