Summarizing empirical information on between‐study heterogeneity for Bayesian random‐effects meta‐analysis

Abstract

In Bayesian meta‐analysis, the specification of prior probabilities for the between‐study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the set‐up of such prior distributions, the consultation of available empirical data on a set of relevant past analyses sometimes plays a role. How exactly to summarize historical data sensibly is not immediately obvious; in particular, the investigation of an empirical collection of heterogeneity estimates will not target the actual problem and will usually only be of limited use. The commonly used normal‐normal hierarchical model for random‐effects meta‐analysis is extended to infer a heterogeneity prior. Using an example data set, we demonstrate how to fit a distribution to empirically observed heterogeneity data from a set of meta‐analyses. Considerations also include the choice of a parametric distribution family. Here, we focus on simple and readily applicable approaches to then translate these into (prior) probability distributions.