When calculating sample size or power for stepped wedge or other types of longitudinal cluster randomized trials, it is critical that the planned sampling structure be accurately specified. One common assumption is that participants will provide measurements in each trial period, that is, a closed cohort, and another is that each participant provides only one measurement during the course of the trial. However some studies have an "open cohort" sampling structure, where participants may provide measurements in variable numbers of periods. To date, sample size calculations for longitudinal cluster randomized trials have not accommodated open cohorts. Feldman and McKinlay (1994) provided some guidance, stating that the participant-level autocorrelation could be varied to account for the degree of overlap in different periods of the study, but did not indicate precisely how to do so. We present sample size and power formulas that allow for open cohorts and discuss the impact of the degree of "openness" on sample size and power. We consider designs where the number of participants in each cluster will be maintained throughout the trial, but individual participants may provide differing numbers of measurements. Our results are a unification of closed cohort and repeated cross-sectional sample results of Hooper et al (2016), and indicate precisely how participant autocorrelation of Feldman and McKinlay should be varied to account for an open cohort sampling structure. We discuss different types of open cohort sampling schemes and how open cohort sampling structure impacts on power in the presence of decaying within-cluster correlations and autoregressive participant-level errors.

中文翻译：

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开放队列纵向集群随机试验的样本量和功效计算。

在计算阶梯楔形或其他类型的纵向整群随机试验的样本量或功效时，准确指定计划的抽样结构至关重要。一个常见的假设是参与者将在每个试验期间提供测量，即一个封闭的队列，另一个是每个参与者在试验过程中只提供一次测量。然而，一些研究采用“开放队列”抽样结构，参与者可以提供不同时期的测量值。迄今为止，纵向整群随机试验的样本量计算尚未适应开放队列。Feldman 和 McKinlay (1994) 提供了一些指导，指出参与者级别的自相关可以变化以解释研究不同时期的重叠程度，但没有具体说明如何这样做。我们提出了允许开放队列的样本量和功效公式，并讨论了“开放”程度对样本量和功效的影响。我们考虑的设计是在整个试验期间保持每个集群中的参与者数量，但个体参与者可能提供不同数量的测量值。我们的结果是 Hooper 等人 (2016) 的封闭队列和重复横截面样本结果的统一，并准确地表明了 Feldman 和 McKinlay 的参与者自相关应该如何变化以解释开放队列抽样结构。