Censored Regression Quantiles

Abstract

Using quantile regression to analyze survival times offers an valuable complement to traditional Cox proportional hazards modelling. Unfortunately, this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the Kaplan–Meier estimator and applies under standard assumptions for censored regression models. Here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the Kaplan–Meier estimator. Specifically, the asymptotic behavior is directly analogous to that of the Kaplan–Meier estimator, and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case. Some preliminary examples suggest the strong potential of these methods as a complement to the use of Cox models.