A kernel nonparametric quantile estimator for right-censored competing risks data

In medical and epidemiological studies, it is often interest to study time-to-event distributions under competing risks that involve two or more failure types. Nonparametric analysis of competing risks is typically focused on the cumulative incidence function or nonparametric quantile function. However, the existing estimators may be very unstable due to their unsmoothness. In this paper, we propose a kernel nonparametric quantile estimator for right-censored competing risks data, which is a smoothed version of Peng and Fine's nonparametric quantile estimator. We establish the Bahadur representation of the proposed estimator. The convergence rate of the remainder term for the proposed estimator is substantially faster than Peng and Fine's quantile estimator. The pointwise confidence intervals and simultaneous confidence bands of the quantile functions are also derived. Simulation studies illustrate the good performance of the proposed estimator. The methodology is demonstrated with two applications of the Supreme Court Judge data and AIDSSI data.