Variable Selection via Generalized SELO-Penalized Cox Regression Models

The seamless-L0 (SELO) penalty is a smooth function that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO (GSELO) penalized log partial likelihood (PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton (SQN) with continuation algorithm. The authors propose a consistent modified BIC (MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL- MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method.