A re-evaluation of random-effects meta-analysis.

Area of Science:

• Statistics
• Biostatistics
• Medical Research Methodology

Background:

• Unexplained heterogeneity in meta-analysis is often addressed using random-effects models, assuming study effects derive from a normal distribution.
• Current random-effects meta-analyses may not consistently provide essential findings for estimation, prediction, and hypothesis testing.

Purpose of the Study:

• To critically examine the justification and interpretation of random-effects models in meta-analysis.
• To explore alternative statistical approaches, including distribution-free, classical, and Bayesian methods, for handling unexplained heterogeneity.
• To propose improvements for both classical and Bayesian meta-analysis, enhancing prediction and uncertainty quantification.

Main Methods:

• Comparative analysis of random-effects models versus distribution-free, classical, and Bayesian approaches.
• Investigation into inference for the mean versus the entire distribution within random-effects models.
• Development and application of a novel prediction interval for classical meta-analysis and extensions for Bayesian meta-analysis.

Main Results:

• Random-effects meta-analyses may fall short in delivering crucial results, necessitating alternative methodologies.
• Bayesian approaches offer advantages in fully capturing uncertainty, particularly for predictive inference.
• Classical methods can be enhanced with new prediction intervals, and Bayesian methods can be extended for improved practice.

Conclusions:

• The Bayesian approach provides a robust framework for handling uncertainty in meta-analysis, though computational demands and prior sensitivity are considerations.
• Classical meta-analysis can be improved with the proposed prediction interval.
• Extensions to Bayesian meta-analysis are suggested to enhance its practical application, illustrated by an eating disorders study example.