Due to ethical and economical reasons, sequential single-arm trial designs are used for assessing the therapeutic efficacy of new treatments in phase II trials. Simon's 2-stage design and Lan-DeMets' $\alpha$-spending function method with O'Brien-Fleming type are widely recognized as the traditional methods for futility stopping and efficacy stopping, respectively. These methods have two practical problems, which are the difficulty of interpretation for stopping under staggered entry and the inflation of error rate due to a small-sample trial. In this research, we propose the exact sequential design making the threshold value for efficacy fixed, and compare with traditional designs in sample size. Since the maximum sample size and average sample number of the proposed design are generally smaller than those of traditional designs containing fixed design, the proposed design is expected to be enrolled fewer subjects. In addition, we evaluate several kinds of point estimators and confidence intervals at the end of trials in the proposed design. If one is concerned with bias, the bias-adjusted estimator may be better. As for a confidence interval, the mid-p approach will be a good choice.

翻译：出于伦理和经济原因，顺序单臂试验设计被用于II期试验中评估新治疗方法的疗效。Simon的两阶段设计和采用O'Brien-Fleming类型的Lan-DeMets α花费函数方法分别被广泛认为是无效性停止和有效性停止的传统方法。这些方法存在两个实际问题：交错入组条件下停止决策的解释困难，以及小样本试验导致的误差率膨胀。在本研究中，我们提出了一种使疗效阈值固定的精确顺序设计，并与传统设计在样本量上进行了比较。由于所提设计的最大样本量和平均样本数通常小于包括固定设计在内的传统设计，预计所提设计能招募更少的受试者。此外，我们评估了所提设计在试验结束时几种点估计量和置信区间的性能。若关注偏差，偏差校正估计量可能更优；对于置信区间，mid-p方法将是良好的选择。