On lasso for censored data

In this paper, we propose a new lasso-type estimator for censored data after one-step imputatation. While several penalized likelihood estimators have been proposed for censored data variable selection through hazards regression, many such estimators require parametric or proportional hazards assumptions. The proposed estimator, on the other hand, is based on the linear model and least-squares principles. Iterative penalized Buckley-James estimators are also popular in this setting but have been shown to be unstable and unreliable. Unlike path-based learning based on least-squares approximation, our method requires no covariance assumption and the method is valid for even modest sample sizes. Our calibration estimator is the minimizer of a convex loss function using synthetic data and yields reproducible coefficient estimates and coefficient paths. The numerical algorithms are fast, reliable, and readily available because they build on existing software for complete, uncensored data. We examine the large and small sample properties of our estimator and illustrate the method through simulation studies and application to two real data sets.