Kimani Peter K, Todd Susan, Stallard Nigel
Warwick Medical School, The University of Warwick, Coventry, CV4 7AL, U.K.
Department of Mathematics and Statistics, The University of Reading, RG6 6AX, Reading, U.K.
Stat Med. 2015 Aug 15;34(18):2581-601. doi: 10.1002/sim.6506. Epub 2015 Apr 22.
During the development of new therapies, it is not uncommon to test whether a new treatment works better than the existing treatment for all patients who suffer from a condition (full population) or for a subset of the full population (subpopulation). One approach that may be used for this objective is to have two separate trials, where in the first trial, data are collected to determine if the new treatment benefits the full population or the subpopulation. The second trial is a confirmatory trial to test the new treatment in the population selected in the first trial. In this paper, we consider the more efficient two-stage adaptive seamless designs (ASDs), where in stage 1, data are collected to select the population to test in stage 2. In stage 2, additional data are collected to perform confirmatory analysis for the selected population. Unlike the approach that uses two separate trials, for ASDs, stage 1 data are also used in the confirmatory analysis. Although ASDs are efficient, using stage 1 data both for selection and confirmatory analysis introduces selection bias and consequently statistical challenges in making inference. We will focus on point estimation for such trials. In this paper, we describe the extent of bias for estimators that ignore multiple hypotheses and selecting the population that is most likely to give positive trial results based on observed stage 1 data. We then derive conditionally unbiased estimators and examine their mean squared errors for different scenarios.
在新疗法的研发过程中，测试一种新治疗方法是否比现有治疗方法对所有患有某种疾病的患者（总体人群）或总体人群的一个子集（亚组人群）效果更好，这种情况并不罕见。可用于此目的的一种方法是进行两项独立试验，在第一项试验中，收集数据以确定新治疗方法是否对总体人群或亚组人群有益。第二项试验是一项确证性试验，用于在第一项试验中选定的人群中测试新治疗方法。在本文中，我们考虑更有效的两阶段自适应无缝设计（ASD），其中在第1阶段，收集数据以选择在第2阶段进行测试的人群。在第2阶段，收集额外数据以对选定人群进行确证性分析。与使用两项独立试验的方法不同，对于ASD，第1阶段的数据也用于确证性分析。尽管ASD很有效，但将第1阶段的数据同时用于选择和确证性分析会引入选择偏差，从而在进行推断时带来统计挑战。我们将专注于此类试验的点估计。在本文中，我们描述了忽略多个假设并根据观察到的第1阶段数据选择最有可能给出阳性试验结果的人群时估计量的偏差程度。然后我们推导条件无偏估计量，并检查它们在不同情况下的均方误差。
