Shrinkage variable selection and estimation in proportional hazards models with additive structure and high dimensionality

Variable selection and estimation in proportional hazards models with additive relative risk is considered. Both objectives are achieved using a penalized partial likelihood with a group nonconcave penalty. Oracle properties of the estimator are demonstrated, when the dimensionality is allowed to be larger than sample size. To deal with the computational challenges when p>np>n, an active-set-type algorithm is proposed. Finally, the method is illustrated with simulation examples and a real microarray study.