In data sets with many more features than observations, independent screening
based on all univariate regression models leads to a computationally convenient
variable selection method. Recent efforts have shown that in the case of
generalized linear models, independent screening may suffice to capture all
relevant features with high probability, even in ultra-high dimension. It is
unclear whether this formal sure screening property is attainable when the
response is a right-censored survival time. We propose a computationally very
efficient independent screening method for survival data which can be viewed as
the natural survival equivalent of correlation screening. We state conditions
under which the method admits the sure screening property within a general
class of single-index hazard rate models with ultra-high dimensional features.
An iterative variant is also described which combines screening with penalized
regression in order to handle more complex feature covariance structures. The
methods are evaluated through simulation studies and through application to a
real gene expression dataset.Comment: 32 pages, 3 figure