Braun Thomas M
Department of Biostatistics, University of Michigan, 1420 Washington Heights, M4063 SPH II, Ann Arbor, MI 48109, USA.
Biom J. 2007 Jun;49(3):394-405. doi: 10.1002/bimj.200510280.
Generalized estimating equations (GEE) are used in the analysis of cluster randomized trials (CRTs) because: 1) the resulting intervention effect estimate has the desired marginal or population-averaged interpretation, and 2) most statistical packages contain programs for GEE. However, GEE tends to underestimate the standard error of the intervention effect estimate in CRTs. In contrast, penalized quasi-likelihood (PQL) estimates the standard error of the intervention effect in CRTs much better than GEE but is used less frequently because: 1) it generates an intervention effect estimate with a conditional, or cluster-specific, interpretation, and 2) PQL is not a part of most statistical packages. We propose taking the variance estimator from PQL and re-expressing it as a sandwich-type estimator that could be easily incorporated into existing GEE packages, thereby making GEE useful for the analysis of CRTs. Using numerical examples and data from an actual CRT, we compare the performance of this variance estimator to others proposed in the literature, and we find that our variance estimator performs as well as or better than its competitors.
广义估计方程（GEE）用于整群随机试验（CRT）的分析，原因如下：1）所得的干预效应估计值具有所需的边际或总体平均解释；2）大多数统计软件包都包含GEE程序。然而，GEE往往会低估CRT中干预效应估计值的标准误差。相比之下，惩罚拟似然法（PQL）在估计CRT中干预效应的标准误差方面比GEE要好得多，但使用频率较低，原因如下：1）它生成的干预效应估计值具有条件性或特定于整群的解释；2）PQL不是大多数统计软件包的一部分。我们建议采用PQL的方差估计量，并将其重新表示为一种易于纳入现有GEE软件包的三明治型估计量，从而使GEE可用于CRT的分析。通过数值示例和来自实际CRT的数据，我们将这种方差估计量的性能与文献中提出的其他估计量进行了比较，发现我们的方差估计量与其他竞争者的表现相当或更好。
