Model selection in nonparametric hazard regression

We propose a novel model selection method for a nonparametric extension of the Cox proportional hazard model, in the framework of smoothing splines ANOVA models. The method automates the model building and model selection processes simultaneously by penalizing the reproducing kernel Hilbert space norms. On the basis of a reformulation of the penalized partial likelihood, we propose an efficient algorithm to compute the estimate. The solution demonstrates great flexibility and easy interpretability in modeling relative risk functions for censored data. Adaptive choice of the smoothing parameter is discussed. Both simulations and a real example suggest that our proposal is a useful tool for multivariate function estimation and model selection in survival analysis.