Xi Dong, Tamhane Ajit C
IIS Statistical Methodology, Novartis Pharmaceuticals Corporation, One Health Plaza, East Hanover, NJ, 07936, USA.
Biom J. 2015 Jan;57(1):90-107. doi: 10.1002/bimj.201300157. Epub 2014 Oct 30.
Graphical approaches have been proposed in the literature for testing hypotheses on multiple endpoints by recycling significance levels from rejected hypotheses to unrejected ones. Recently, they have been extended to group sequential procedures (GSPs). Our focus in this paper is on the allocation of recycled significance levels from rejected hypotheses to the stages of the GSPs for unrejected hypotheses. We propose a delayed recycling method that allocates the recycled significance level from Stage r onward, where r is prespecified. We show that r cannot be chosen adaptively to coincide with the random stage at which the hypothesis from which the significance level is recycled is rejected. Such an adaptive GSP does not always control the FWER. One can choose r to minimize the expected sample size for a given power requirement. We illustrate how a simulation approach can be used for this purpose. Several examples, including a clinical trial example, are given to illustrate the proposed procedure.
文献中已提出通过将被拒绝假设的显著性水平回用到未被拒绝的假设上来对多个终点进行假设检验的图形方法。最近，它们已被扩展到成组序贯程序（GSPs）。本文我们关注的是将被拒绝假设的回用显著性水平分配到GSPs中未被拒绝假设的各个阶段。我们提出一种延迟回用法，该方法从第r阶段开始分配回用的显著性水平，其中r是预先指定的。我们表明，r不能自适应地选择以与回用显著性水平的假设被拒绝的随机阶段相一致。这样的自适应GSP并不总是能控制族系误差率（FWER）。对于给定的检验效能要求，可以选择r以使预期样本量最小化。我们说明了如何使用模拟方法来实现这一目的。给出了几个例子，包括一个临床试验例子，以说明所提出的程序。
