Model-free screening procedure for ultrahigh-dimensional survival data based on Hilbert-Schmidt independence criterion

Abstract

How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. Sure independent screening procedure has been demonstrated to be an effective method to reduce the dimensionality of data from a large scale to a relatively moderate scale. For censored survival data, the existing screening methods mainly adopt the Kaplan--Meier estimator to handle censoring, which may not perform well for scenarios which have heavy censoring rate. In this article, we propose a model-free screening procedure based on the Hilbert-Schmidt independence criterion (HSIC). The proposed method avoids the complication to specify an actual model from a large number of covariates. Compared with existing screening procedures, this new approach has several advantages. First, it does not involve the Kaplan--Meier estimator, thus its performance is much more robust for the cases with a heavy censoring rate. Second, the empirical estimate of HSIC is very simple as it just depends on the trace of a product of Gram matrices. In addition, the proposed procedure does not require any complicated numerical optimization, so the corresponding calculation is very simple and fast. Finally, the proposed procedure which employs the kernel method is substantially more resistant to outliers. Extensive simulation studies demonstrate that the proposed method has favorable exhibition over the existing methods. As an illustration, we apply the proposed method to analyze the diffuse large-B-cell lymphoma (DLBCL) data and the ovarian cancer data