Robustness of generalized estimating equation (GEE) tests of significance against misspecification of the error structure model
Robustness of generalized estimating equation (GEE) tests of significance against misspecification of the error structure model
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DOI：
10.1002/bimj.200210017
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发表时间：
2004-04-01
影响因子：
1.7
通讯作者：
Tonidandel, S
中科院分区：
文献类型：
--
作者：
Overall, JE;Tonidandel, S
重复测量的广义线性模型分析通常依赖于误差协方差结构的简化数学模型来检验随时间变化模式差异的显著性。显著性检验的稳健性不仅取决于指定的数学模型与实际总体数据结构之间的一致程度，还取决于拟合指定协方差结构的计算准则的精度和稳健性。利用鲁棒经验三明治估计器对误差结构进行建模的广义估计方程（GEE）解与利用常用的限制极大似然（REML）过程的一般线性混合模型（GLMM）解进行了比较。在考虑的条件下，GEE和GLMM程序在假设数据为正态分布和数据的方差-协方差结构为用户指定的情况下是相同的。本文讨论的问题是，当用替代程序拟合误差协方差结构模型时，治疗效果的显著性检验对不同程度的错误说明的相对敏感性。除自回归协方差结构和因dropouts导致的数据缺失外，对等斜率假设的实际I型误差和检验功率进行蒙特卡罗评估的模拟数据符合重复测量的普通线性模型ANOVA的假设。模拟重复测量的实际组内相关结构在分级步骤中从AR(1)到复合对称，而GEE和GLMM公式将各自的误差结构模型限制为AR(I)、复合对称（CS）或非结构化（UN）。利用经验三明治估计准则的基于ge的检验被证明对协方差结构模型的错误说明相对不敏感，而依赖于限制最大似然（REML）的GLMM检验对误差相关结构的相对适度的错误说明高度敏感，即使正态性、方差同质性和线性在模拟数据中不存在问题。在确定GLMM误差结构模型的相对较小的错误说明导致对等斜率假设的检验的alpha保护不足的情况下，拟合优度统计几乎没有效用。无论重复测量的实际相关结构如何，依赖于非结构化（UN）误差模型规范的GEE和GLMM公式都会产生非保守结果。随机系数模型产生了在所有条件下具有竞争力的稳健测试。
Generalized linear model analyses of repeated measurements typically rely on simplifying mathematical models of the error covariance structure for testing the significance of differences in patterns of change across time. The robustness of the tests of significance depends, not only on the degree of agreement between the specified mathematical model and the actual population data structure, but also on the precision and robustness of the computational criteria for fitting the specified covariance structure to the data. Generalized estimating equation (GEE) solutions utilizing the robust empirical sandwich estimator for modeling of the error structure were compared with general linear mixed model (GLMM) solutions that utilized the commonly employed restricted maximum likelihood (REML) procedure. Under the conditions considered, the GEE and GLMM procedures were identical in assuming that the data are normally distributed and that the variance-covariance structure of the data is the one specified by the user.The question addressed in this article concerns relative sensitivity of tests of significance for treatment effects to varying degrees of misspecification of the error covariance structure model when fitted by the alternative procedures. Simulated data that were subjected to monte carlo evaluation of actual Type I error and power of tests of the equal slopes hypothesis conformed to assumptions of ordinary linear model ANOVA for repeated measures except for autoregressive covariance structures and missing data due to dropouts. The actual within-groups correlation structures of the simulated repeated measurements ranged from AR(1) to compound symmetry in graded steps, whereas the GEE and GLMM formulations restricted the respective error structure models to be either AR(I), compound symmetry (CS), or unstructured (UN). The GEE-based tests utilizing empirical sandwich estimator criteria were documented to be relatively insensitive to misspecification of the covariance structure models, whereas GLMM tests which relied on restricted maximum likelihood (REML) were highly sensitive to relatively modest misspecification of the error correlation structure even though normality, variance homogeneity, and linearity were not an issue in the simulated data. Goodness-of-fit statistics were of little utility in identifying cases in which relatively minor misspecification of the GLMM error structure model resulted in inadequate alpha protection for tests of the equal slopes hypothesis. Both GEE and GLMM formulations that relied on unstructured (UN) error model specification produced nonconservative results regardless of the actual correlation structure of the repeated measurements. A random coefficients model produced robust tests with competitive power across all conditions examined.