A multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis

For patients on dialysis, hospitalizations remain a major risk factor for mortality and morbidity. We use data from a large national database, United States Renal Data System, to model time‐varying effects of hospitalization risk factors as functions of time since initiation of dialysis. To account for the three‐level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities, 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. The proposed MME‐VCM also includes multilevel covariates, where baseline demographics and comorbidities are among the patient‐level factors, and staffing composition and facility size are among the facility‐level risk factors. To address the challenge of 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. The finite sample performance of the proposed estimation procedure is studied through simulations.