Background/Aims: This article studies the effect of attrition in the cluster randomized crossover trial. The focus is on the two-treatment two-period AB/BA design where attrition occurs during the washout period. Attrition may occur at either the subject level or the cluster level. In the latter case, clusters drop out entirely and provide no measurements in the second period. Subject attrition can only occur in the cohort design, where each subject receives both treatments. Cluster attrition can also occur in the cross-sectional design, where different subjects are measured in the two time periods. Furthermore, this article explores two different strategies to account for potential levels of attrition: increasing sample size and replacing those subjects who drop out by others. Methods: The statistical model that takes into account the nesting of subjects within clusters, and the nesting of repeated measurements within subjects is presented. The effect of attrition is evaluated on the basis of the efficiency of the treatment effect estimator. Matrix algebra is used to derive the relation between efficiency, the degree of attrition, cluster size and the intraclass correlations: the within-cluster within-period correlation, the within-cluster between-period correlation and (in the case of a cohort design) the within-subject correlation. The methodology is implemented in two Shiny Apps. Results: Attrition in a cluster randomized crossover trial implies a loss of efficiency. Efficiency decreases with an increase of the attrition rate. The loss of efficiency due to attrition of subjects in a cohort design is largest for small number of subjects per cluster-period, but it may be repaired to a large degree by increasing the number of subjects per cluster-period or by replacing those subjects who drop out by others. Attrition of clusters results in a larger loss of efficiency, but this loss does not depend on the number of subjects per cluster-period. Repairing for this loss requires a large increase in the number of subjects per cluster-period. The methodology of this article is illustrated by an example on the effect of lavender scent on dental patients’ anxiety. Conclusion: This article provides the methodology of exploring the effect of attrition in cluster randomized crossover trials, and to repair for attrition. As such, it helps researchers plan their trial in an appropriate way and avoid underpowered trials. To use the methodology, prior estimates of the degree of attrition and intraclass correlation coefficients are needed. It is advocated that researchers clearly report the estimates of these quantities to help facilitate planning future trials.

中文翻译：

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集群随机交叉试验：AB/BA 设计中损耗的影响以及如何在样本量计算中考虑它

背景/目的：本文研究了集群随机交叉试验中损耗的影响。重点是两次处理两阶段 AB/BA 设计，其中在冲洗期间发生磨损。损耗可能发生在主题级别或集群级别。在后一种情况下，集群完全退出并且在第二个时期不提供任何测量。受试者流失只能发生在队列设计中，每个受试者都接受两种治疗。集群损耗也可能发生在横截面设计中，其中在两个时间段内测量不同的主题。此外，本文探讨了两种不同的策略来解释潜在的流失水平：增加样本量和替换那些被其他人退出的受试者。方法：提出了考虑集群内对象嵌套和对象内重复测量嵌套的统计模型。损耗的影响是根据处理效果估计器的效率来评估的。矩阵代数用于推导效率、损耗程度、集群大小和类内相关性之间的关系：集群内周期内相关性、集群内周期间相关性和（在队列设计的情况下）被试内的相关性。该方法在两个 Shiny 应用程序中实现。结果：集群随机交叉试验中的损耗意味着效率的降低。效率随着损耗率的增加而降低。在队列设计中，由于每个集群周期的受试者数量较少而导致的效率损失最大，但可以通过增加每个集群周期的受试者数量或替换那些被别人退学。集群的损耗会导致更大的效率损失，但这种损失不取决于每个集群周期的受试者数量。修复这种损失需要大量增加每个集群周期的受试者数量。本文的方法论以薰衣草香味对牙科患者焦虑的影响为例进行说明。结论：本文提供了探索磨损在集群随机交叉试验中的影响，并修复磨损的方法。因此，它可以帮助研究人员以适当的方式计划他们的试验并避免动力不足的试验。要使用该方法，需要预先估计磨损程度和类内相关系数。提倡研究人员清楚地报告这些数量的估计，以帮助规划未来的试验。