Nonparametric inference on cause-specific quantile residual life

In medical research, investigators are often interested in inferring time-to-event distributions under competing risks. It is well known, however, that the naive approach based on the Kaplan-Meier method to estimate the proportion of cause-specific events overestimates the true quantity. In this paper, we show that the quantile residual life function, a natural and popular summary measure of survival data, could be also seriously affected by the competing events. An existing two-sample test statistic for inference on median residual life is modified for competing risks data, which does not involve estimation of the improper probability density function of the subdistribution of cause-specific events under censoring. Simulation results demonstrate that the test statistic controls the type 1 error probabilities reasonably well. The proposed method is applied to a real data example from a large-scale phase III breast cancer study.