Spatial survival models based on Weibull random fields

We propose a novel spatial survival model based on a Weibull random field, designed to overcome the limitations of existing copula-based approaches; particularly those relying on the Farlie–Gumbel–Morgenstern (FGM) copula. Although the FGM model only captures weak dependence and enforces reflection symmetry and a forced nugget effect, our model allows for stronger spatial dependence, reflection asymmetry, and mean-square continuity. These properties provide a more flexible and realistic framework for analyzing spatially correlated time-to-event data. The model unifies the proportional hazards (PH), the accelerated failure time (AFT), and the mean parameterizations of the Weibull distribution, allowing a clear interpretation of the effects of the covariates. Due to the analytical intractability of the full likelihood, parameter estimation is performed using a weighted pairwise composite likelihood method based on nearest neighbors. This method offers computational efficiency and robustness to right-censored data. Simulation studies confirm the effectiveness of the proposed model, and an application to real housing data illustrates its practical value.