van Breukelen Gerard Jp, Candel Math Jjm, Berger Martijn Pf
Department of Methodology and Statistics, Maastricht University, Maastricht, The Netherlands.
Stat Methods Med Res. 2008 Aug;17(4):439-58. doi: 10.1177/0962280206079018. Epub 2007 Aug 14.
Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance patients within clinics or pupils within schools. Although equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible. This paper addresses the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in cluster randomized trials and in multicentre trials with person randomization within centres, assuming a quantitative outcome. Starting from maximum likelihood estimation, the RE is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the RE as a function of the mean and variance of cluster sizes and the intraclass correlation. The accuracy of this approximation is checked and found to be good. It is concluded that the loss of efficiency for variance component estimation due to variation of cluster sizes rarely exceeds 20% and can be compensated by sampling 25% more clusters.
整群随机多中心试验评估治疗措施对嵌套于群组中的个体（如诊所内的患者或学校内的学生）的效果。尽管通常每个群组具有相等的样本量对于参数估计最为理想，但实际中很少可行。本文探讨了在整群随机试验以及中心内个体随机化的多中心试验中，对于定量结局，不等群组大小与相等群组大小在估计方差分量时的相对效率（RE）。从最大似然估计出发，针对一系列群组大小分布，对相对效率进行了数值研究。给出了一个近似公式，用于计算作为群组大小均值、方差以及组内相关函数的相对效率。经检验，该近似的准确性良好。得出的结论是，由于群组大小变化导致的方差分量估计效率损失很少超过20%，并且可以通过多抽取25%的群组来弥补。
