Schlömer Patrick, Brannath Werner
Department of Mathematics, University of Bremen, Bremen, Germany.
Stat Med. 2013 Dec 10;32(28):4875-89. doi: 10.1002/sim.5950. Epub 2013 Aug 23.
In the recent years there have been numerous publications on the design and the analysis of three-arm 'gold standard' noninferiority trials. Whenever feasible, regulatory authorities recommend the use of such three-arm designs including a test treatment, an active control, and a placebo. Nevertheless, it is desirable in many respects, for example, ethical reasons, to keep the placebo group size as small as possible. We first give a short overview on the fixed sample size design of a three-arm noninferiority trial with normally distributed outcomes and a fixed noninferiority margin. An optimal single stage design is derived that should serve as a benchmark for the group sequential designs proposed in the main part of this work. It turns out, that the number of patients allocated to placebo is substantially low for the optimal design. Subsequently, approaches for group sequential designs aiming to further reduce the expected sample sizes are presented. By means of choosing different rejection boundaries for the respective null hypotheses, we obtain designs with quite different operating characteristics. We illustrate the approaches via numerical calculations and a comparison with the optimal single stage design. Furthermore, we derive approximately optimal boundaries for different goals, for example, to reduce the overall average sample size. The results show that the implementation of a group sequential design further improves the optimal single stage design. Besides cost and time savings, the possible early termination of the placebo arm is a key advantage that could help to overcome ethical concerns.
近年来，有许多关于三臂“金标准”非劣效性试验设计与分析的出版物。只要可行，监管机构就建议使用这种三臂设计，包括一个试验治疗组、一个活性对照组和一个安慰剂组。然而，出于多方面的考虑，例如伦理原因，希望将安慰剂组的样本量尽可能缩小。我们首先简要概述具有正态分布结果和固定非劣效性界值的三臂非劣效性试验的固定样本量设计。我们推导了一种最优单阶段设计，该设计应作为本文主要部分提出的组序贯设计的基准。结果表明，对于最优设计，分配到安慰剂组的患者数量相当少。随后，我们提出了旨在进一步减少预期样本量的组序贯设计方法。通过为各个原假设选择不同的拒绝边界，我们得到了具有截然不同操作特征的设计。我们通过数值计算以及与最优单阶段设计的比较来说明这些方法。此外，我们还为不同目标推导了近似最优边界，例如减少总体平均样本量。结果表明，实施组序贯设计进一步改进了最优单阶段设计。除了节省成本和时间外，安慰剂组可能提前终止是一个关键优势，有助于克服伦理问题。
