Model-free slice screening for ultrahigh-dimensional survival data

For ultrahigh-dimensional data, independent feature screening has been demonstrated both theoretically and empirically to be an effective dimension reduction method with low computational demanding. Motivated by the Buckley-James method to accommodate censoring, we propose a fused Kolmogorov-Smirnov filter to screen out the irrelevant dependent variables for ultrahigh-dimensional survival data. The proposed model-free screening method can work with many types of covariates (e.g. continuous, discrete and categorical variables) and is shown to enjoy the sure independent screening property under mild regularity conditions without requiring any moment conditions on covariates. In particular, the proposed procedure can still be powerful when covariates are strongly dependent on each other. We further develop an iterative algorithm to enhance the performance of our method while dealing with the practical situations where some covariates may be marginally unrelated but jointly related to the response. We conduct extensive simulations to evaluate the finite-sample performance of the proposed method, showing that it has favourable exhibition over the existing typical methods. As an illustration, we apply the proposed method to the diffuse large-B-cell lymphoma study.