Meta-analysis with Jeffreys priors: Empirical frequentist properties

Area of Science:

• Biostatistics
• Statistical Modeling

Background:

• Frequentist meta-analysis methods can produce wide confidence intervals and biased heterogeneity estimates in small studies.
• Bayesian methods offer an alternative, particularly when using specific priors like the Jeffreys prior.

Purpose of the Study:

• To evaluate the frequentist performance of Bayesian methods employing the invariant Jeffreys prior for random-effects meta-analysis.
• To compare these Bayesian approaches against established frequentist methods in small meta-analyses.

Main Methods:

• A large simulation study was conducted to assess Bayesian methods using two forms of the Jeffreys prior (Jeffreys1 and Jeffreys2).
• Performance was evaluated for point and interval estimation of both the mean and heterogeneity parameters.
• Methods were compared against optimal frequentist approaches for small meta-analyses of binary and continuous outcomes.

Main Results:

• For small meta-analyses with binary outcomes, the Jeffreys2 prior demonstrated advantages in point and interval estimation of the mean, improving efficiency and frequentist coverage.
• For small meta-analyses with continuous outcomes, standard frequentist methods were found to be superior.
• The optimal method for estimating heterogeneity depended on the specific heterogeneity values.

Conclusions:

• The Jeffreys2 Bayesian prior shows promise for enhancing meta-analysis of binary outcomes, particularly in small sample sizes.
• Frequentist methods remain the recommended approach for small meta-analyses of continuous data.
• The bayesmeta R package implements these Jeffreys priors and extends them to meta-regression.