Censored mean variance sure independence screening for ultrahigh dimensional survival data

Abstract

Feature screening has become an indispensable statistical modeling tool for ultrahigh dimensional data analysis. This article introduces a new model-free marginal feature screening approach for ultrahigh dimensional survival data with right censoring. The new procedure could be used for survival data with both ultrahigh dimensional categorical and continuous covariates. Motivated by Cui et al. (2015), a censored mean variance index (cMV) is proposed to measure the dependence between a survival outcome and a categorical covariate. Then a slice-and-fuse method is exploited to modify the cMV index adaptive to continuous covariates. The sure independence screening based on the censored mean variance index (cMV-SIS) is proposed to identify the important covariates for ultrahigh dimensional data with censored survival outcomes. It enjoys many appealing merits inherited in the mean variance index. It is model-free and thus robust to model misspecification. It is also robust to heavy tails and outliers in covariates. Moreover, the sure screening properties are theoretically investigated for both categorical and continuous covariates under some mild technical conditions. Extensive numerical simulations and a real data example have demonstrated the competitive performances of the proposed feature screening method.