We propose a Bayesian optimal phase 2 design for jointly monitoring efficacy and toxicity, referred to as BOP2-TE, to improve the operating characteristics of the BOP2 design proposed by Zhou et al. (2017). BOP2-TE utilizes a Dirichlet-multinomial model to jointly model the distribution of toxicity and efficacy endpoints, making go/no-go decisions based on the posterior probability of toxicity and futility. In comparison to the original BOP2 and other existing designs, BOP2-TE offers the advantage of providing rigorous type I error control in cases where the treatment is toxic and futile, effective but toxic, or safe but futile, while optimizing power when the treatment is effective and safe. As a result, BOP2-TE enhances trial safety and efficacy. We also explore the incorporation of BOP2-TE into multiple-dose randomized trials for dose optimization, and consider a seamless design that integrates phase I dose finding with phase II randomized dose optimization. BOP2-TE is user-friendly, as its decision boundary can be determined prior to the trial's onset. Simulations demonstrate that BOP2-TE possesses desirable operating characteristics. We have developed a user-friendly web application as part of the BOP2 app, which is freely available at www.trialdesign.org.

翻译：我们提出了一种用于联合监测疗效与毒性的贝叶斯最优II期设计，称为BOP2-TE，旨在改进Zhou等人（2017）提出的BOP2设计的操作特性。BOP2-TE采用狄利克雷-多项模型联合建模毒性终点与疗效终点的分布，并基于毒性与无效性的后验概率作出继续/终止决策。相较于原始BOP2设计及其他现有设计，BOP2-TE的优势在于：当治疗手段具有毒性且无效、有效但有毒、或安全但无效时，能提供严格的I类错误控制；同时在治疗有效且安全的情况下优化检验效能。因此，BOP2-TE提升了试验的安全性与有效性。我们还探讨了将BOP2-TE应用于多剂量随机试验以进行剂量优化，并考虑了一种无缝整合I期剂量探索与II期随机剂量优化的设计方案。BOP2-TE具有用户友好性，其决策边界可在试验开始前预先确定。模拟研究表明BOP2-TE具备优良的操作特性。我们已开发了用户友好的网络应用程序作为BOP2应用的一部分，该程序可在www.trialdesign.org免费获取。