UC Irvine

In a longitudinal cohort study, a group of subjects is chosen based on certain characteristicsand then followed at routine intervals over time. At each visit, some measurements are recorded and the goal is oftentimes to model how they develop over time. During the followup, the collection of the data can be stopped by a terminal event. In this dissertation, we study several statistical methods for modeling longitudinal data while adjusting for the terminal event. In Chapter II, we propose a nonparametric bivariate time-varying coefficient model for longitudinal measurements with the occurrence of a terminal event that is subject to right censoring. The time-varying coefficients capture the longitudinal trajectories of covariate effects along with both the followup time and the residual lifetime, in contrast to the existing work that either models longitudinal measures as a function of only the forward time or the backward time, or poses strong parametric assumptions. We consider a kernel smoothing method for estimating regression coefficients in our model and use cross-validation for bandwidth selection, applying undersmoothing in the final analysis to eliminate the asymptotic bias of the kernel estimator. We show that the kernel estimates follow a finite-dimensional normal distribution asymptotically under mild regularity conditions, and provide an easily computed sandwich covariance matrix estimator. In Chapter III, we study the lifetime Medicare spending patterns of patients with end-stage renal disease (ESRD) stratified by waitlisting and kidney transplant. In addition to the terminal event, a non-terminal event that happened in the follow-up could also have an impact on the longitudinal measures. To study the heterogeneous Medicare cost trajectories across groups stratified by waitlisting and transplant, we proposed two models: a semiparametric regression model with both fixed and bivariate time-varying coefficients to compare unwaitlisted and waitlisted groups, and a bivariate time-varying coefficient model with different starting times (time since the first ESRD service and time since the kidney transplant) to compare untransplanted and transplanted groups. We use sandwich variance estimators to construct confidence intervals and validate inference procedures through simulations. Our analysis of the Medicare claims data reveals that waitlisting is associated with a lower daily medical cost at the beginning of ESRD service among waitlisted patients which gradually increases over time. Averaging over lifespan, however, there is no difference between waitlisted and unwaitlisted groups. A kidney transplant, on the other hand, reduces the medical cost significantly after an initial spike. In Chapter IV, we study how the onset of a non-terminal events is associated with the terminal event. Existing methods under the framework of multi-state model or the semi-competing risks model rely on certain semiparametric assumptions for modeling the joint distribution of these two events, thus may subject to model misspecification and lack clear interpretations of their association. Moreover, they assume the independence between the censoring time C and both event times (S, T), which can be easily violated in realistic situations. We propose to estimate the onset of non-terminal event conditional on the terminal event time using a generalized Beran’s estimator. We consider a left truncation time L in addition to the right censoring time C and only need a relaxed assumption of the independence between (L,C) and the non-terminal event time S conditional on the terminal event time T. Such estimates also enjoy more meaningful interpretations.