Nonparametric quantile inference with competing risks data

Abstract

A conceptually simple quantile inference procedure is proposed for cause-specific failure probabilities with competing risks data. The quantiles are defined using the cumulative incidence function, which is intuitively meaningful in the competing-risks set-up. We establish the uniform consistency and weak convergence of a nonparametric estimator of this quantile function. These results form the theoretical basis for extensions of standard one-sample and two-sample quantile inference for independently censored data. This includes the construction of confidence intervals and bands for the quantile function, and two-sample tests. Simulation studies and a real data example illustrate the practical utility of the methodology.