Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY 40536, USA.
Stat Med. 2013 Jul 20;32(16):2850-8. doi: 10.1002/sim.5709. Epub 2012 Dec 16.
Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference.
广义估计方程（GEE）常用于相关数据的边缘分析。GEE 的效率取决于工作协方差结构与真实结构的接近程度，因此准确建模数据的工作相关性很重要。一种流行的方法是使用非结构工作相关矩阵，因为它不像可交换和 AR-1 等更简单的结构那样具有限制性，因此理论上可以提高效率。然而，由于需要估计大量相关参数的可能性，当使用非结构工作相关矩阵时，回归参数估计的方差可能会大于理论上的预期。因此，标准误差估计可能会出现负偏差。为了考虑这种额外的有限样本可变性，我们推导出一种偏差校正，可以应用于参数估计协方差矩阵的典型估计器。通过模拟和在纵向研究中的应用，我们表明我们提出的校正可以改进标准误差估计和统计推断。
