Zhu Han, Yu Qingzhao, Mercante Donald E
Pharmaceutical Product Development, LLC., Austin, TX, USA.
Biostatistics Program, School of Public Health, LSUHSC, New Orleans, LA, USA.
Pharm Stat. 2017 May;16(3):192-200. doi: 10.1002/pst.1805. Epub 2017 Mar 2.
Several researchers have proposed solutions to control type I error rate in sequential designs. The use of Bayesian sequential design becomes more common; however, these designs are subject to inflation of the type I error rate. We propose a Bayesian sequential design for binary outcome using an alpha-spending function to control the overall type I error rate. Algorithms are presented for calculating critical values and power for the proposed designs. We also propose a new stopping rule for futility. Sensitivity analysis is implemented for assessing the effects of varying the parameters of the prior distribution and maximum total sample size on critical values. Alpha-spending functions are compared using power and actual sample size through simulations. Further simulations show that, when total sample size is fixed, the proposed design has greater power than the traditional Bayesian sequential design, which sets equal stopping bounds at all interim analyses. We also find that the proposed design with the new stopping for futility rule results in greater power and can stop earlier with a smaller actual sample size, compared with the traditional stopping rule for futility when all other conditions are held constant. Finally, we apply the proposed method to a real data set and compare the results with traditional designs.
几位研究人员提出了在序贯设计中控制I型错误率的解决方案。贝叶斯序贯设计的应用变得更加普遍；然而，这些设计存在I型错误率膨胀的问题。我们提出了一种用于二元结局的贝叶斯序贯设计，使用α消耗函数来控制总体I型错误率。给出了计算所提出设计的临界值和检验效能的算法。我们还提出了一种新的无效性停止规则。进行了敏感性分析，以评估先验分布参数和最大总样本量的变化对临界值的影响。通过模拟，使用检验效能和实际样本量对α消耗函数进行了比较。进一步的模拟表明，当总样本量固定时，所提出的设计比传统的贝叶斯序贯设计具有更高的检验效能，传统设计在所有期中分析中设置相等的停止界限。我们还发现，与在所有其他条件保持不变时的传统无效性停止规则相比，所提出的带有新的无效性停止规则的设计具有更高的检验效能，并且可以以更小的实际样本量更早地停止。最后，我们将所提出的方法应用于一个真实数据集，并将结果与传统设计进行比较。
