35: SVD-PICAR Bayesian Kernel Machine Regression for Spatio-Temporal Count Data

Thomas M. Menino Convention & Exhibition Center 

Bayesian kernel machine regression (BKMR) has become a widely used tool for studying the health effects of complex exposure mixtures, with extensions to over dispersed count outcomes now available. However, existing BKMR models for count data handle spatial and temporal structure separately rather than as a unified random field, leaving the joint space-time dependency in the data unmodeled. No existing method therefore combines nonlinear mixture modeling, a neighborhood-based spatio-temporal random effect, and an over dispersed count likelihood in a single computationally workable framework.

We address this gap by proposing SVD-PICAR NB-BKMR, which extends the PICAR framework from the spatial to the spatio-temporal setting through a Kronecker product of spatial and temporal bases. However, this spatiotemporal basis contains redundant components that expand the dimension of the latent random field, produce highly correlated posterior draws, and make the full-rank ICAR field ill-conditioned, weakening exposure-effect estimates and slowing MCMC sampling. We resolve this by incorporating a truncated singular value decomposition (SVD) into the spatio-temporal PICAR basis, retaining only the dominant orthogonal directions, reducing the latent field to a manageable dimension, and separating background spatio-temporal variation from the nonlinear exposure-response pattern.
We compare three competing models: a fixed effect model (M1), a full-rank mixed effect model (M2), and the proposed SVD-PICAR mixed effect model (M3). Models are evaluated through simulation and an application to county level thyroid cancer and pesticide exposure data from Nebraska (1992–2014). In simulation, M3 achieves the best predictive fit by the Watanabe-Akaike Information Criterion (WAIC), the highest MCMC efficiency by effective sample size per second (ESS/sec), and the most stable exposure identification. In the Nebraska application, Atrazine and Alachlor emerge as the leading contributors to thyroid cancer risk, with nonlinear exposure-response relationships that remain robust after spatio-temporal correction. The SVD-PICAR framework offers a principled and practically workable approach for mixture analysis in spatio-temporal count data settings.

Spatio-temporal count data


Bayesian kernel machine regression

projection based intrinsic conditional autoregression

singular value decomposition

basis representation

negative binomial