Assessing the impact of neighborhood structures in Bayesian disease mapping.

In Bayesian disease mapping, defining the neighborhood structure is crucial when fitting the conditional auto-regressive model. Yet, there has been little assessment of how different structures affect the model performance in case of fine-scale data. This paper explores this gap. In a case study examining COVID-19 pandemic effects, 2020 mortality is contrasted with pre-pandemic rates in small areas in Limburg (Belgium). Data are modeled using BYM and BYM2, with three broadening queen-neighborhood structures up to the fifth-order neighbors and two weight schemes. A simulation study assesses model performance in reproducing the pairwise spatial correlation at different neighbor orders. Models are compared regarding WAIC, goodness-of-fit, parameter estimates, and computation time. Results show that the order-based weight matrix performs better than the binary matrix. The simple first-order neighborhood structure shows comparable performance to larger higher-order structures while requiring much less computation time. The BYM model is more impacted by the choice of the neighborhood as compared to the BYM2 model. Our findings suggest minimal advantages in employing higher-order neighborhood matrices. In conclusion, our study indicates that opting for a simple first-order neighborhood structure is a pragmatic and suitable choice when applying a conditional auto-regressive model to fine-scale data in Bayesian disease mapping.