Nonparametric quantile inference with competing–risks data

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. Copyright 2007, Oxford University Press.