ABSTRACT

Sample size calculations for trials with time-to-event outcomes are usually based on the assumption that an event – prototypically death in survival analysis – occurs only once per sample unit. However, events like changes in disease status or switches between treatment modalities may repeat over time. In trials with such outcomes, standard sample size formulae derived from the classical survival time models are not applicable. Instead, modeling the repeating transition events must precede the actual sample size calculation. Markov chains are an obvious choice to model transitions. Accordingly, in order to determine the sample size for a one-arm feasibility and acceptability study of a new drug intake route, we model switches of administration routes by a homogeneous finite-state, higher-order Markov chain. Assumptions about its transition matrix translate into multinomial distributions of the preferred administration routes at given points in time. From these distributions, the required sample size can then be calculated according to the study’s specific question. In this manuscript, we first introduce the method for the case of drug intake preferences, before we briefly discuss how the proposed method can also be used for power-based sample size calculation in multi-arm trials.

摘要

具有时间到事件结果的试验的样本量计算通常基于这样一个假设，即一个事件——在生存分析中的原型死亡——每个样本单位只发生一次。然而，疾病状态的变化或治疗方式之间的转换等事件可能会随着时间的推移而重复发生。在具有此类结果的试验中，源自经典生存时间模型的标准样本量公式不适用。相反，必须在实际样本量计算之前对重复转换事件进行建模。马尔可夫链是对转换进行建模的明显选择。因此，为了确定新药物摄入途径的单臂可行性和可接受性研究的样本量，我们通过同质有限状态高阶马尔可夫链对给药途径的转换进行建模。关于其转换矩阵的假设转化为给定时间点的首选给药途径的多项分布。从这些分布中，然后可以根据研究的具体问题计算所需的样本量。在这份手稿中，我们首先介绍了药物摄入偏好案例的方法，然后我们简要讨论了所提出的方法如何也可用于多臂试验中基于功效的样本量计算。