Guo Xu, Pan Wei, Connett John E, Hannan Peter J, French Simone A
Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455, USA.
Stat Med. 2005 Nov 30;24(22):3479-95. doi: 10.1002/sim.2161.
The sandwich variance estimator of generalized estimating equations (GEE) may not perform well when the number of independent clusters is small. This could jeopardize the validity of the robust Wald test by causing inflated type I error and lower coverage probability of the corresponding confidence interval than the nominal level. Here, we investigate the small-sample performance of the robust score test for correlated data and propose several modifications to improve the performance. In a simulation study, we compare the robust score test to the robust Wald test for correlated Bernoulli and Poisson data, respectively. It is confirmed that the robust Wald test is too liberal whereas the robust score test is too conservative for small samples. To explain this puzzling operating difference between the two tests, we consider their applications to two special cases, one-sample and two-sample comparisons, thus motivating some modifications to the robust score test. A modification based on a simple adjustment to the usual robust score statistic by a factor of J/(J - 1) (where J is the number of clusters) reduces the conservativeness of the generalized score test. Simulation studies mimicking group-randomized clinical trials with binary and count responses indicated that it may improve the small-sample performance over that of the generalized score and Wald tests with test size closer to the nominal level. Finally, we demonstrate the utility of our proposal by applying it to a group-randomized clinical trial, trying alternative cafeteria options in schools (TACOS).
当独立聚类的数量较少时，广义估计方程（GEE）的三明治方差估计量可能表现不佳。这可能会破坏稳健Wald检验的有效性，导致第一类错误膨胀，并且相应置信区间的覆盖概率低于名义水平。在此，我们研究了相关数据稳健得分检验的小样本性能，并提出了几种改进方法以提高其性能。在一项模拟研究中，我们分别将稳健得分检验与相关伯努利和泊松数据的稳健Wald检验进行了比较。结果证实，对于小样本，稳健Wald检验过于宽松，而稳健得分检验过于保守。为了解释这两种检验之间令人困惑的操作差异，我们考虑了它们在两种特殊情况（单样本和两样本比较）中的应用，从而促使对稳健得分检验进行一些改进。基于对通常的稳健得分统计量简单地乘以J /（J - 1）（其中J是聚类的数量）进行调整的一种改进方法，降低了广义得分检验的保守性。模拟研究模仿了具有二元和计数响应的群组随机临床试验，结果表明，与广义得分检验和Wald检验相比，它可能会改善小样本性能，检验规模更接近名义水平。最后，我们通过将其应用于一项群组随机临床试验——在学校尝试替代自助餐厅选项（TACOS），展示了我们提议的实用性。
