  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.
