Bayesian sample size determination using commensurate priors to leverage pre-experimental data.

Area of Science:

• Biostatistics
• Experimental Design
• Bayesian Inference

Background:

• Traditional sample size calculations often neglect valuable pre-experimental data.
• Incorporating prior information can lead to more efficient and robust experimental designs.
• Bayesian methods offer a flexible framework for integrating diverse data sources.

Purpose of the Study:

• To develop Bayesian sample size formulae for two-group comparisons.
• To enable the incorporation of pre-experimental information from multiple sources into prior distributions.
• To provide methods for controlling aspects of the posterior distribution for sample size determination.

Main Methods:

• Development of commensurate predictive priors for information borrowing.
• Utilizing Gamma mixture priors on precisions to model parameter commensurability.
• Sample size determination based on criteria controlling posterior distribution properties (e.g., coverage probability, region length).
• Application to comparisons of normal means, proportions, and event times, including unknown nuisance parameters.

Main Results:

• Formulation of Bayesian sample size calculations applicable to various data types.
• Demonstration of exact solutions for most criteria and a search procedure for intractable cases.
• Successful illustration in clinical trial design, leveraging pre-trial expert opinion.
• Comprehensive performance evaluation of the proposed Bayesian methodology.

Conclusions:

• The proposed Bayesian approach provides robust sample size determination by effectively utilizing prior information.
• This methodology enhances the design of experiments, particularly in complex scenarios like clinical trials with rare diseases.
• The flexible framework accommodates various data types and unknown parameters, offering practical advantages.