On path restoration for censored outcomes

Dimension reduction, model and variable selection are ubiquitous concepts in modern statistical science and deriving new methods beyond the scope of current methodology is noteworthy. This article briefly reviews existing regularization methods for penalized least squares and likelihood for survival data and their extension to a certain class of penalized estimating function. We show that if one's goal is to estimate the entire regularized coefficient path using the observed survival data, then all current strategies fail for the Buckley-James estimating function. We propose a novel two-stage method to estimate and restore the entire Dantzig-regularized coefficient path for censored outcomes in a least-squares framework. We apply our methods to a microarray study of lung andenocarcinoma with sample size n = 200 and p = 1036 gene predictors and find 10 genes that are consistently selected across different criteria and an additional 14 genes that merit further investigation. In simulation studies, we found that the proposed path restoration and variable selection technique has the potential to perform as well as existing methods that begin with a proper convex loss function at the outset.