Department of Biostatistics and Epidemiology, College of Public Health, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA.
Stat Med. 2010 Feb 20;29(4):464-73. doi: 10.1002/sim.3776.
Multilevel nested, correlated data often arise in biomedical research. Examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools. In some settings, cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters. When cluster sizes are large, fitting marginal regression models using Generalized Estimating Equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates. Also, the use of patterned, nested working correlation structures may not be efficient when correlation varies across clusters. This paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations. Particular within-cluster and between-cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters. The method involves estimation of the covariance matrix only for the vector of component estimating equations (which is typically of small dimension) rather than the covariance matrix of the observations within a cluster (which may be of large dimension). In settings where the number of clusters is large relative to the cluster size, the method is stable and is highly efficient, while maintaining appropriate coverage levels. Performance of the method is investigated with simulation studies and an application to a periodontal study.
多水平嵌套相关数据在生物医学研究中经常出现。例如，牙齿嵌套在口腔的象限内，或者学生嵌套在学校的教室里。在某些情况下，与独立聚类的数量相比，聚类的大小可能较大，并且聚类之间的相关性可能有所不同。当聚类的大小较大时，使用具有灵活相关性结构的广义估计方程拟合边缘回归模型，以反映嵌套结构，可能无法收敛并导致协方差估计不稳定。此外，当聚类之间的相关性发生变化时，使用模式化嵌套工作相关结构可能效率不高。本文描述了一种基于估计方程最优组合的灵活边缘回归建模方法。使用特定的聚类内和聚类间数据对比，而无需指定工作协方差结构，也无需估计协方差参数。该方法仅估计组件估计方程的协方差矩阵（通常维度较小），而不是估计聚类内观测值的协方差矩阵（可能维度较大）。在聚类数量相对于聚类大小较大的情况下，该方法是稳定且高效的，同时保持适当的覆盖水平。通过模拟研究和牙周研究的应用对该方法的性能进行了研究。
