A Multi-State Model for Designing Clinical Trials for Testing Overall Survival Allowing for Crossover after Progression

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.

在设计旨在对比两种或多种治疗方案总生存期（overall survival, OS）的临床试验时，学界通常会采用比例风险假设（proportional hazards assumption，以下简称PH假设）。然而在诸多癌症临床试验中，患者在死亡前会经历多种疾病状态，因此可能接受并非最初分配的治疗方案。例如，患者可能在疾病进展时从对照治疗组交叉进入试验性治疗组。即便未发生交叉治疗，疾病进展后的生存模式与进展前的生存模式也可能存在显著差异。上述情形下PH假设将不再成立，基于该假设计算的试验设计检验效能也将不准确。本文提出一种简洁直观的多状态模型（multi-state model），可涵盖疾病进展、进展前死亡、进展后生存以及进展后交叉治疗等情形，并将该模型应用于对比两种治疗方案总生存期的临床试验设计。针对多状态模型的给定参数值，我们模拟了达到指定检验效能所需的死亡例数，以及达到该死亡例数所需的时间分布。所得结果与基于常规PH假设推导的结果可能存在显著差异。本文的补充材料可在线获取。