In the first chapter of this work, we characterize the dynamics of cardiovascular event risk trajectories for patients on dialysis while
conditioning on survival status via multiple time indices: (1) time since the start of dialysis, (2) time since the pivotal
initial infection-related hospitalization and (3) the patient's age at the start of dialysis. This is achieved by using a new
class of generalized multiple-index varying coefficient (GM-IVC) models utilizing a multiplicative structure and one-dimensional
varying coefficient functions along each time and age index. We develop a two-step estimation procedure for the GM-IVC models based on local maximum likelihood, and report new insights on the dynamics of cardiovascular events risk among the dynamic cohort of survivors using the United States Renal Data System database, which collects data on nearly all patients with end-stage renal disease in the U.S.
In the second chapter of this work, we develop time-varying effects modeling tools in order to
examine the CV outcome risk trajectories during the time periods before and after an initial infection-related hospitalization. For this,
we propose partly conditional and fully conditional partially linear generalized varying coefficient models (PL-GVCMs) for modeling time-varying effects in longitudinal data with substantial
follow-up truncation by death. We compare and contrast partly and fully conditional PL-GVCMs in our aforementioned application and develop generalized likelihood ratio tests.
In the third chapter of this work, we introduce a time-varying standardized dynamic ratio (SDR) to aid in the evaluation of a dialysis facility's performance with respect to patient readmission rates as a function of time that patients are on dialysis. The estimation of SDR consists of two steps. First, we model the dependence of readmission events on facilities and patient-level characteristics using a multilevel varying coefficient model (MVCM) with fixed facility time-varying effects, with or without subject random effects. Second, using results from the models, standardization is achieved by computing the ratio of the sum of the predicted number of 30-day readmissions to the sum of the predicted number of 30-day readmissions assuming a reference standard and given the case-mix in that facility. A challenging aspect of our data application is that the number of model parameters is very large, and the estimation of high-dimensional parameters is troublesome. To overcome this problem, we propose a Newton Rhapson algorithm for the MVCM without the random effects, and an approximate EM algorithm for the MVCM with random effects. We propose a test statistic to facilitate in the identification of facilities whose outcomes are outside of normal expectations, and obtain p-values using re-sampling and simulation techniques. Finally, our method of identifying outlier facilities involves converting the observed p-values to Z-statistics and using the empirical null distribution, which accounts for over dispersion in the data.