Background:Knowing the predictive factors of the variation in a center-level continuous outcome of interest is valuable in the design and analysis of parallel-arm cluster randomized trials. The symbolic two-step method for sample size planning that we present incorporates this knowledge while simultaneously accounting for patient-level characteristics. Our approach is illustrated through application to cluster randomized trials in cancer care delivery research. The required number of centers (clusters) depends on the between- and within-center variance; the within-center variance is a function of estimates obtained by regressing the log within-center variance on predictive factors. Obtaining accurate estimates of the components needed to characterize the within-center variation is challenging.Methods:Using our previously derived sample size formula, our objective in the current research is to directly account for the imprecision in these estimates, using a Bayesian approach, to safeguard against designing an underpowered study when using the symbolic two-step method. Using estimates of the required components, including the number of centers that contribute to those estimates, we make formal allowance for the imprecision in these estimates on which a sample size will be based.Results:The mean of the distribution for power is consistently smaller than the single point estimate that the sample size formula yields. The reduction in power is more pronounced in the presence of increased uncertainty about the estimates with the reduction becoming more attenuated with increased numbers of centers that contribute to the estimates.Conclusions:Accounting for imprecision in the estimates of the components required for sample size estimation using the symbolic two-step method in the design of a cluster randomized trial yields conservative estimates of power.

中文翻译：

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应用于癌症护理研究的象征性两步法：通过考虑中心内和中心间变异的不精确性，防止设计具有连续结果的动力不足的整群随机试验

背景：了解感兴趣的中心水平连续结果变化的预测因素对于平行臂整群随机试验的设计和分析很有价值。我们提出的样本量规划的象征性两步法结合了这些知识，同时考虑了患者水平的特征。我们的方法通过应用于癌症护理研究中的集群随机试验来说明。所需的中心（簇）数量取决于中心间和中心内方差；中心内方差是通过对预测因素的中心内方差对数进行回归而获得的估计值的函数。获得表征中心内变化所需的组件的准确估计具有挑战性。方法：使用我们之前导出的样本量公式，我们当前研究的目标是使用贝叶斯方法直接解释这些估计中的不精确性，以使用符号两步法时，可以防止设计动力不足的研究。使用对所需组成部分的估计，包括对这些估计做出贡献的中心数量，我们正式考虑到这些估计中的不精确性，样本量将基于这些估计。结果：功率分布的平均值始终小于样本量公式产生的单点估计。在估计的不确定性增加的情况下，功效的降低更加明显，随着参与估计的中心数量的增加，功效的降低变得更加减弱。结论：使用整群随机试验设计中的符号两步法可得出功效的保守估计。