The Dantzig Selector in Cox's Proportional Hazards Model


Anestis Antoniadis, Laboratoire Jean Kuntzmann, Département de Statistique, Université Joseph Fourier, B.P. 53, 38041 Grenoble Cedex 9, France.


Abstract.  The Dantzig selector (DS) is a recent approach of 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 (PH) function regression models using a framework that extends the theory, the computational advantages and the optimal asymptotic rate properties of the DS to the class of Cox's PH under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach with other methods and illustrate it on a well-known microarray gene expression data set for predicting survival from gene expressions.