Department of Biostatistics, Harvard TH Chan School of Public Health, Boston, Massachusetts.
Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, Massachusetts.
Biometrics. 2020 Sep;76(3):951-962. doi: 10.1111/biom.13164. Epub 2019 Nov 14.
Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW-CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under-powered study. We investigate the relative efficiency of a SW-CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model-a commonly used approach for analyzing data from cluster randomized trials. When cluster sizes vary, the power of a SW-CRT depends on the order in which clusters receive the intervention, which is determined through randomization. We first derive a variance formula that corresponds to any particular realization of the randomized sequence and propose efficient algorithms to identify upper and lower bounds of the power. We then obtain an "expected" power based on a first-order approximation to the variance formula, where the expectation is taken with respect to all possible randomization sequences. Finally, we provide a variance formula for more general settings where only the cluster size arithmetic mean and coefficient of variation, instead of exact cluster sizes, are known in the design stage. We evaluate our methods through simulations and illustrate that the average power of a SW-CRT decreases as the variation in cluster sizes increases, and the impact is largest when the number of clusters is small.
标准的阶乘群组随机试验（SW-CRT）样本量计算公式假设群组大小相等。当群组大小存在显著差异时，忽略这种变化可能会导致研究结果无效。我们研究了群组大小变化的 SW-CRT 与群组大小相等的 SW-CRT 的相对效率，并推导出了在混合效应模型下考虑这种变化的干预效果方差估计值，这是一种常用于分析群组随机试验数据的方法。当群组大小变化时，SW-CRT 的功效取决于群组接受干预的顺序，这是通过随机化决定的。我们首先推导出一个与随机序列的任何特定实现相对应的方差公式，并提出了有效的算法来确定功效的上限和下限。然后，我们基于方差公式的一阶近似值获得“预期”功效，其中期望是针对所有可能的随机化序列进行的。最后，我们提供了一个更一般的方差公式，其中在设计阶段仅知道群组大小的算术平均值和变异系数，而不是确切的群组大小。我们通过模拟评估了我们的方法，并说明随着群组大小变化的增加，SW-CRT 的平均功效会降低，当群组数量较小时，这种影响最大。
