Robust feature screening for ultra-high dimensional right censored data via distance correlation

Ultra-high dimensional data with right censored survival times are frequently collected in large-scale biomedical studies, for which feature screening has become an indispensable statistical tool. In this paper, we propose two new feature screening procedures based on distance correlation. The first approach performs feature screening through replacing the response and covariate by their cumulative distribution functions' Kaplan-Meier estimator and empirical distribution function respectively, while the second one modifies the distance correlation via an idea of composite quantile regression. The sure screening properties are established under some rather mild technical assumptions, which allow that the dimensionality increases at an exponential rate of the sample size. The proposed methods have three desirable characteristics. Firstly, they are model-free and thus robust to model misspecification. Secondly, they behave reliably when some features contain outliers or follow heavy-tailed distributions. Thirdly, our procedures have better convergence rate than that of distance correlation screening in Li et al. (2012b). Both simulated and real examples show that the proposed methods perform competitively.