Two-arm phase II clinical trials often benefit from an interim analysis that allows early stopping for futility, but Bayesian calibration of such designs is usually based on computationally intensive Monte Carlo simulation. In this work, a simulation-free methodology is developed to obtain Bayesian optimal two-stage designs in two-arm phase II trials with binary endpoints using Bayes factors as the primary measure of evidence. Building on recent matrix-search methods for fixed-sample two-arm Bayes factor designs and earlier correction formulas for one-arm two-stage designs, the proposed approach derives exact expressions for the operating characteristics of a two-stage two-arm design with a single futility interim. Bayesian power and type-I error are obtained by correcting the corresponding fixed-sample quantities for trajectories that would have been removed by early stopping, yielding a fully numerical calibration procedure that avoids Monte Carlo error entirely. The resulting method searches over admissible interim and final sample sizes to identify the optimal design that satisfies target constraints on Bayesian power, type-I error, and the probability of compelling evidence in favour of the null hypothesis, while minimizing the expected sample size under the null hypothesis. The methodology is illustrated in realistic phase II settings, including a detailed re-analysis of the riociguat trial in systemic sclerosis. Overall, the approach extends simulation-free Bayes factor design methodology to the practically important setting of two-arm two-stage phase II trials and provides a transparent basis for Bayesian design calibration and sensitivity analysis.

翻译：两臂II期临床试验常通过期中分析实现因无效而提前终止，但此类设计的贝叶斯校准通常依赖于计算密集的蒙特卡洛模拟。本研究提出一种免模拟方法，以贝叶斯因子作为主要证据度量，构建二项终点两臂II期试验的贝叶斯最优两阶段设计。基于固定样本两臂贝叶斯因子设计的近期矩阵搜索方法以及单臂两阶段设计的早期校正公式，本方法推导出含单次无效性期中分析的两阶段两臂设计操作特征精确表达式。通过校正相应固定样本量下会被早期终止的轨迹，获得贝叶斯检验效能与I类错误率，从而建立完全数值化校准流程，彻底规避蒙特卡洛误差。该方法在所有可接受的期中及最终样本量范围内进行搜索，识别出满足贝叶斯检验效能、I类错误率及支持零假设确凿证据概率等目标约束的最优设计，同时最小化零假设下的期望样本量。通过真实II期试验场景（包括对系统性硬化症中riociguat试验的详细再分析）验证该方法有效性。总体而言，本研究将免模拟贝叶斯因子设计方法论拓展至具有重要实践意义的两臂两阶段II期试验场景，为贝叶斯设计校准与敏感性分析提供了透明基础。