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

具有达到事件发生时间结果的试验的样本量计算通常基于以下假设：每个样本单位仅发生一次事件，即生存分析中的典型死亡。但是，随着时间的推移，诸如疾病状态变化或治疗方式之间切换之类的事件可能会重复发生。在具有此类结果的试验中，不适用源自经典生存时间模型的标准样本量公式。取而代之的是，对重复的过渡事件建模必须在实际样本量计算之前进行。马尔可夫链是建模过渡的明显选择。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，我们通过均质的有限状态，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首选管理路径在给定时间点的多项式分布。从这些分布中，可以根据研究的特定问题来计算所需的样本量。在此手稿中，我们首先介绍针对药物摄入偏好的方法，然后简要讨论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。