The L1/2 regularization method for variable selection in the Cox model

Abstract

In this paper, we investigate to use the L1/2 regularization method for variable selection based on the Cox's proportional hazards model. The L1/2 regularization can be taken as a representative of Lq (0 < q < 1) regularizations and has been demonstrated many attractive properties. To solve the L1/2 penalized Cox model, we propose a coordinate descent algorithm with a new univariate half thresholding operator which is applicable to high-dimensional biological data. Simulation results based on standard artificial data show that the L1/2 regularization method can be more accurate for variable selection than Lasso and SCAD methods. The results from real DNA microarray datasets indicate the L1/2 regularization method performs competitively.