A new class of Dantzig selectors for censored linear regression models

The Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. A key advantage is that it does not pertain to a particular likelihood or objective function, as opposed to the existing penalized likelihood methods, and hence has the potential for wide applicability. To our knowledge, limited work has been done for the Dantzig selector when the outcome is subject to censoring. This paper proposes a new class of Dantzig variable selectors for linear regression models for right-censored outcomes. We first establish the finite sample error bound for the estimator and show the proposed selector is nearly optimal in the `2 sense. To improve model selection performance, we further propose an adaptive Dantzig variable selector and discuss its large sample properties, namely, consistency in model selection and asymptotic normality of the estimator. The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply the proposed methods to a myeloma clinical trial and identify important predictive genes for patients ’ survival