Bayesian Estimation of the Binomial Parameter in Adaptive Designs With Treatment Selection

Area of Science:

• Biostatistics
• Clinical Trial Design

Background:

• Adaptive multi-arm experiments with treatment selection are prone to bias.
• Existing methods may not fully account for selection bias in binary outcome analysis.

Purpose of the Study:

• To develop a unified Bayesian approach for point and interval estimations in adaptive multi-arm experiments.
• To address and mitigate bias introduced by treatment selection processes.

Main Methods:

• Utilized a comprehensive Bayesian framework with design-dependent priors derived from reference prior theory.
• Applied the method to experiments with binary outcomes and randomized parallel arms, incorporating preplanned interim analyses.
• Evaluated frequentist characteristics of posterior estimators and compared them with alternative methods.

Main Results:

• The proposed Bayesian approach effectively estimates binomial parameters from all accrued observations in the selected best arm.
• The method is robust across various treatment selection rules and can accommodate control arms.
• Introduced tools for evaluating estimation methods in binary data analysis, demonstrating the influence of selection rules and prior corrections.

Conclusions:

• The Bayesian approach offers a unified and practical solution for unbiased estimation in adaptive clinical trials.
• The methodology is easy to implement and aids researchers in treatment selection during interim analyses.
• Provides a framework for robust statistical inference in adaptive experimental designs with binary outcomes.