Simultaneous variable selection and estimation for a partially linear Cox model.

We consider simultaneous variable selection and estimation for a deep neural network-based partially linear Cox model and propose a novel penalized approach. In particular, a two-step iterative algorithm is developed with the use of the minimum information criterion to ensure sparse estimation. The proposed method circumvents the curse of dimensionality while facilitating the interpretability of linear covariate effects on survival, and the algorithm greatly reduces the computational burden by avoiding the need to select the optimal tuning parameters that is usually required by many other popular penalties. The convergence rate and asymptotic properties of the resulting estimator are established along with the consistency of variable selection. The performance of the procedure is demonstrated through extensive simulation studies and an application to a myeloma dataset.