Spatial Proportional Hazards Model with Differential Regularization

This paper introduces a novel Spatial Proportional Hazards model that incorporates spatial dependence through differential regularization. We address limitations of existing methods that overlook domain geometry by proposing an approach based on the Generalized Spatial Regression with PDE Penalization. Our method handles complex-shaped domains, enabling accurate modeling of spatial fields in survival data. Using a penalized log-likelihood functional, we estimate both covariate effects and the spatial field. The methodology is implemented via finite element methods, efficiently handling irregular domain geometries. We demonstrate its efficacy through simulations and apply it to real-world data.