ABSTRACT
This chapter discusses how quantile regression models can be extended so as to handle time-to-event data which are characterized by censoring. It presents basic concepts and models that are commonly adopted in survival analysis. The chapter examines developments in quantile regression for censored data and their relation to some existing survival models. It also discusses popular models used for the failure time distribution of a homogeneous population. The chapter presents a rich category of semiparametric regression models that enable statisticians to relate the survival time of a population to its corresponding covariate observations. It deals with estimating the distribution of the median of the survival time. Median estimation can be further generalized to quantile estimation. Quantile regression is a valuable alternative to the celebrated Cox proportional hazards model. The Buckley–James type estimator, however, appears to be more efficient for estimating one set of model parameters for a particular quantile value.
