A NONPARAMETRIC SURVIVAL FUNCTION ESTIMATOR VIA CENSORED KERNEL QUANTILE REGRESSIONS

Abstract

In survival data analysis, a central interest is to identify the relationship between a possibly censored survival time and explanatory covariates. In this article, a new censored quantile regression method is proposed and studied in the framework of reproducing kernel Hilbert spaces (RKHS). We first establish the joint piecewise linearity of the regression parameters as a function of regularization parameter lambda and quantile level iota. An efficient algorithm is then developed to compute the entire two-dimensional solution surface over the (lambda x iota)-plane. Finally, a piecewise linear conditional survival function estimator is constructed based on the solution surface. The method provides a new and flexible survival function estimator without requiring such rigid model assumptions as linearity of the survival time or proportionality of the hazards. One important advantage of the estimator is that it can handle moderately high-dimensional covariates. We carry out an asymptotic analysis to justify the proposed method theoretically, and numerical results are shown to illustrate its competitive finite-sample performance under various simulated scenarios and real applications.