A Hierarchical Bayesian Framework for Spatially Varying Coefficient Models With Copula‐Based Dependence

ABSTRACT Spatially clustered survival data arise when event times are recorded within geographic units, where accounting for both spatial variation in covariate effects and within‐cluster dependence is important for reliable survival analysis. This study develops a hierarchical Bayesian framework that integrates spatially varying coefficients into a copula‐based likelihood, capturing both spatial heterogeneity and within‐cluster dependence. Furthermore, to enable efficient and flexible estimation of the spatially varying coefficients, we propose a spatial softmax mixture prior that expresses region‐specific coefficients as convex combinations of shared latent components, inducing spatial smoothness and clustering without the need for nonparametric truncation. Simulation studies and a real data application to acute myeloid leukaemia demonstrate that the proposed prior achieves improved estimation accuracy and effectively detects meaningful spatial variation in covariate effects.