Multilevel Varying Coefficient Spatiotemporal Model

Over 785,000 individuals in the U.S. have end-stage renal disease (ESRD) with about 70% of patients on dialysis, a life-sustaining treatment. Dialysis patients experience frequent hospitalizations. In order to identify risk factors of hospitalizations, we utilize data from the large national database, United States Renal Data System (USRDS). To account for the hierarchical structure of the data, with longitudinal hospitalization rates nested in dialysis facilities and dialysis facilities nested in geographic regions across the U.S., we propose a multilevel varying coefficient spatiotemporal model (M-VCSM) where region- and facility-specific random deviations are modeled through a multilevel Karhunen-Loéve (KL) expansion. The proposed M-VCSM includes time-varying effects of multilevel risk factors at the region- (e.g., urbanicity and area deprivation index) and facility-levels (e.g., patient demographic makeup) and incorporates spatial correlations across regions via a conditional autoregressive (CAR) structure. Efficient estimation and inference is achieved through the fusion of functional principal component analysis (FPCA) and Markov Chain Monte Carlo (MCMC). Applications to the USRDS data highlight significant region- and facility-level risk factors of hospitalizations and characterize time periods and spatial locations with elevated hospitalization risk. Finite sample performance of the proposed methodology is studied through simulations.