Model Validation for Survival Analysis by Smoothed Predictive Likelihood

Assessing the predictive performance is a crucial aspect in survival modeling, essential for model selection, tuning parameter determination, and evaluating additional predictive ability. The predictive log-likelihood has been recommended as a suitable evaluation measure, particularly for survival models, which generally return entire survival curves rather than point predictions. However, applying predictive likelihood in semiparametric and nonparametric survival models is problematic since the survival curves are step-functions, which result in zero predictive likelihood when events occur at previously unobserved time points. The most well-known existing solution, Verweij's predictive partial likelihood, is limited to Cox models. In this article, we propose a novel approach based on nearest-neighbor kernel smoothing that is usable in general semi- and nonparametric survival models. We show that our new method performs competitively with existing methods in the Cox setting while offering broader applicability, including testing for the presence of a frailty term and determining the optimal level of smoothness in penalized additive hazards models.