Li Bingbing, Grambsch Patricia
Global Biostatistics & Clinical Technology, Wyeth Pharmaceuticals, Collegeville, Pennsylvania 19426, USA.
Clin Trials. 2006;3(4):349-59. doi: 10.1177/1740774506069155.
Most methods of sample size calculations for survival trials adjust the estimated outcome event rates for noncompliance based on the assumption that non-compliance is independent of the risk of the outcome event although there has been published evidence that noncompliers are often at a higher risk than compliers. More recent work has started to consider the situations of informative noncompliance and different risks for noncompliers. However, the possibility of a time-varying association between noncompliance and risk has been ignored. Our analysis indicated a strong time-varying relationship between noncompliance defined as permanent discontinuation of study treatments and risk of the outcome event in the CONVINCE trial.
The purpose of this research is to develop methods for the log-rank sample size calculations for two-arm clinical trials that allow for the relationship between risk and noncompliance to vary over time and to study how sample size requirements vary with different patterns of the time relationship.
The method developed takes Lakatos' Markov chain approach as a basis, modifying it to incorporate time dynamics, and emphasizing permanent discontinuation of study medication as the form of noncompliance to be considered.
Results with our method show that sample size depends on the relative rates of noncompliance in the two arms, the hazard for the outcome event following non-compliance, whether it involves switching to the hazard of the opposite arm or is common to both arms, and whether noncompliance occurs early or late in the trial. These factors interact with each other in complex ways, precluding simple summaries.
This research focuses on two-arm clinical trials with time to event as primary outcome measure. The method developed is not directly applicable to trials with more complicated designs and/or trials with other types of primary outcome.
The pattern of the relationship between noncompliance and risk can have a dramatic impact on the sample size and power calculations in survival studies. The method introduced provides a useful tool for investigators to explore the optimal sample size accounting for various dynamic associations between noncompliance and risk.
大多数生存试验的样本量计算方法基于非依从性与结局事件风险无关的假设来调整因非依从性导致的估计结局事件发生率，尽管已有证据表明，不依从者的风险通常高于依从者。最近的研究开始考虑信息性非依从性的情况以及不依从者的不同风险。然而，非依从性与风险之间随时间变化的关联可能性却被忽视了。我们的分析表明，在“说服”（CONVINCE）试验中，定义为永久停止研究治疗的非依从性与结局事件风险之间存在很强的随时间变化的关系。
本研究的目的是开发用于双臂临床试验对数秩样本量计算的方法，该方法允许风险与非依从性之间的关系随时间变化，并研究样本量要求如何随时间关系的不同模式而变化。
所开发的方法以拉卡托斯的马尔可夫链方法为基础，对其进行修改以纳入时间动态，并强调将永久停止研究用药作为要考虑的非依从性形式。
我们方法的结果表明，样本量取决于双臂中的非依从性相对率、非依从后结局事件的风险、它是否涉及切换到对侧臂的风险或双臂共同的风险，以及非依从性在试验早期还是晚期发生。这些因素以复杂的方式相互作用，无法进行简单总结。
本研究聚焦于以事件发生时间作为主要结局指标的双臂临床试验。所开发的方法不适用于设计更复杂的试验和/或具有其他类型主要结局的试验。
非依从性与风险之间的关系模式可能对生存研究中的样本量和效能计算产生巨大影响。所介绍的方法为研究人员提供了一个有用的工具，用于探索考虑非依从性与风险之间各种动态关联的最佳样本量。
