  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.
