A Quantile Regression Model for Failure-Time Data with Time-Dependent Covariates

TL;DR

This paper introduces a new quantile regression model for survival analysis that incorporates time-dependent covariates and right censoring, using instrumental variables and a doubly-robust estimator, with theoretical and empirical validation.

Contribution

It presents a novel quantile regression approach for survival data with time-dependent covariates, including a doubly-robust estimator and rigorous asymptotic analysis.

Findings

Estimator has desirable asymptotic properties.

Simulation studies show good finite-sample performance.

Application to heart transplant data demonstrates practical utility.

Abstract

Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This paper provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset.