In designing a clinical trial for comparing two or more treatments with respect to overall survival (OS), a proportional hazards assumption is commonly made. However, in many cancer clinical trials, patients pass through various disease states prior to death and because of this may receive treatments other than originally assigned. For example, patients may crossover from the control treatment to the experimental treatment at progression. Even without crossover, the survival pattern after progression may be very different than the pattern prior to progression. The proportional hazards assumption will not hold in these situations and the design power calculated on this assumption will not be correct. In this article, we describe a simple and intuitive multi-state model allowing for progression, death before progression, post-progression survival, and crossover after progression and apply this model to the design of clinical trials for comparing the OS of two treatments. For given values of the parameters of the multi-state model, we simulate the required number of deaths to achieve a specified power and the distribution of time required to achieve the requisite number of deaths. The results may be quite different from those derived using the usual PH assumption. Supplementary materials for this article are available online.

在设计比较两种或多种治疗方法的总生存期 (OS) 的临床试验时，通常会做出比例风险假设。然而，在许多癌症临床试验中，患者在死亡前会经历各种疾病状态，因此可能会接受最初指定以外的治疗。例如，患者可能在进展时从对照治疗交叉到实验治疗。即使没有交叉，进展后的生存模式也可能与进展前的模式有很大不同。在这些情况下，比例风险假设将不成立，并且根据该假设计算的设计功效将不正确。在本文中，我们描述了一个简单直观的多状态模型，允许进展、进展前死亡、进展后生存和进展后交叉，并将该模型应用于临床试验设计以比较两种治疗的 OS。对于给定的多状态模型参数值，我们模拟达到指定功效所需的死亡人数以及达到所需死亡人数所需的时间分布。结果可能与使用通常 PH 假设得出的结果有很大不同。本文的补充材料可在线获取。