Phase II clinical trials in oncology are used to initially evaluate the therapeutic efficacy of a new treatment. In the past, the total response was a frequently used endpoint to access the effectiveness of the treatment. When the total response is modest, clinicians may also be interested in disease control (defined as the total response or stable disease) since it may better predict clinical outcomes. Thus, formally testing both the total response and disease control in a phase II trial has an important clinical implication. In this paper, we propose a new method to construct optimal subset designs for one-stage and two-stage phase II clinical trials with two binary endpoints, i.e. the total response and disease control. A new set of hypotheses under the framework of intersection-union tests is provided in which the treatment is considered promising if both the total response and disease control are good. We show that the power function for each test in a large family of tests is nondecreasing in both the total response rate and disease control rate; identify the parameter configurations at which the maximum Type I error rate and minimum power are achieved and derive level-$\alpha$ tests. We also provide optimal one-stage designs with the minimum sample size and optimal two-stage designs with the least expected total sample size.

肿瘤学的II期临床试验用于初步评估新疗法的疗效。过去，总反应是获得治疗效果的常用终点。当总反应中等时，临床医生也可能会对疾病控制（定义为总反应或疾病稳定）感兴趣，因为它可以更好地预测临床结果。因此，在II期试验中正式测试总应答和疾病控制具有重要的临床意义。在本文中，我们提出了一种新的方法来构建具有两个二进制终点（即总反应和疾病控制）的一阶段和两阶段II期临床试验的最佳子集设计。在交叉联合检验的框架下，提供了一组新的假设，其中，如果总体反应和疾病控制都良好，则该治疗被认为是有前途的。我们表明，在一个大型测试系列中，每个测试的功效函数在总缓解率和疾病控制率上都没有下降；确定实现最大I型错误率和最小功率的参数配置，并推导等级-$\alpha$测试。我们还提供具有最小样本量的最佳一阶段设计，以及具有最小预期总样本量的最佳两阶段设计。