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.

翻译：本文提出了一种新颖的空间比例风险模型，该模型通过微分正则化方法纳入空间依赖性。针对现有方法忽略区域几何结构的局限性，我们提出了一种基于偏微分方程惩罚的广义空间回归方法。该方法能够处理复杂形状区域，从而实现对生存数据中空间场的精确建模。通过使用惩罚对数似然泛函，我们同时估计协变量效应和空间场。该方法的实现采用有限元方法，能够高效处理不规则区域几何结构。我们通过仿真实验验证了其有效性，并将其应用于实际数据。