On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis

TL;DR

This paper investigates how to specify weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis, especially when few studies are involved, providing guidance for better prior choices.

Contribution

It offers new insights and guidance on selecting weakly informative priors for heterogeneity in Bayesian meta-analysis with limited studies.

Findings

Provides a systematic approach for prior specification

Improves inference accuracy in small-study meta-analyses

Guides practitioners on weakly informative prior choices

Abstract

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly, and Bayesian meta-analysis has been suggested as a potential solution. The Bayesian approach, however, requires the sensible specification of prior distributions. While non-informative priors are commonly used for the overall mean effect, the use of weakly informative priors has been suggested for the heterogeneity parameter, in particular in the setting of (very) few studies. To date, however, a consensus on how to generally specify a weakly informative heterogeneity prior is lacking. Here we investigate the problem more closely and provide some guidance on prior specification.