  This paper develops a new scalable sparse Cox regression tool for sparse
high-dimensional massive sample size (sHDMSS) survival data. The method is a
local $L_0$-penalized Cox regression via repeatedly performing reweighted
$L_2$-penalized Cox regression. We show that the resulting estimator enjoys the
best of $L_0$- and $L_2$-penalized Cox regressions while overcoming their
limitations. Specifically, the estimator is selection consistent, oracle for
parameter estimation, and possesses a grouping property for highly correlated
covariates. Simulation results suggest that when the sample size is large, the
proposed method with pre-specified tuning parameters has a comparable or better
performance than some popular penalized regression methods. More importantly,
because the method naturally enables adaptation of efficient algorithms for
massive $L_2$-penalized optimization and does not require costly data driven
tuning parameter selection, it has a significant computational advantage for
sHDMSS data, offering an average of 5-fold speedup over its closest competitor
in empirical studies.
