Multivariate Varying Coefficient Spatiotemporal Model

As of 2020, 807,920 individuals in the U.S. had end-stage kidney disease (ESKD) with about 70% of patients on dialysis, a life-sustaining treatment. Dialysis patients experience high mortality rates, where frequent hospitalizations are a major contributor to morbidity and mortality. There is growing interest in identifying the risk factors for the correlated outcomes of hospitalization and mortality among dialysis patients across the U.S. Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multivariate varying coefficient spatiotemporal model to study the time-dynamic effects of risk factors (e.g., urbanicity and area deprivation index) on the multivariate outcome of hospitalization and mortality rates, as a function of time on dialysis. While capturing time-varying effects of risk factors on the mean, the proposed model also incorporates spatiotemporal patterns of the residuals for efficient inference. Estimation is based on the fusion of functional principal component analysis and Markov Chain Monte Carlo techniques, following basis expansions of the varying coefficient functions and multivariate Karhunen–Loéve expansion of region-specific random deviations. The finite sample performance of the proposed method is studied through extensive simulations. Novel applications to the USRDS data highlight significant risk factors of hospitalizations and mortality as well as characterizing time periods on dialysis and spatial locations across U.S. with elevated hospitalization and mortality risks.