In the presence of longitudinal data with nonignorable dropouts, we propose improved estimators for generalized partial linear models that accommodate both the within-subject correlations and nonignorable missing data. To address the identifiability problem, an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates, is used to construct sufficient instrumental estimating equations. Subsequently, the nonparametric function is approximated by B-spline basis functions and then we construct bias-corrected generalized estimating equations based on the inverse probability weighting. In order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function and hybrid-GEE to construct the improved empirical likelihood procedures. Under some regularity conditions, we establish asymptotic normality of the proposed estimators for the parametric components and convergence rate of the estimators for the nonparametric functions. The finite-sample performance of the proposed estimators is studied through simulations and an application to HIV-CD4 data set is also presented.

在存在具有不可忽略丢失的纵向数据的情况下，我们为广义部分线性模型提出了改进的估计器，该模型同时包含主体内相关性和不可忽略的缺失数据。为了解决可识别性问题，使用与响应变量相关但与给定响应变量和其他协变量的倾向无关的工具协变量来构建足够的工具估计方程。随后，通过B样条基函数逼近非参数函数，然后我们构建基于逆概率加权的偏差校正广义估计方程。为了在信息丰富的工作相关结构下合并主题内的相关性，我们借用二次推理函数和混合 GEE 的思想来构建改进的经验似然程序。在一定的规律性条件下，我们建立了参数分量估计量的渐近正态性和非参数函数估计量的收敛速度。通过模拟研究了所提出的估计器的有限样本性能，并且还介绍了对 HIV-CD4 数据集的应用。