Bayesian monitoring strategies based on predictive probabilities are widely used in phase II clinical trials that involve a single efficacy binary variable. The essential idea is to control the predictive probability that the trial will show a conclusive result at the scheduled end of the study, given the information at the interim stage and the prior beliefs. In this paper, we present an extension of this approach to incorporate toxicity considerations in single-arm phase II trials. We consider two binary endpoints representing response and toxicity of the experimental treatment and define the result as successful at the conclusion of the study if the posterior probability of an high efficacy and that of a small toxicity are both sufficiently large. At any interim look, the Multinomial-Dirichlet distribution provides the predictive probability of each possible combination of future efficacy and toxicity outcomes. It is exploited to obtain the predictive probability that the trial will yield a positive outcome, if it continues to the planned end. Different possible interim situations are considered to investigate the behaviour of the proposed predictive rules and the differences with the monitoring strategies based on posterior probabilities are highlighted. Simulation studies are also performed to evaluate the frequentist operating characteristics of the proposed design and to calibrate the design parameters.

基于预测概率的贝叶斯监测策略已广泛用于涉及单个功效二进制变量的II期临床试验中。基本思想是控制中间阶段的信息和先前的信念，从而控制试验在预定的研究结束时显示结论性结果的预测可能性。在本文中，我们提出了这种方法的扩展，将毒性考虑因素纳入了单臂II期试验。我们认为两个二进制终点分别代表实验治疗的反应和毒性，并且如果高疗效和小毒性的后验概率都足够大，则在研究结束时将结果定义为成功。在任何临时外观下，多项式-狄利克雷分布提供了未来功效和毒性结果的每种可能组合的预测概率。如果可以继续进行到计划的结束，就可以利用该方法来获得试验将产生积极结果的预测概率。考虑了不同的可能临时情况，以调查所提出的预测规则的行为，并强调了与基于后验概率的监控策略的差异。还进行了仿真研究，以评估所提出设计的惯常操作特性并校准设计参数。考虑了不同的可能临时情况，以调查所提出的预测规则的行为，并强调了与基于后验概率的监控策略的差异。还进行了仿真研究，以评估所提出设计的惯常操作特性并校准设计参数。考虑了不同的可能临时情况，以调查所提出的预测规则的行为，并强调了与基于后验概率的监视策略的差异。还进行了仿真研究，以评估所提出设计的惯常操作特性并校准设计参数。