  Broken adaptive ridge (BAR) is a computationally scalable surrogate to
$L_0$-penalized regression, which involves iteratively performing reweighted
$L_2$ penalized regressions and enjoys some appealing properties of both $L_0$
and $L_2$ penalized regressions while avoiding some of their limitations. In
this paper, we extend the BAR method to the semi-parametric accelerated failure
time (AFT) model for right-censored survival data. Specifically, we propose a
censored BAR (CBAR) estimator by applying the BAR algorithm to the Leurgan's
synthetic data and show that the resulting CBAR estimator is consistent for
variable selection, possesses an oracle property for parameter estimation {and
enjoys a grouping property for highly correlation covariates}. Both low and
high dimensional covariates are considered. The effectiveness of our method is
demonstrated and compared with some popular penalization methods using
simulations. Real data illustrations are provided on a diffuse large-B-cell
lymphoma data and a glioblastoma multiforme data.
