Xu Xun, Yuan Ying, Lee J Jack
Department of Biostatistics and Data Science, School of Public Health, University of Texas, Houston 77030, TX, United States; Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston 77030, TX, United States.
Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston 77030, TX, United States.
Contemp Clin Trials. 2025 Jul;154:107939. doi: 10.1016/j.cct.2025.107939. Epub 2025 May 3.
Bayesian optimal phase II (BOP2) design serves to screen the efficacy and/or toxicity of a new treatment, determining whether it warrants further development. When employing the BOP2 design to jointly monitor the efficacy-toxicity tradeoff, the correlation between them plays an important role in achieving good performance on the statistical power while controlling Type I error. However, in practice, this correlation is usually unknown, posing challenges in the trial design and data analysis. In this study, the phi coefficient is chosen to measure the correlation. The influence of the efficacy-toxicity tradeoff on the power of BOP2 designs is first evaluated in the design stage and the data analysis stage, separately, then, overall considerations are given. In the design stage, we observe that the power increases as phi increases. Upon performing the sensitivity analysis in the data analysis stage, we find that the power decreases as phi increases given the pre-determined stopping boundaries. Simulations demonstrate instances of overpowering with inflated Type I error when the assumed phi in the design stage exceeds the true phi in the data analysis stage. Conversely, underpowering occurs with controlled Type I error when the assumed phi is lower than the true phi in the data analysis stage. To obtain the power under controlled Type I error in design, we recommend the use of independent correlation when the efficacy and toxicity are likely to be positively correlated. Conversely, for cases of likely negative correlation, taking a phi value close to the lower bound is advisable.
贝叶斯最优II期（BOP2）设计用于筛选新疗法的疗效和/或毒性，以确定其是否值得进一步开发。在采用BOP2设计联合监测疗效-毒性权衡时，它们之间的相关性对于在控制I型错误的同时实现良好的统计功效起着重要作用。然而，在实际中，这种相关性通常是未知的，这给试验设计和数据分析带来了挑战。在本研究中，选择phi系数来衡量相关性。首先分别在设计阶段和数据分析阶段评估疗效-毒性权衡对BOP2设计功效的影响，然后进行综合考虑。在设计阶段，我们观察到功效随着phi的增加而增加。在数据分析阶段进行敏感性分析时，我们发现给定预先确定的停止边界，功效随着phi的增加而降低。模拟表明，当设计阶段假设的phi超过数据分析阶段的真实phi时，会出现I型错误膨胀导致的功效过高情况。相反，当假设的phi低于数据分析阶段的真实phi时，会出现I型错误得到控制但功效不足的情况。为了在设计中获得I型错误得到控制时的功效，我们建议在疗效和毒性可能呈正相关时使用独立相关性。相反，对于可能呈负相关的情况，可取接近下限的phi值。
