  Semiparametric accelerated failure time (AFT) models are a useful alternative
to Cox proportional hazards models, especially when the assumption of constant
hazard ratios is untenable. However, rank-based criteria for fitting AFT models
are often non-differentiable, which poses a computational challenge in
high-dimensional settings. In this article, we propose a new alternating
direction method of multipliers algorithm for fitting semiparametric AFT models
by minimizing a penalized rank-based loss function. Our algorithm scales well
in both the number of subjects and number of predictors; and can easily
accommodate a wide range of popular penalties. To improve the selection of
tuning parameters, we propose a new criterion which avoids some common problems
in cross-validation with censored responses. Through extensive simulation
studies, we show that our algorithm and software is much faster than existing
methods (which can only be applied to special cases), and we show that
estimators which minimize a penalized rank-based criterion often outperform
alternative estimators which minimize penalized weighted least squares
criteria. Application to nine cancer datasets further demonstrates that
rank-based estimators of semiparametric AFT models are competitive with
estimators assuming proportional hazards model in high-dimensional settings,
whereas weighted least squares estimators are often not. A software package
implementing the algorithm, along with a set of auxiliary functions, is
available for download at github.com/ajmolstad/penAFT.
