A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).
翻译:在设计临床试验时,一个中心目标是找到一种测试,在受I类误差限制的情况下,为找到真正的研究假设而使权力最大化(或同等地最大限度地减少所需的样本规模),以找到受I类误差制约的真正研究假设。如果存在不止一种测试,例如在多端点临床试验中,最佳设计和最佳政策的问题就变得更加复杂。在本文件中,我们讨论了如何界定此类最佳测试以及如何找到最佳测试的问题。我们审视了不同的权力概念及其与研究目标的关系,还考虑了I类误差控制的要求和政策的性质。这导致我们把最佳政策问题设计成一个明确的最佳优化问题,其目标和限制描述了它的具体面貌。我们描述了为两种假设制定最佳政策的全面解决方案,这些假设具有理想的单一性,而且计算起来非常简单。对于一些优化方案来说,它产生了与现行政策相同的最佳政策,例如Hommel程序或Bittman等人的程序(2009年),而对于另一些政策则产生了完全的新颖和较强的政策。我们展示了我们的新政策的性质及其在2016年CON模拟中改进的实力。