Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models

Area of Science:

• Biostatistics
• Statistical Modeling
• Meta-Analysis

Background:

• Accurate estimation of meta-parameters in meta-analysis relies on understanding between-sample heterogeneity.
• Bayesian meta-analysis for binary data uses sample clustering and model selection to quantify heterogeneity.
• Bayesian model averaging is employed for meta-parameter estimation.

Purpose of the Study:

• To investigate the impact of different priors on Bayesian meta-analysis models for binary data.
• To evaluate the performance of four alternative model priors under varying study numbers and sample sizes.
• To assess the sensitivity of meta-parameter estimation to the choice of model prior.

Main Methods:

• Proposed a Bayesian meta-analysis framework for binary data incorporating sample clustering and model selection.
• Focused on the influence of priors over the cluster models, considering four distinct alternatives.
• Conducted frequentist validation using simulated data to analyze prior distribution properties across different scenarios.

Main Results:

• Posterior model probabilities are highly sensitive to the chosen model prior, underscoring the importance of prior selection.
• Hierarchical Poisson and uniform priors perform well under homogeneity or large sample sizes.
• The uniform prior demonstrates superior ability in detecting intermediate models, even with small sample sizes and few studies.

Conclusions:

• The selection of an appropriate model prior is critical for robust Bayesian meta-analysis.
• The uniform prior offers advantages in identifying complex heterogeneity structures.
• Real-data example confirms the significant influence of model priors on meta-parameter estimation.