Modeling Exposure Mixtures and Spatiotemporal Dependence in Count Data Using Bayesian Kernel Machine Regression

We propose a Bayesian kernel machine regression (BKMR) framework for count outcomes with dynamic spatiotemporal dependence. The proposed model, termed Negative Binomial BKMR with spatiotemporal effects (NB-BKMR), integrates (i) a negative binomial likelihood to accommodate overdispersion, (ii) a kernel-based exposure–response surface for complex mixtures, (iii) hierarchical group-wise variable selection and (iv) a dynamic spatiotemporal random effect structure based on a Leroux conditional autoregressive (CAR) prior evolving over time. Posterior inference is conducted in a fully Bayesian framework using Polya-Gamma data augmentation. Through simulation studies, under varying nonlinear exposure–response functions, correlation structures, and spatiotemporal dependence patterns, we show that NB-BKMR yields well-calibrated uncertainty quantification and robust identification of dominant mixture drivers, even when exposures are highly correlated. An application to the U.S. state-level traffic fatality counts (1982–1988) illustrates how the model uncovers nonlinear effects and interactions among socioeconomic and behavioral predictors while improving predictive performance relative to generalized additive models with spatiotemporal smooths. This work extends existing BKMR methodology by unifying mixture modeling, count outcomes, and dynamic spatial dependence in a single coherent framework, with particular relevance for areal public health surveillance data.