The Bayesian optimal two-stage design for clinical phase II trials based on Bayes factors

2025-11-28

AI Summary

Existing Bayesian sequential designs rely on Monte Carlo simulation for calibration, suffering from poor reproducibility, high computational cost, and reliability dependent on standard error estimation—primarily due to the absence of analytic or efficient numerical calibration methods for Bayesian factor–based designs. Method: For phase II clinical trials, we propose an optimal two-stage Bayesian sequential design grounded in the Bayes factor. We introduce, for the first time, a trinomial tree branching model to analytically characterize how interim analysis affects operating characteristics; combined with numerical optimization, the design directly minimizes expected sample size while guaranteeing a prespecified probability of providing strong evidence against the null hypothesis. Results: Our method exactly recovers Simon’s two-stage design as a special case, outperforms conventional non-sequential Bayesian approaches, eliminates the need for Monte Carlo simulation, and substantially improves computational efficiency, reproducibility, and design reliability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Sequential trial design is an important statistical approach to increase the efficiency of clinical trials. Bayesian sequential trial design relies primarily on conducting a Monte Carlo simulation under the hypotheses of interest and investigating the resulting design characteristics via Monte Carlo estimates. This approach has several drawbacks, namely that replicating the calibration of a Bayesian design requires repeating a possibly complex Monte Carlo simulation. Furthermore, Monte Carlo standard errors are required to judge the reliability of the simulation. All of this is due to a lack of closed-form or numerical approaches to calibrate a Bayesian design which uses Bayes factors. In this paper, we propose the Bayesian optimal two-stage design for clinical phase II trials based on Bayes factors. The optimal two-stage Bayes factor design is a sequential clinical trial design that is built on the idea of trinomial tree branching, a method we propose to correct the resulting design characteristics for introducing a single interim analysis. We build upon this idea to invent a calibration algorithm which yields the optimal Bayesian design that minimizes the expected sample size under the null hypothesis. Examples show that our design recovers Simon's two-stage optimal design as a special case, improves upon non-sequential Bayesian design based on Bayes factors, and can be calibrated quickly, as it makes use only of standard numerical techniques instead of time-consuming Monte Carlo simulations. Furthermore, the design allows to ensure a minimum probability on compelling evidence in favour of the null hypothesis, which is not possible with other designs. As the idea of trinomial tree branching is neither dependent on the endpoint, nor on the use of Bayes factors, the design can therefore be generalized to other settings, too.

Problem

• Lacks closed-form methods for calibrating Bayesian sequential trial designs
• Requires time-consuming Monte Carlo simulations for design calibration
• Existing designs cannot ensure minimum evidence probability for null hypothesis

Innovation

• Bayes factor-based two-stage clinical trial design
• Trinomial tree branching for interim analysis correction
• Numerical calibration algorithm minimizing expected sample size