This paper presents a semiparametric proportional hazards model designed to handle spatially varying covariate functions, applicable to both geostatistical and areal data observed on irregular spatial domains. The model is estimated through the maximization of a penalized partial likelihood, with a roughness penalty term based on a differential of the spatial field over the target domain. The finite element method is employed for efficient estimation, enabling a piecewise polynomial surface representation of the spatial field. We apply this method to analyze response time data from the London Fire Brigade.

翻译：本文提出了一种半参数比例风险模型，旨在处理空间变化的协变量函数，适用于在非规则空间域上观测的地统计数据和面状数据。该模型通过最大化惩罚部分似然函数进行估计，其粗糙度惩罚项基于目标域上空间场的微分。采用有限元方法实现高效估计，从而获得空间场的分段多项式曲面表示。我们将此方法应用于分析伦敦消防队的响应时间数据。