Estimation in the l1-Regularized Accelerated Failure Time Model

This note variable selection in the semiparametric linear regression model for censored data. Semiparametric linear regression for censored data is a natural extension of the linear model for uncensored data; however, random censoring introduces substantial theoretical and numerical challenges. By now, a number of authors have made significant contributions for estimation and inference in the semiparametric linear model but none of these authors have considered regularized estimation and subsequent variable selection. Our estimator is defined as a consistent solution to a suitably penalized, weighted logrank estimating function. For general weight function, this estimating function is known to be non-monotone in the regression coefficients and may contain multiple roots. Nevertheless, it is one of the more popular estimators which does not assume proportional hazards. The proposed method uses linear and quadratic programming techniques for l1-regularized estimation and can be implemented easily in R. We illustrate the utility of our approach in real and simulated data.