Variable selection in the cox regression model with covariates missing at random

We consider variable selection in the Cox regression model (Cox, 1975, Biometrika 362, 269-276) with covariates missing at random. We investigate the smoothly clipped absolute deviation penalty and adaptive least absolute shrinkage and selection operator (LASSO) penalty, and propose a unified model selection and estimation procedure. A computationally attractive algorithm is developed, which simultaneously optimizes the penalized likelihood function and penalty parameters. We also optimize a model selection criterion, called the IC(Q) statistic (Ibrahim, Zhu, and Tang, 2008, Journal of the American Statistical Association 103, 1648-1658), to estimate the penalty parameters and show that it consistently selects all important covariates. Simulations are performed to evaluate the finite sample performance of the penalty estimates. Also, two lung cancer data sets are analyzed to demonstrate the proposed methodology.