Heo Moonseong, Xue Xiaonan, Kim Mimi Y
Division of Biostatistics, Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, New York, USA.
Comput Stat Data Anal. 2013 Apr 1;60:169-178. doi: 10.1016/j.csda.2012.11.016.
In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study.
在纵向整群随机临床试验（整群随机对照试验）中，受试者嵌套于诊所等更高层次的单位中，并在研究期间对结局进行反复评估。这种研究设计产生了一个三级分层数据结构。当主要目标是检验一项干预措施对结局随时间变化率有影响这一假设，且个体间斜率差异很大时，个体特定斜率通常在混合效应线性模型中被建模为随机系数。在本文中，我们提出了基于普通最小二乘法（OLS）估计来确定三级分层试验设计各层级样本量的方法，用于在斜率被建模为随机时检测两个干预组之间平均斜率的差异。值得注意的是，样本量不是二级或三级随机截距方差的函数，仅通过它们的乘积依赖于二级和三级数据单元的数量。模拟结果表明，即使在聚类大小不同的情况下，基于OLS的检验效能和样本量与基于经验最大似然估计的结果几乎相同。还比较了随机斜率模型与固定斜率模型的样本量。结果表明，随机斜率的方差对样本量的确定影响巨大。因此，当预期个体间结局趋势差异显著时，基于固定斜率模型确定样本量可能导致研究检验效能严重不足。
