Modeling multivariate lattice data with Dirichlet process mixture spatial random effects

Many multivariate Bayesian spatial models for joint disease mapping assume Gaussian distributions for the spatial random effects, which can be restrictive when the true distributions are unknown. We develop a nonparametric Bayesian methodology that uses a Dirichlet process mixture prior to model spatial random effects in the joint analysis of multiple diseases. Unlike mixture-based approaches, the Dirichlet process mixture infers the number of components from the data, captures complex or multimodal distributions, and accounts for distributional uncertainty. The proposed methodology is extended to jointly model multiple spatially correlated random effects. Simulation studies indicate that our proposed approach is comparable in terms of accuracy to the bivariate normal spatial model but shows superior predictive performance, making it particularly valuable for forecasting outcomes in sparse small-area health survey data. An empirical study using district-level HIV prevalence and antiretroviral therapy (ART) coverage data in South Africa shows that the proposed bivariate nonparametric model outperforms the bivariate conditional autoregressive Gaussian model.