Multivariate spatiotemporal functional principal component analysis for modeling hospitalization and mortality rates in the dialysis population

Dialysis patients experience frequent hospitalizations and a higher mortality rate compared to other Medicare populations, in whom hospitalizations are a major contributor to morbidity, mortality, and healthcare costs. Patients also typically remain on dialysis for the duration of their lives or until kidney transplantation. Hence, there is growing interest in studying the spatiotemporal trends in the correlated outcomes of hospitalization and mortality among dialysis patients as a function of time starting from transition to dialysis across the United States Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multivariate spatiotemporal functional principal component analysis model to study the joint spatiotemporal patterns of hospitalization and mortality rates among dialysis patients. The proposal is based on a multivariate Karhunen-Loéve expansion that describes leading directions of variation across time and induces spatial correlations among region-specific scores. An efficient estimation procedure is proposed using only univariate principal components decompositions and a Markov Chain Monte Carlo framework for targeting the spatial correlations. The finite sample performance of the proposed method is studied through simulations. Novel applications to the USRDS data highlight hot spots across the United States with higher hospitalization and/or mortality rates and time periods of elevated risk.