Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Robert A. Perera


Longitudinal studies of change abound in the fields of epidemiology and public health to evaluate individual growth over time. Analyzing this type of data poses various interesting statistical challenges. Our motivating dataset in this project arises from an osteoarthritis study, where the change patterns of the metrics of interested are theorized to be in two phases. The aim is to identify an individual inflection point (i.e., knot) for each patient's trajectory corresponding to their short-term and long-term recovery periods from treatment. In addition, since we cannot directly observe which subpopulation a patient belongs to, we need to group and label those trajectories (into good and poor outcome groups) and identify patient-level characteristics associated with those labels. Finally, we must account for the varying time points at which patients are observed.

There are two main objectives of this dissertation. The first objective is to investigate the characteristics of nonlinear change patterns with an unknown knot for a single population. For Aim 1, we developed a pair of bilinear spline growth models with time-invariant covariates (BLSGMs-TICs) to estimate a knot and its variability as well as to investigate predictors of individual trajectories with the individual-varying time points (ITPs). Our simulation studies demonstrated that the proposed BLSGMs-TICs were capable of estimating and testing the knot variance while correctly controlling for type I error rates. More importantly, the estimated parameters were unbiased, precise, and exhibited appropriate confidence interval coverage.


© Jin Liu

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission


Available for download on Sunday, November 21, 2219