Bayesian sample size determination using commensurate priors to leverage preexperimental data.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Methodology

Background:

• Traditional sample size calculations often neglect valuable pre-experimental data.
• Incorporating prior information can lead to more efficient and informative experimental designs.

Purpose of the Study:

• To develop Bayesian sample size formulae for two-group comparisons.
• To enable robust incorporation of pre-experimental information from multiple sources.
• To provide methods applicable to normal means, proportions, and event times.

Main Methods:

• Utilizes commensurate predictive priors for information borrowing.
• Employs Gamma mixture priors on precisions to model parameter commensurability.
• Determines sample sizes based on controlling posterior distribution properties (e.g., coverage, length).
• Handles unknown nuisance parameters by specifying prior distributions from pre-experimental data.

Main Results:

• Develops exact solutions for Bayesian sample size determination under various criteria.
• Describes a search procedure for cases lacking closed-form expressions.
• Demonstrates application in clinical trial design, including rare-disease scenarios with expert priors.

Conclusions:

• The proposed Bayesian methodology offers a flexible framework for sample size determination.
• Leveraging pre-experimental data enhances the efficiency and robustness of experimental design.
• The methods are applicable across diverse statistical comparisons and experimental settings.