Bayesian consensus-based sample size criteria for binomial proportions.

Area of Science:

• Statistics
• Bayesian Inference
• Statistical Methodology

Background:

• Existing sample size methods include frequentist power calculations and Bayesian approaches using credible intervals.
• Bayesian methods incorporate prior information, but the choice of prior can be challenging due to differing interpretations of evidence.
• Robust Bayesian designs can accommodate divergent opinions using mixtures or contaminated priors, but methods for a 'community of priors' are lacking.

Purpose of the Study:

• To develop novel sample size methods that account for variability in prior opinions within a Bayesian framework.
• To ensure sufficient sample size for data to overwhelm diverse prior views and achieve posterior agreement.
• To provide a framework for sample size determination that addresses the 'community of priors' concept.

Main Methods:

• Development of Bayesian sample size calculation methods that consider a range of plausible prior densities.
• Utilizing the concept of inducing posterior agreement to a prespecified degree.
• Application of methods to one- and two-sample binomial outcome scenarios.

Main Results:

• The proposed methods provide sample sizes required to achieve consensus across a 'community of priors'.
• Comparison of sample sizes derived from considering a family of priors versus traditional interval-based Bayesian criteria.
• Demonstration of the methods' utility through prototypic examples for binomial data.

Conclusions:

• The developed methods offer a robust approach to sample size determination in the presence of diverse prior beliefs.
• These methods enhance Bayesian experimental design by ensuring sufficient data to bridge divergent prior opinions.
• The findings contribute to more reliable statistical inference by explicitly addressing prior uncertainty.