Moderately clipped LASSO for high-dimensional Cox proportional hazards models

Cox proportional hazard model is widely used in survival analysis to model the relationship between timeto-event responses and predictive variables.For high-dimensional survival data with right censoring, various survival models have been proposed to analyze large-scale survival data, including the least absolute shrinkage and selection operator (LASSO), ridge, and smoothly clipped absolute deviation (SCAD) penalized Cox models.The penalized Cox models enable to achieve both predicting relative risk for each individual and select relevant predictive variables.In this paper, we propose a novel penalized method for the Cox model, called the moderetely clipped LASSO (MCL) which is designed by combining the minimax concave penalty (MCP) and LASSO penalty.Hence, it preserves the advantages of the LASSO and MCP.We develop an efficient algorithm that is a good mixture of the concave convex procedure, modified local quadratic approximation, and the coordinate descent algorithm.Simulation studies and real data applications demonstrate that the proposed method achieves superior variable selection and prediction performances compared to the other existing methods.