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

Area of Science:

• Biostatistics
• Statistical Modeling
• Meta-Analysis

Background:

• The normal-normal hierarchical model (NNHM) is a standard framework for meta-analysis.
• Standard inference methods perform poorly with few studies.
• Bayesian meta-analysis is a potential solution, requiring careful prior specification.

Purpose of the Study:

• To address the lack of consensus on specifying weakly informative priors for the heterogeneity parameter in Bayesian meta-analysis.
• To provide guidance on prior specification for the heterogeneity parameter within the NNHM framework, especially for meta-analyses with few studies.

Main Methods:

• Investigation of prior specification challenges in Bayesian meta-analysis.
• Focus on the normal-normal hierarchical model (NNHM) with few contributing studies.
• Exploration of weakly informative priors for the heterogeneity parameter.

Main Results:

• Identified poor performance of standard inference with few studies in meta-analysis.
• Highlighted the need for sensible prior distributions in Bayesian meta-analysis.
• Proposed guidance for specifying weakly informative heterogeneity priors in NNHM.

Conclusions:

• Bayesian meta-analysis, particularly using NNHM, is beneficial when study numbers are small.
• Weakly informative priors for heterogeneity are recommended in NNHM with few studies.
• This research offers practical guidance for improved Bayesian meta-analysis prior specification.