For chronic dialysis patients, a unique population requiring continuous medical care, hospitalizations remain a major risk factor for mortality and morbidity. Methodologies to monitor patient hospitalizations over time, after transition to dialysis, are of particular interest. We utilize data from a large national database, United States Renal Data System (USRDS), to model patients’ hospitalization risks in the dialysis cohort as a function of time since initiation of dialysis. In the first chapter of this work, we study the time-varying effects of multilevel covariates on dialysis patient hospitalization risks. The covariates considered include demographics and comorbidities at patient-level and facility size and staffing composition at the dialysis facility-level. We develop a varying coefficient model for multilevel risk factors (VCM-MR) that includes subject-specific random effects to account for within-subject correlation and dialysis facility-specific fixed effect varying coefficient functions to allow for modeling of flexible time-varying facility-specific risk trajectories. An approximate EM algorithm and an iterative Newton-Raphson approach are proposed to address the challenge of estimation of high-dimensional parameters (varying coefficient functions) for thousands of dialysis facilities across the United States. The proposed modeling allows for comparisons between time-varying effects of multilevel risk factors as well as testing of facility-specific fixed effects.

In the second chapter of this work, we propose a multilevel mixed effects varying coefficient model (MME-VCM) where multilevel (patient- and facility-level) random effects are used to model the dependence structure of the data, accounting for the three-level hierarchical structure where hospitalizations are nested in patients and patients are nested in dialysis facilities. The proposed MME-VCM also includes multilevel covariates, similar to the first chapter. To address the challenge of evaluating high-dimensional integrals due to the hierarchical structure of the random effects, we propose a novel two-step approximate EM algorithm based on the fully exponential Laplace approximation. Inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions. In the USRDS data application, VCM-MR and MME-VCM identify significant multilevel risk factors for patient hospitalizations, providing insights into health care strategies for the reduction of patient hospitalization risk.

In the third chapter of this work, we develop a novel multilevel spatiotemporal functional model (MST-FM) to study spatiotemporal patterns of hospitalization rates among dialysis facilities. Hospitalization rates of dialysis facilities are considered as spatially nested functional data with longitudinal hospitalizations nested in dialysis facilities and dialysis facilities nested in geographic regions. A multilevel Karhunen-Lo�ve expansion is utilized to model the two-level (facility and region) functional data, where spatial correlations are induced among region-specific principal component scores accounting for regional variation. A new efficient algorithm based on functional principal component analysis and Markov Chain Monte Carlo is proposed for estimation and inference. The analysis using USRDS data identified specific regions and dialysis facilities therein, as well as specific time periods such as the first year after transitioning to dialysis, with high hospitalizations for further investigation in an effort to reduce the hospitalization burden in the dialysis population.