Date of Award

2018

Document Type

Open Access Dissertation

Department

Statistics

Sub-Department

The Norman J. Arnold School of Public Health

First Advisor

Jiajia Zhang

Abstract

In this dissertation, we aim to address three important questions in practice, which can be solved through complex survival models. The first project focuses on studying the longitudinal fitness effect on cardiovascular disease (CVD) mortality. In the second project, we study the disease-death relation between CVD and all-cause mortality and evaluate important covariate effects on the disease or death transitions. In the third project, we compare antiretroviral treatment (ART) for HIV patients and consider both treatment effect and side effect of the drugs. The first two projects are motivated by the Aerobics Center Longitudinal Study (ACLS) datasets and the third project is based on the Health Sciences South Carolina (HSSC) HIV datasets.

The ACLS is a prospective study and involves patients in the Cooper Clinic in Dallas, TX. Participants had repeated measures of cardiorespiratory fitness (fitness), which is an objective measure of physical activity, during the study. Fatal outcomes, such as the CVD or all-cause mortality information, are available by the end of study. In the first project, we develop a novel joint model that allows the estimation of a timevarying exposure on a survival outcome with a varying coefficient model. Specifically, the flexible generalized odds rate models are applied to CVD mortality with an agedependent coefficient to account for nonlinear age varying effect of fitness.

For the second project, we consider the interval censored disease incidence time, which is caused by the intermittent observations, and apply the Markov illness-death regression models to study the transition intensities among three states: disease-free, CVD and death, and estimate the covariate effects, such as age, fitness, smoking etc., on these transitions. We adopt the Expectation-Maximization (EM) algorithm to estimate the proposed models in the first two projects, and the covariance matrix of the estimated parameters is approximated numerically based on the profile likelihood.

HSSC is a biomedical research collaborative consisting of four of the state’s largest health systems. We are interested in comparing the antiretroviral treatment (ART) for HIV patients in the HSSC. The HIV datasets in HSSC include both the time to treatment or virologic failures and side effects after drug administration. In the last project, we propose to model time to treatment or virologic failure and time to severe side effects of ART under the competing risks model framework. A restricted optimal treatment regime is defined based on cumulative incidence functions, where we minimize the risk of treatment or virologic failures while controlling the risk of serious drug-induced side effects. The estimation approach is derived using a penalized value search method.

The proposed models and their estimation algorithms are validated through extensive simulation studies and applied to either the ACLS datasets or the HSSC HIV datasets to achieve the purposes of the study.

Rights

© 2018, Jie Zhou

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