协变量含测量误差的删失分位数回归

Censored quantile regression has emerged as a more appealing tool to analyze and model the survival data in recent research because the survival times, potentially subject to right censoring, tend to be highly right-skewed. Many studies involve covariates that are measured with errors instead of being accurately ascertained due to either the technical limitation or experimental cost and so on. Covariate measurement error has been the repeated theme of statistical research and the related well-developed methods have been successfully applied in the mean regression or survival analysis. However, most of these methods rely on the likelihood and hence cannot be applied directly in the framework of censored quantile regression with covariate measurement error and the related methodology development is extremely lacking although valuable. This proposal targets at developing methods and theory to establish the statistical inference procedures for censored quantile regression with covariate measurement error and thus lightening the research blind of this area. Specifically, this proposal develops the method of approximately and smoothly corrected estimating functions, employs nonparametric techniques of kernel smoothing and B-spline approximation, combines with the related theory of empirical processes and the Volterra integral equation, investigates the effects of the censored survival times and the covariates measurement errors on the quantile regression relationship of survival times given covariates, and establishes a series of statistical inference procedures for three forms of censored quantile regression models with covariate measurement error. Furthermore, extensive simulation studies will be conducted and an ongoing lung cancer study analyzed to demonstrate the practical utility of the proposed methods.

生存分析中可能发生删失的生存时间通常是右偏的，因此采用删失分位数回归分析与建模生存数据更加合适和直接，其研究近年来备受关注。由于受技术条件、试验成本等因素的制约，某些协变量难以精确测量，从而存在测量误差。测量误差问题也一直是统计研究的热点之一。多数传统的测量误差的统计方法由于依赖于似然函数从而在删失分位数回归框架下不再适用；含测量误差的删失分位数回归问题几乎是研究的盲点。本项目拟在该问题上开展一些原创性和拓展性的工作。在申请者现有的工作基础上，本项目提出逼近的光滑的修正估计函数方法，采用非参数的核光滑和B样条逼近的技术，结合经验过程和积分方程的有关理论，研究生存时间发生删失和测量误差如何影响生存时间于协变量的分位数回归关系等关键问题，建立一系列含测量误差的删失分位数回归模型的统计推断方法。同时，通过丰富的计算机模拟阐明所提出方法的实用性，并将之应用于一项正在进行的肺癌的研究中。

本项目主要研究删失分位数回归下的测量误差问题。受本项目的资助，申请者出色地完成了项目中拟进行研究的问题。关于项目中提出的采用光滑的修正估计函数的统计方法的研究于2015年被统计学顶尖学术期刊Journal of the American Statistical Association接受并在线发表。与项目的主要研究内容删失分位数回归直接相关的两项研究成果分别于2013年在统计学顶尖学术期刊Journal of the American Statistical Association正式发表和2015年在统计学顶尖学术期刊Biometrika正式发表。此外，还有若干研究成果在统计学主流刊物上发表或者审稿之中。申请者的研究表明，本项目提出的统计分析方法是可行的，可以有效地克服测量误差对删失分位数回归参数的统计推断所带来的负面影响，从而给出正确的推断方法，为临床试验者的数据分析提供理论保障与应用支持。

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