Bayesian sample size calculations in clinical trials usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power often lack closed-form or approximate numerical solutions. In this paper, we focus on power and sample size calculations for Bayes factors in the two-arm binomial setting of phase II trials. We cover point-null versus composite and directional hypothesis tests, derive the corresponding Bayes factors, and discuss relevant aspects to consider when pursuing Bayesian design of experiments with the introduced approach. Based on these Bayes factors, we propose a numerical approach which allows to determine the necessary sample size to obtain prespecified bounds of Bayesian power and type-I-error rate in a computationally efficient way. Our method does not rely on Monte Carlo simulations and instead solely relies on standard numerical methods. Real-world examples of phase II trials from oncology and autoimmune diseases illustrate the advantage of the proposed calibration method. In summary, our approach allows for a Bayes-frequentist compromise by providing a Bayesian analogue to a frequentist power analysis for various Bayes factors in the two-arm binomial setting of a phase II clinical trial. The methods are implemented in our R package bfbin2arm.

翻译：在临床试验中，贝叶斯样本量计算通常依赖于复杂的蒙特卡洛模拟。获取贝叶斯假阳性率与功效的边界往往缺乏闭式解或近似数值解。本文聚焦于II期试验双臂二项分布设定下贝叶斯因子的功效与样本量计算。我们涵盖点零假设与复合及方向性假设检验，推导相应的贝叶斯因子，并讨论采用所提方法进行贝叶斯实验设计时需考虑的相关问题。基于这些贝叶斯因子，我们提出一种数值方法，能以计算高效的方式确定获得预设贝叶斯功效与I类错误率边界所需的样本量。该方法不依赖蒙特卡洛模拟，仅基于标准数值方法。来自肿瘤学和自身免疫性疾病领域的II期试验实际案例展示了所提校准方法的优势。总之，我们的方法通过为II期临床试验双臂二项分布设定下的各类贝叶斯因子提供频率学派功效分析的贝叶斯类比，实现了贝叶斯与频率学派的折衷。相关方法已在我们开发的R包bfbin2arm中实现。