Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross-validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real dataset.

翻译：纵向数据回归模型(GEE)广泛采用通用估计方程(GEE),同时考虑到同一主题中的潜在关联性。虽然通用的GEE标准在所有主体中采用共同回归系数,但当各主体的回归系数存在潜在差异时,这种假设可能不切实际。在本文中,我们开发了一种灵活和可解释的方法,称为组合的GEEE分析,以模拟长方程数据,允许回归系数的异质。拟议方法假定,主题被分成一个有限数目的组群和同一组群内各组群,同一组群内各主题的共具有相同的回归系数。我们为组合主体提供了简单的算法,同时估算回归系数,并展示了拟议的估计值的无症状特性。可用平均法的交叉比较法确定组数。我们通过模拟研究和对真实数据集的应用来展示拟议的方法。