UC Riverside

Motivated by Womens' Interagency HIV Study (WIHS), we propose an intuitive time-varying joint model (TV-JM) for longitudinal and time-to-event outcomes. In this model, conditional on a set of random effects, a joint likelihood is constructed which accounts for the dependence of the two outcomes and correlation among the repeated measurements. We allow all the coefficients in both longitudinal and survival submodels to vary as smooth functions of time, and hence, this method will allow researchers to explore the dynamic response-predictor as well as response-response relationships in a longitudinal data efficiently and accurately. For estimation of the model parameters, we employ an Expectation-Maximization algorithm. In the E-step of the algorithm, the underlying random effects are estimated and in the M-step, we employ local linear regression techniques to fit the time-varying coefficients. The finite sample performance of the proposed method is illustrated via extensive simulation studies. The proposed method is demonstrated by jointly analyzing CD4 cell percentage and time to death outcomes from WIHS.

In the second part of this dissertation, we study the performance of generalized varying coefficient models (GVCM) under missing data mechanisms via extensive simulation studies. This work was motivated by the Midlife in the United States (MIDUS) data, where significant number of missing observations exist and our main goal is to perform a novel application of GVCM to provide impactful insights to research on aging. We present the results of our simulation studies and apply GVCM to analyze data from MIDUS.