Censored quantile regression with time-dependent covariates

Abstract We propose a new class of censored quantile regression models with time-dependent covariates for right-censored failure time data. While time-dependent covariates naturally arise in time-to-event analysis, existing works in the literature discuss treatments for data collected either under an independent censoring mechanism or a longitudinal setting. Our formulation extends the current scope so that the conventional setting of time-dependent covariates can be properly handled. The new framework also generalizes the definition of quantiles and offers a new dynamic perspective for interpretation. Asymptotic properties of the recursive estimator are established. Numerical studies are also presented to illustrate the effectiveness of our proposal.