一般偏差右删失数据下剩余寿命分位数回归

孙桂萍, 赵目, 周勇

数学学报 ›› 2022, Vol. 65 ›› Issue (4) : 607-624.

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数学学报 ›› 2022, Vol. 65 ›› Issue (4) : 607-624. DOI: 10.12386/A20210019
论文

一般偏差右删失数据下剩余寿命分位数回归

    孙桂萍1,2, 赵目3, 周勇4,5
作者信息 +

Quantile Residual Regression Model with General Biased and Right-Censored Data

    Gui Ping SUN1,2, Mu ZHAO3, Yong ZHOU4,5
Author information +
文章历史 +

摘要

剩余寿命是刻画个体预期寿命的一个重要度量，对剩余寿命的早期研究主要集中在剩余均值上.然而当总体生存函数偏态或厚尾时剩余均值函数可能不存在，因此统计学者建议用剩余寿命分位数来刻画预期寿命.在完全数据和右删失数据下，剩余寿命分位数的建模和理论已经很完善.但是，在实际的调查研究中经常会遇到偏差抽样数据.例如，临床医学中的左截断数据，流行病学中的病例队列抽样数据，医学大型队列研究中的长度偏差抽样数据等等.忽略抽样偏差会导致参数估计有偏和不合理的推断结果.本文考虑一般偏差右删失数据下剩余寿命分位数回归的统计推断问题.首先，我们提出了一个一般偏差右删失数据下的剩余寿命分位数回归模型，并利用一般估计方程方法对模型中的参数进行了估计.针对已有文献常用的删失变量与协变量独立性假设，本文重点考虑了删失变量依赖于协变量场合.其次，由于估计量的渐近方差中涉及非参密度函数，在估计渐近方差时，本文采用Bootstrap方法.最后，数值模拟显示本文提出的方法有限样本性质表现很好.

Abstract

Residual life is an important quantity to characterize the individual life expectancy. Early studies on the residual life mainly focus on the mean residual life. However, when the potential survival function of population is skewed or heavy-tailed, the mean residual life does not exist. So the statisticians suggest the quantile residual life to characterize the individual life expectancy. With the complete data and the right censored data, the modeling and theoretical properties of the quantile residual life have been established well. However, biased sampling data are often encountered in practical investigations. For example, left truncated data are often encountered in clinical trial, case cohort sampling data frequently occur in epidemiology, length biased sampling data also frequently occur in large medical cohort studies. Ignoring sampling biases will lead to biased estimators and unreasonable inferences. We consider a quantile residual life regression model under the general biased and right censored data. First, we propose a quantile regression model of residual life with the general biased and right censored data. Estimation procedures by using general estimation equation method are proposed. Comparing to the independent assumption of the censored variables and the covariates, which is commonly used in the existing literatures, this paper mainly considers that censored variables depend on the covariates. Second, because the asymptotic variance of the estimator involves the non-parametric density functions, so a bootstrap method is adopted. Finally, the simulation results show that the proposed estimators have good finite sample properties.

关键词

剩余寿命 / 一般偏差 / 分位数回归

Key words

residual life / biased data / residual quantile regression

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孙桂萍, 赵目, 周勇. 一般偏差右删失数据下剩余寿命分位数回归. 数学学报, 2022, 65(4): 607-624 https://doi.org/10.12386/A20210019
Gui Ping SUN, Mu ZHAO, Yong ZHOU. Quantile Residual Regression Model with General Biased and Right-Censored Data. Acta Mathematica Sinica, Chinese Series, 2022, 65(4): 607-624 https://doi.org/10.12386/A20210019

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基金

国家自然科学基金（71931004，92046005）；中央高校基本科研业务费专项资金（2722020PY040）；中南财经政法大学青年教师创新研究专项（2722021BX023）
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