A Bayesian Spatially-Clustered Coefficient Model with Temporal Structures

Abstract

A plethora of health data, such as hepatitis A and COVID-19 infection cases, are collected over spatial and temporal domains. Also, demographical and socioeconomic covariates, including population density and per capita income, are gathered over space and time units. Thus, the association between infectious disease outcomes and risk factors may differ across space and time. In particular, some sub-regions may have a heterogeneous association with others, while there may be a homogeneous temporal structure within the sub-region. Therefore, it is reasonable to claim that the effects of covariates on disease outcomes vary across space and time domains. On top of that, the common spatial model with space-time random components might not distinguish risk effects from space random effects. It meant that the estimates of coefficients could change considerably or shrink to zero due to the spatial confounding bias. Thus, we adopted the Bayesian two-stage framework in the model to reduce the spatial collinearity. As a result, we developed a Bayesian spatially-clustered coefficient model with temporal trends to estimate the sub-regions with the temporally-varying risk effects. In addition, we employed the two-stage approach to remedy the spatial confounding bias. We applied the proposed model to the number of patients with hepatitis A in the Republic of Korea and investigated the performance of the suggested model using a variety of model assessment measures.