Division of Public Health Sciences, Dept. of Surgery, Washington University School of Medicine (WUSM), St Louis, Missouri, 63110, USA.
Division of Biostatistics, Washington University School of Medicine (WUSM), St Louis, Missouri, 63110, USA.
J Biopharm Stat. 2021 Mar;31(2):191-206. doi: 10.1080/10543406.2020.1814795. Epub 2020 Sep 24.
To calculate sample sizes in cluster randomized trials (CRTs), the cluster sizes are usually assumed to be identical across all clusters for simplicity. However, equal cluster sizes are not guaranteed in practice, especially when the number of clusters is limited. Therefore, it is important to understand the relative efficiency (RE) of equal versus unequal cluster sizes when designing CRTs with a limited number of clusters. In this paper, we are interested in the RE of two bias-corrected sandwich estimators of the treatment effect in the Generalized Estimating Equation (GEE) models for CRTs with a small number of clusters. Specifically, we derive the RE of two bias-corrected sandwich estimators for binary, continuous, or count data in CRTs under the assumption of an exchangeable working correlation structure. We consider different scenarios of cluster size distributions and investigate RE performance through simulation studies. We conclude that the number of clusters could be increased by as much as 42% to compensate for efficiency loss due to unequal cluster sizes. Finally, we propose an algorithm of increasing the number of clusters when the coefficient of variation of cluster sizes is known and unknown.
为了计算群组随机试验 (CRT) 的样本量,通常为了简单起见,假设所有群组的群组大小都是相同的。然而,在实践中,并不保证群组大小相等,特别是当群组数量有限时。因此,当设计具有有限群组数量的 CRT 时,了解相等和不等群组大小的相对效率 (RE) 非常重要。在本文中,我们感兴趣的是在具有少量群组的 CRT 中使用广义估计方程 (GEE) 模型时,两种校正偏差的治疗效果的三明治估计量的 RE。具体来说,我们在可交换工作相关结构的假设下,推导出两种校正偏差的三明治估计量在 CRT 中对二项式、连续或计数数据的 RE。我们考虑了不同的群组大小分布情况,并通过模拟研究调查了 RE 性能。我们得出结论,通过增加群组数量,最多可以增加 42%来弥补由于不等群组大小而导致的效率损失。最后,我们提出了一种当已知和未知群组大小的变异系数时增加群组数量的算法。