It has long been recognized that sample size calculations for cluster randomized trials require consideration of the correlation between multiple observations within the same cluster. When measurements are taken at anything other than a single point in time, these correlations depend not only on the cluster but also on the time separation between measurements and additionally, on whether different participants (cross-sectional designs) or the same participants (cohort designs) are repeatedly measured. This is particularly relevant in trials with multiple periods of measurement, such as the cluster cross-over and stepped-wedge designs, but also to some degree in parallel designs. Several papers describing sample size methodology for these designs have been published, but this methodology might not be accessible to all researchers. In this article we provide a tutorial on sample size calculation for cluster randomized designs with particular emphasis on designs with multiple periods of measurement and provide a web-based tool, the Shiny CRT Calculator, to allow researchers to easily conduct these sample size calculations. We consider both cross-sectional and cohort designs and allow for a variety of assumed within-cluster correlation structures. We consider cluster heterogeneity in treatment effects (for designs where treatment is crossed with cluster), as well as individually randomized group-treatment trials with differential clustering between arms, for example designs where clustering arises from interventions being delivered in groups. The calculator will compute power or precision, as a function of cluster size or number of clusters, for a wide variety of designs and correlation structures. We illustrate the methodology and the flexibility of the Shiny CRT Calculator using a range of examples.

中文翻译：

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使用 Shiny CRT 计算器计算多周期聚类随机平行、交叉和阶梯楔形试验的样本量的教程。

人们很早就认识到，聚类随机试验的样本量计算需要考虑同一聚类内多个观察值之间的相关性。当在单个时间点以外的任何地方进行测量时，这些相关性不仅取决于集群，还取决于测量之间的时间间隔，此外还取决于不同参与者（横截面设计）还是相同参与者（队列设计） ) 被重复测量。这在多周期测量的试验中尤其重要，例如簇交叉和阶梯楔形设计，而且在某种程度上也与并行设计相关。已经发表了几篇描述这些设计的样本量方法的论文，但这种方法可能不适用于所有研究人员。在本文中，我们提供了有关聚类随机设计的样本量计算的教程，特别强调具有多个测量周期的设计，并提供基于 Web 的工具 Shiny CRT 计算器，以便研究人员能够轻松地进行这些样本量计算。我们考虑横截面设计和队列设计，并考虑各种假设的簇内相关结构。我们考虑治疗效果中的聚类异质性（对于治疗与聚类交叉的设计），以及各组之间具有差异聚类的单独随机分组治疗试验，例如，聚类是由分组提供的干预措施产生的设计。该计算器将为各种设计和相关结构计算功效或精度，作为簇大小或簇数量的函数。我们使用一系列示例来说明 Shiny CRT 计算器的方法和灵活性。