The Dantzig Selector in Cox’s Proportional Hazards Model

The Dantzig Selector is a recent approach to estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression coefficients exactly to zero, thus performing variable selection. However, such a framework, contrary to the LASSO, has never been used in regression models for survival data with censoring. A key motivation of this article is to study the estimation problem for Cox’s proportional hazards function regression models using a framework that extends the theory, the computational advantages and the optimal asymptotic rate properties of the Dantzig selector to the class of Cox’s proportional hazards under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach to other methods and illustrate it on a well-known microarray gene expression data set for predicting survival from gene expressions. Some key words: VARIABLE SELECTION; GENERALIZED LINEAR MODELS; DANTZIG SELECTOR; LASSO; PENALIZED PARTIAL LIKELIHOOD; PROPORTIONAL HAZARDS MODEL;