Simulation-Free Bayesian Power and Sample Size Calculations for Bayes Factors in Single-Arm Phase II Trials with Binary Endpoints

2026-07-27

AI Summary

This study addresses the limitations of conventional p-value–based sample size calculations in phase II single-arm clinical trials, which fail to quantify the strength of evidence favoring either the null or alternative hypothesis. While existing Bayesian factor approaches offer a principled framework, they rely on computationally intensive Monte Carlo simulations. To overcome this, the authors propose an efficient analytical method that combines numerical integration with pre-specified Bayesian factor thresholds to directly calibrate Bayesian and frequentist operating characteristics—including power, type I error, and the probability of strong evidence in favor of the null hypothesis. This is the first approach enabling Bayesian factor–driven sample size determination for single-arm trials with binary endpoints without simulation, thereby harmonizing Bayesian and frequentist metrics while substantially improving computational efficiency. The method’s validity is demonstrated through two oncology case studies and implemented in the R package bfbin2arm, offering a practical tool for Bayesian adaptive trial design.

Abstract

Bayes factors provide a coherent Bayesian measure of evidence for competing hypotheses and have recently been used as the basis for single-arm phase II trial designs with binary endpoints. In contrast to classical power analyses based on test statistics and p-values, Bayes-factor based sample size calculations target high probabilities of obtaining compelling evidence either for a relevant treatment effect or for the null hypothesis, given pre-specified Bayes-factor thresholds. This paper explains how to design single-arm phase II binomial trials using Bayes factors with a focus on simulation-free calibration of Bayesian and frequentist power, type-I-error, and the probability of compelling evidence for the null. Two oncology-motivated examples illustrate the approach and are implemented in the bfbin2arm R package, with code provided in an appendix. The methodology fits naturally into current efforts to innovate and modernize clinical trial design through Bayesian and adaptive methods.

Problem

• Bayes factors
• sample size calculation
• single-arm phase II trials
• binary endpoints
• Bayesian power

Innovation

• Bayes factor
• simulation-free
• sample size calculation
• single-arm phase II trial
• binary endpoint