Bayesian Methods for Meta-Analyses of Binary Outcomes: Implementations, Examples, and Impact of Priors

Area of Science:

• Statistics
• Biostatistics
• Medical Research

Background:

• Frequentist meta-analysis methods rely on potentially unrealistic assumptions.
• Bayesian methods offer flexibility by incorporating prior information but require complex statistical coding.
• User-friendly software for frequentist approaches limits the adoption of Bayesian methods.

Purpose of the Study:

• To provide a practical review of Bayesian meta-analysis implementations.
• To demonstrate Bayesian methods for meta-analyses focusing on odds ratios for binary outcomes.
• To summarize and illustrate various prior distribution choices for between-studies heterogeneity variance.

Main Methods:

• Focus on Bayesian meta-analysis for binary outcomes (odds ratio).
• Summarize common prior distributions for heterogeneity variance: inverse-gamma, uniform, half-normal, and log-normal.
• Illustrate methods with five real-world examples and provide statistical code.

Main Results:

• Bayesian methods can yield different results from frequentist approaches, impacting statistical significance.
• Prior choice significantly influences results with limited data, necessitating sensitivity analyses.
• Convergence issues may arise with sparse data, requiring careful examination and interpretation.

Conclusions:

• Bayesian meta-analysis is a reliable alternative when frequentist assumptions are violated.
• Practical implementation guidance and code are provided for practitioners.
• Careful consideration of priors and convergence is crucial for accurate Bayesian meta-analysis.