病例队列研究下带约束的Cox模型中参数的一种加权估计方法  

A Weighted Estimation for Cox Model with Parameter Constraints in Case-Cohort Studies

作　　者：邓立凤 丁洁丽[2] 潘莹丽 杨昌鸣 尹洁 Li Feng DENG;Jie Li DING;Ying Li PAN;Chang Ming YANG;Jie YIN(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,P.R.China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China;Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,P.R.China)

机构地区：[1]山东科技大学数学与系统科学学院,青岛266590 [2]武汉大学数学与统计学院,武汉430072 [3]湖北大学数学与统计学学院,武汉430062

出　　处：《数学学报（中文版）》2023年第3期569-588,共20页Acta Mathematica Sinica：Chinese Series

基　　金：丁洁丽获得国家自然科学基金资助项目(11671310)。

摘　　要：许多大型队列研究的主要预算和成本通常来自昂贵的关键协变量的采集与测量.在有限的预算或者时间下,观测大型队列中所有研究对象的昂贵协变量往往是不可行和低效的.因此,研究人员一直致力于寻找和使用能节约成本并能达到预设效率的抽样设计方法.对于生存数据,病例队列设计正是这样一种具有成本效益的有偏抽样机制.进一步,在病例队列研究中,为了利用更多的数据先验信息来提高研究的效率,可以在统计建模过程中对模型参数进行合理的假设和约束.本文研究病例队列设计下带约束的Cox模型中参数的估计方法.我们提出了一种加权约束估计的方法,并建立了所提出估计的渐近理论.发展了一种新的约束MM算法来实现所提出的加权约束估计的数值计算.通过统计模拟研究评估了所提出方法在有限样本量下的表现.分析了一个肾母细胞瘤的实际数据来展示所提出方法的实际应用价值.In many large cohort studies,the major budget and cost typically arise from the assembling of expensive covariates.Collecting information on expensive covariates for all subjects in a large cohort may not be feasible due to a limited budget or time.Therefore,researchers have been trying to find sampling design that can save costs and achieve preset efficiency.In this situation,the case-cohort design is one of the most popular sampling scheme for time-to-event data.Case cohort design is such a cost-effective biased sampling scheme for time-to-event data.Furthermore,in case cohort studies,take reasonable assumptions and constraints on parameters into consideration in the modeling process can utilize more data prior information and acquire more eficiency.In this paper,we fit the Cox model with constraints to case-cohort data and develop an inverse probability weighted approach for regression analysis.We establish asymptotic properties of the proposed estimator and develop a constrained minorization-maximization algorithm for the implementation.Simulation studies are conducted to evaluate the finite-sample performance.A data example from a Wilms tumor study is analyzed to demonstrate the application of the proposed method.

关 键 词：病例队列设计 逆概率加权 COX模型 KKT条件 MM算法 

分 类 号：O212.2[理学—概率论与数理统计]