Model-free feature screening for high-dimensional survival data

Abstract

With the rapid-growth-in-size scientific data in various disciplines, feature screeningplays an important role to reduce the high-dimensionality to a moderate scale in many scientific fields. In this paper,we introducea unified and robust model-free feature screening approach for high-dimensional survival data with censoring,which has several advantages: it is a model-free approach under a general model framework, and hence avoidsthe complication to specify an actual model form with huge number of candidate variables;under mild conditions without requiring the existenceof any moment of the response, it enjoys the ranking consistency and sure screening properties in ultra-high dimension.In particular, we impose a conditional independenceassumption of the response and the censoring variable given each covariate, instead of assuming the censoringvariable is independent of the response and the covariates.Moreover, we also propose a more robust variant to the new procedure, which possesses desirable theoretical properties withoutany finite moment condition of the predictors and the response.The computation of the newly proposed methodsdoes not require any complicated numerical optimization and it is fast and easy to implement.Extensive numerical studies demonstrate that the proposed methods perform competitively for variousconfigurations. Application is illustrated with an analysis of a genetic data set.