Smoothed quantile regression for censored residual life

TL;DR

This paper introduces a smoothed quantile regression method for censored residual life data, enabling efficient estimation and inference with improved numerical stability and robustness, validated through simulations and a dental study application.

Contribution

It proposes a novel smoothed estimating equation approach for quantile regression of censored residual life, improving computational stability and inference accuracy.

Findings

The method provides consistent and asymptotically normal estimators.

Simulation studies demonstrate superior finite sample performance.

Application to dental data illustrates practical utility.

Abstract

We consider a regression modeling of the quantiles of residual life, remaining lifetime at a specific time. We propose a smoothed induced version of the existing non-smooth estimating equations approaches for estimating regression parameters. The proposed estimating equations are smooth in regression parameters, so solutions can be readily obtained via standard numerical algorithms. Moreover, the smoothness in the proposed estimating equations enables one to obtain a robust sandwich-type covariance estimator of regression estimators aided by an efficient resampling method. To handle data subject to right censoring, the inverse probability of censoring weight are used as weights. The consistency and asymptotic normality of the proposed estimator are established. Extensive simulation studies are conducted to validate the proposed estimator's performance in various finite samples settings. We apply the proposed method to dental study data evaluating the longevity of dental restorations.