Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty. Designs with adaptive sample size need to account for their optional stopping to guarantee strict type-I error-rate control. A variety of different methods to maintain type-I error-rate control after unplanned changes of the initial sample size have been proposed in the literature. This makes interim analyses for the purpose of sample size recalculation feasible in a regulatory context. Since the sample size is usually determined via an argument based on the power of the trial, an interim analysis raises the question of how the final sample size should be determined conditional on the accrued information. Conditional power is a concept often put forward in this context. Since it depends on the unknown effect size, we take a strict estimation perspective and compare assumed conditional power, observed conditional power, and predictive power with respect to their properties as estimators of the unknown conditional power. We then demonstrate that pre-planning an interim analysis using methodology for unplanned interim analyses is ineffective and naturally leads to the concept of optimal two-stage designs. We conclude that unplanned design adaptations should only be conducted as reaction to trial-external new evidence, operational needs to violate the originally chosen design, or post hoc changes in the objective criterion. Finally, we show that commonly discussed sample size recalculation rules can lead to paradoxical outcomes and propose two alternative ways of reacting to newly emerging trial-external evidence.
翻译:将试验的最后抽样规模与审判期间积累的证据相适应,是解决规划不确定性的一种自然方式。适应性抽样规模的设计需要说明其可选的停止,以保证严格的类型I误差率控制。文献中提出了在初步抽样规模发生意外变化后维持类型I错误率控制的各种不同方法。这使得为抽样规模重新计算目的进行临时分析在监管背景下是可行的。由于样本规模通常通过基于审判权力的论据确定,临时分析提出了如何根据累积信息确定最终样本规模的问题。有条件能力是在这种情况下经常提出的一个概念。由于它取决于未知的影响规模,我们从严格的估计角度来比较假设的有条件实力、观察到的有条件实力和预测力,以其特性作为未知有条件实力的估测点。我们然后表明,利用计划性临时分析方法规划临时规模的临时分析通常无效,自然导致最佳的两阶段设计概念。我们的结论是,计划性设计调整只能作为对实验性规模的反动,因此,我们采取严格的估计观点,并比较假定有条件的有条件能力,观察到有条件的、有条件的和预测性能力,我们最终会提出新的选择的汇率标准,从而确定新的结果。我们最后会违反新的选择的外部证据。我们讨论的汇率标准,最终需要提出新的选择的汇率性原则,从而最终显示新的结果。