A primary focus of current methods for cluster randomized trials (CRTs) has been for continuous, binary, and count outcomes, with relatively less attention given to right-censored, time-to-event outcomes. In this article, we detail considerations for sample size requirement and statistical inference in CRTs with time-to-event outcomes when the intervention effect parameter is specified through the additive hazards mixed model (AHMM), which includes a frailty term to explicitly account for the dependency between the failure times. First, we discuss improved inference for the treatment effect parameter via bias-corrected sandwich variance estimators and randomization-based test under AHMM, addressing potential small-sample biases in CRTs. Next, we derive a new sample size formula for AHMM analysis of CRTs accommodating both equal and unequal cluster sizes. When the cluster sizes vary, our sample size formula depends on the mean and coefficient of variation of cluster sizes, based on which we articulate the impact of cluster size variation in CRTs with time-to-event outcomes. Furthermore, we obtain the insight that the classical variance inflation factor for CRTs with a non-censored outcome can in fact apply to CRTs with a time-to-event outcome, providing that an appropriate definition of the intraclass correlation coefficient is considered under AHMM. Simulation studies are carried out to illustrate key design and analysis considerations in CRTs with a small to moderate number of clusters. The proposed sample size procedure and analytical methods are further illustrated using the context of the STrategies to Reduce Injuries and Develop Confidence in Elders CRT.

中文翻译：

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加性危险混合模型下具有事件发生时间结果的整群随机试验的设计和分析

当前整群随机试验 (CRT) 方法的主要关注点是连续、二元和计数结果，而对右删失、事件发生时间结果的关注相对较少。在本文中，我们详细介绍了当通过加性危险混合模型 (AHMM) 指定干预效果参数时，CRT 中样本量要求和统计推断与事件发生时间结果的考虑因素，其中包括一个脆弱项来明确解释失效时间之间的依赖性。首先，我们讨论通过偏差校正夹心方差估计器和 AHMM 下基于随机化的测试改进治疗效果参数的推断，解决 CRT 中潜在的小样本偏差。接下来，我们推导出一个新的样本大小公式，用于 CRT 的 AHMM 分析，同时容纳相等和不相等的簇大小。当簇大小变化时，我们的样本大小公式取决于簇大小的平均值和变异系数，基于此，我们阐明了 CRT 中簇大小变化对事件发生时间结果的影响。此外，我们还发现，如果在 AHMM 下考虑类内相关系数的适当定义，则具有非审查结果的 CRT 的经典方差膨胀因子实际上可以适用于具有事件时间结果的 CRT。进行仿真研究是为了说明具有中小数量集群的 CRT 的关键设计和分析注意事项。使用减少伤害和增强老年人 CRT 信心的策略背景进一步说明了拟议的样本量程序和分析方法。