Modeling time-varying effects of multilevel risk factors of hospitalizations in patients on dialysis.

For chronic dialysis patients, a unique population requiring continuous medical care, methodologies to monitor patient outcomes, such as hospitalizations, over time, after initiation of dialysis, are of particular interest. Contributing to patient hospitalizations is a number of multilevel covariates such as demographics and comorbidities at the patient level and staffing composition at the dialysis facility level. We propose a varying coefficient model for multilevel risk factors (VCM-MR) to study the time-varying effects of covariates on patient hospitalization risk as a function of time on dialysis. The proposed VCM-MR also includes subject-specific random effects to account for within-subject correlation and dialysis facility-specific fixed effect varying coefficient functions to allow for the 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 in 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. The method is applied to model hospitalization risk using the rich hierarchical data available on dialysis patients initiating dialysis between January 1, 2006 and December 31, 2008 from the United States Renal Data System, a large national database, where 331 443 hospitalizations over time are nested within patients, and 89 889 patients are nested within 2201 dialysis facilities. Patients are followed-up until December 31, 2013, where the follow-up time is truncated five years after the initiation of dialysis. Finite sample properties are studied through extensive simulations.