Bayesian estimation of the binomial parameter in sequential experiments

Area of Science:

• Statistics
• Biostatistics
• Clinical Trial Methodology

Background:

• Group sequential designs are crucial for adaptive clinical trials, allowing early termination based on accumulating data.
• Accurate estimation of treatment effects (binomial parameter) is essential for decision-making in these trials.
• Traditional methods may not fully leverage design information in the estimation process.

Purpose of the Study:

• To develop and present an objective Bayesian approach for estimating the binomial parameter in group sequential experiments.
• To establish a theoretical framework justifying the incorporation of experimental design into Bayesian priors.
• To propose a unified method for point and interval estimation with good frequentist properties.

Main Methods:

• Derivation of design-dependent priors, including those based on Jeffreys criterion and reference prior theory.
• Development of a theoretical framework for Bayesian justification of design-dependent priors.
• Application of a generalized reference prior for comprehensive estimation in group sequential designs.

Main Results:

• The proposed Bayesian approach provides accurate point and interval estimates for the binomial parameter.
• Posterior estimators demonstrate favorable frequentist properties when compared to existing methods.
• The impact of prior correction on posterior estimates is analyzed across three classical clinical trial designs.

Conclusions:

• The objective Bayesian approach with design-dependent priors offers a robust and unified framework for group sequential experiments.
• This method provides a theoretically sound and practically advantageous alternative for statistical inference.
• The approach is suggested as a potential default for estimation following the termination of sequential trials.