带终止事件纵向数据半参数部分线性单指标模型  

A partially linear single index model for longitudinal data with terminal event

作　　者：周洁[1] 周晓华 孙六全[3,4] Jie Zhou;Xiaohua Zhou;Liuquan Sun

机构地区：[1]首都师范大学数学科学学院,北京100048 [2]北京大学北京国际数学研究中心,北京100871 [3]中国科学院数学与系统科学研究院,北京100190 [4]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学：数学》2019年第1期73-88,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11671275;11471223;11301355;11690015和11771431);科技创新服务能力建设-基本科研业务费(科研类)(批准号:025185305000/204);首都师范大学青年科研创新团队和NIH/NIA(批准号:U01AG016976)资助项目

摘　　要：在纵向研究中,我们常常会对一些非终止事件感兴趣,例如,与健康相关的生存质量.然而,死亡事件可能会在我们观测到这些感兴趣的变量之前发生,这种情况称之为截断数据.此外,每个个体的观察时间可能是不规律的,而且协变量对于感兴趣事件的影响也可能很复杂.本文提出了一个新的用于拟合被死亡截断的数据的半参数部分线性单指标模型,并用局部线性核方法近似非参数的连接函数,构造了参数部分的估计方程.本文证明了连接函数的局部线性核估计具有一致相合性,但收敛速度低于n^(1/2).为了消除这一低速收敛的影响,本文提出了一种数据分割的方法,证明了参数部分估计量的渐近正态性.本文通过一些数值模拟检验所提方法在有限样本下的表现,并分析了一组老年痴呆症的数据.In longitudinal studies, we may be interested in some non-terminal event, such as health related quality of life. However, before the outcome of interest can be observed, a terminal event, such as death, can occur. If this situation occurs, we call this problem as truncation by death. In addition, observed times for subjects may be irregular, and the effect of covariates on the outcome of interest may be complicated. In this paper, we propose a new semiparametric partially linear single index model in the presence of truncation by death.A local linear approximation is used for the nonparametric link function, and estimating equation approaches are developed. The obtained estimator for the link function is proved to be uniformly consistent with convergence rate under root n. A data-splitting technique is developed to eliminate the side effect of this low convergence rate to establish the asymptotic normality of the parametric part. The finite sample behavior is examined by simulation studies, and an application to Alzheimer’s disease data is illustrated.

关 键 词：纵向数据 部分线性单指标模型 终止事件 

分 类 号：O212[理学—概率论与数理统计]