Over 785,000 individuals in the United States 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 United States, we propose a multilevel varying coefficient spatiotemporal model (M-VCSM) where region- and facility-specific random deviations are modelled 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 are 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.

中文翻译：

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多级变系数时空模型

在美国，超过 785,000 人患有终末期肾病 (ESRD)，其中约 70% 的患者接受透析，这是一种维持生命的治疗。透析患者经常住院。为了确定住院的风险因素，我们利用了来自大型国家数据库美国肾脏数据系统 (USRDS) 的数据。为了解释数据的层次结构，纵向住院率嵌套在透析设施中，透析设施嵌套在美国各地的地理区域中，我们提出了一个多级变系数时空模型 (M-VCSM)，其中区域和设施特定随机偏差通过多级 Karhunen–Loéve (KL) 扩展建模。拟议的 M-VCSM 包括区域多级风险因素的时变影响（例如，城市化和区域剥夺指数）和设施水平（例如，患者人口构成），并通过条件自回归 (CAR) 结构整合跨区域的空间相关性。通过功能主成分分析（FPCA）和马尔可夫链蒙特卡罗（MCMC）的融合实现高效的估计和推理。USRDS 数据的应用突出了住院的重要区域和设施级风险因素，并描述了住院风险升高的时间段和空间位置。通过模拟研究了所提出方法的有限样本性能。通过功能主成分分析（FPCA）和马尔可夫链蒙特卡罗（MCMC）的融合，实现了高效的估计和推理。USRDS 数据的应用突出了住院的重要区域和设施级风险因素，并描述了住院风险升高的时间段和空间位置。通过模拟研究了所提出方法的有限样本性能。通过功能主成分分析（FPCA）和马尔可夫链蒙特卡罗（MCMC）的融合，实现了高效的估计和推理。USRDS 数据的应用突出了住院的重要区域和设施级风险因素，并描述了住院风险升高的时间段和空间位置。通过模拟研究了所提出方法的有限样本性能。