  High-dimensional sparse modeling with censored survival data is of great
practical importance, as exemplified by modern applications in high-throughput
genomic data analysis and credit risk analysis. In this article, we propose a
class of regularization methods for simultaneous variable selection and
estimation in the additive hazards model, by combining the nonconcave penalized
likelihood approach and the pseudoscore method. In a high-dimensional setting
where the dimensionality can grow fast, polynomially or nonpolynomially, with
the sample size, we establish the weak oracle property and oracle property
under mild, interpretable conditions, thus providing strong performance
guarantees for the proposed methodology. Moreover, we show that the regularity
conditions required by the $L_1$ method are substantially relaxed by a certain
class of sparsity-inducing concave penalties. As a result, concave penalties
such as the smoothly clipped absolute deviation (SCAD), minimax concave penalty
(MCP), and smooth integration of counting and absolute deviation (SICA) can
significantly improve on the $L_1$ method and yield sparser models with better
prediction performance. We present a coordinate descent algorithm for efficient
implementation and rigorously investigate its convergence properties. The
practical utility and effectiveness of the proposed methods are demonstrated by
simulation studies and a real data example.
