Department of Methodology and Statistics, Maastricht University, Maastricht, The Netherlands.
Stat Med. 2010 Jun 30;29(14):1488-501. doi: 10.1002/sim.3857.
Adjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second-order penalized quasi-likelihood estimation (PQL). Starting from first-order marginal quasi-likelihood (MQL) estimation of the treatment effect, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. A Monte Carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes, when employing second-order PQL. An approximate, simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial. In many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes. Since current closed-form formulas for sample size calculation are based on first-order MQL, planning a trial also requires a conversion factor to obtain the variance of the second-order PQL estimator. In a second Monte Carlo study, this conversion factor turned out to be 1.25 at most.
当使用混合效应逻辑回归和二阶惩罚拟似然估计 (PQL) 对二分类结局的整群随机试验进行处理效应检验时，本文给出了在不同的群大小下对样本量公式进行调整的方法。本文从处理效应的一阶边缘拟似然 (MQL) 估计出发，推导出不等群大小与等群大小的渐近相对效率。当使用二阶 PQL 时，一项蒙特卡罗模拟研究表明，对于实际的样本量，这种渐近相对效率非常准确。本文还提出了一个近似的、更简单的公式，用于估计由于群大小变化而导致的效率损失，以便在试验规划时使用。在许多情况下，只需多抽取 14%的群组就足以弥补由于群大小变化而导致的效率损失。由于当前基于一阶 MQL 的样本量计算公式，规划试验还需要一个转换因子来获得二阶 PQL 估计量的方差。在第二项蒙特卡罗研究中，该转换因子最多为 1.25。
