Prior Effective Sample Size in Conditionally Independent Hierarchical Models

Area of Science:

• Statistics
• Biostatistics
• Bayesian Inference

Background:

• Prior effective sample size (ESS) is crucial for Bayesian analysis.
• Existing ESS definitions are limited for hierarchical models.

Purpose of the Study:

• To propose two novel definitions of prior ESS for conditionally independent hierarchical models.
• To extend the concept of prior ESS to more complex Bayesian structures.

Main Methods:

• Developed two alternative definitions for prior ESS.
• Focused on first-level and second-level priors within hierarchical models.
• Applied methods to various clinical trial examples.

Main Results:

• The proposed prior ESS definitions are suitable for hierarchical models.
• The methods yield intuitively correct answers in applicable scenarios.
• Demonstrated utility in single-arm, dose-finding, and multicenter randomized trials.

Conclusions:

• The new prior ESS definitions enhance Bayesian analysis for hierarchical models.
• These methods provide valuable insights into prior information quantification.
• Applicable to diverse clinical research settings, improving statistical rigor.