Interpretable survival analysis via regularized functional Cox models

P. González Barquero, J. Goldsmith, Á. Méndez Civieta, R. E. Lillo

In contemporary survival analysis, the integration of functional data, specifically longitudinal measurements like cardiac rhythms or continuous physical activity monitors, offers a detailed perspective on patient health. However, a significant difficulty remains in determining which specific temporal windows within these functional trajectories are truly predictive of events.
We present a refined framework for the functional Cox model that prioritizes structural sparsity and interpretability. Rather than assuming the entire covariate function contributes to the hazard rate, our approach employs a dual-penalty mechanism. By applying regularization to both the coefficient function and its derivatives, the model simultaneously enforces smoothness and performs selection. This ensures that non-essential segments of the functional predictor are shrunk exactly to zero. This methodology offers an interpretable and flexible solution for analyzing functional covariates in survival models.

Keywords: Functional data analysis survival analysis penalized regression

J. A. Cardenas Cardenas, P. Delicado, J. Arjona

S. Díaz-Aranda, J. Aguilar, R. E. Lillo

P. Morala Miguélez, E. Gambín Monserrat, I. Úcar Marqués