Stepped-wedge designs (SWD) are increasingly used to evaluate the impact of changes to the process of care within health care systems. However, to generate definitive evidence, a correct sample size calculation is crucial to ensure such studies are properly powered. The seminal work of Hussey and Hughes (Contemp Clin Trials 28(2):182–91, 2004) provides an analytical formula for power calculations with normal outcomes using a linear model and simple random effects. However, minimal development and evaluation have been done for power calculation with non-normal outcomes on their natural scale (e.g., logit, log). For example, binary endpoints are common, and logistic regression is the natural multilevel model for such clustered data. We propose a power calculation formula for SWD with either normal or non-normal outcomes in the context of generalized linear mixed models by adopting the Laplace approximation detailed in Breslow and Clayton (J Am Stat Assoc 88(421):9–25, 1993) to obtain the covariance matrix of the estimated parameters. We compare the performance of our proposed method with simulation-based sample size calculation and demonstrate its use on a study of patient-delivered partner therapy for STI treatment and a study that assesses the impact of providing additional benchmark prevalence information in a radiologic imaging report. To facilitate adoption of our methods we also provide a function embedded in the R package “swCRTdesign” for sample size and power calculation for multilevel stepped-wedge designs. Our method requires minimal computational power. Therefore, the proposed procedure facilitates rapid dynamic updates of sample size calculations and can be used to explore a wide range of design options or assumptions.

中文翻译：

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具有离散结果的阶梯楔形设计的功效和样本量计算

阶梯楔形设计 (SWD) 越来越多地用于评估医疗保健系统内护理过程变化的影响。但是，要生成明确的证据，正确的样本量计算对于确保此类研究具有适当的效力至关重要。Hussey 和 Hughes 的开创性工作（Contemp Clin Trials 28(2):182–91, 2004）提供了一个分析公式，用于使用线性模型和简单随机效应的正常结果的功效计算。然而，对于自然尺度（例如 logit、log）上的非正态结果的功效计算，已经进行了最少的开发和评估。例如，二元端点很常见，逻辑回归是此类聚类数据的自然多级模型。我们通过采用 Breslow 和 Clayton (J Am Stat Assoc 88(421):9–​​25, 1993) 中详述的拉普拉斯近似，在广义线性混合模型的背景下提出了具有正常或非正常结果的 SWD 的功效计算公式得到估计参数的协方差矩阵。我们将我们提出的方法的性能与基于模拟的样本量计算进行了比较，并证明了其在 STI 治疗的患者提供的合作伙伴治疗研究和评估在放射成像报告中提供额外基准患病率信息的影响的研究中的用途。为了便于采用我们的方法，我们还提供了一个嵌入在 R 包“swCRTdesign”中的函数，用于多级阶梯楔形设计的样本大小和功效计算。我们的方法需要最少的计算能力。所以，