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Censored Interquantile Regression Model with Time-Dependent Covariates
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2023-05-08 , DOI: 10.1080/01621459.2023.2208389
Chi Wing Chu, Tony Sit

Abstract

Conventionally, censored quantile regression stipulates a specific, pointwise conditional quantile of the survival time given covariates. Despite its model flexibility and straightforward interpretation, the pointwise formulation oftentimes yields rather unstable estimates across neighbouring quantile levels with large variances. In view of this phenomenon, we propose a new class of quantile-based regression models with time-dependent covariates for censored data. The models proposed aim to capture the relationship between the failure time and the covariate processes of a target population that falls within a specific quantile bracket. The pooling of information within a homogeneous neighbourhood facilitates more efficient estimates hence more consistent conclusion on statistical significances of the variables concerned. This new formulation can also be regarded as a generalization of the accelerated failure time model for survival data in the sense that it relaxes the assumption of global homogeneity for the error at all quantile levels. By introducing a class of weighted rank-based estimation procedure, our framework allows a quantile-based inference on the covariate effect with a less restrictive set of assumptions. Numerical studies demonstrate that the proposed estimator outperforms existing alternatives under various settings in terms of smaller empirical biases and standard deviations. A perturbation-based resampling method is also developed to reconcile the asymptotic distribution of the parameter estimates. Finally, consistency and weak convergence of the proposed estimator are established via empirical process theory.



中文翻译:

具有时间相关协变量的截尾分位数回归模型

摘要

通常,截尾分位数回归规定了给定协变量的生存时间的特定的逐点条件分位数。尽管模型灵活且解释简单,但逐点公式通常会在具有较大方差的相邻分位数水平上产生相当不稳定的估计。鉴于这种现象,我们提出了一类新的基于分位数的回归模型,该模型具有针对删失数据的时间相关协变量。所提出的模型旨在捕获故障时间与属于特定分位数括号内的目标总体的协变量过程之间的关系。同质邻域内的信息汇集有助于更有效的估计,从而对相关变量的统计显着性得出更一致的结论。这个新公式也可以被视为生存数据的加速故障时间模型的推广,因为它放宽了所有分位数级别错误的全局同质性假设。通过引入一类基于加权等级的估计程序,我们的框架允许使用限制较少的假设集对协变量效应进行基于分位数的推断。数值研究表明,就较小的经验偏差和标准偏差而言,所提出的估计量在各种设置下优于现有替代方案。还开发了一种基于扰动的重采样方法来协调参数估计的渐近分布。最后,通过经验过程理论建立了所提出的估计量的一致性和弱收敛性。

更新日期:2023-05-08
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