Censored regression quantiles

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.