Graduation Year


Document Type




Degree Granting Department

Epidemiology and Biostatistics

Major Professor

Yangxin Huang


Bayesian analysis, HIV dynamics, Markov chain Monte Carlo, mixed-effects model, Skewed distribution


Statistical models have greatly improved our understanding of the pathogenesis of HIV-1 infection

and guided for the treatment of AIDS patients and evaluation of antiretroviral (ARV) therapies.

Although various statistical modeling and analysis methods have been applied for estimating the

parameters of HIV dynamics via mixed-effects models, a common assumption of distribution is

normal for random errors and random-effects. This assumption may lack the robustness against

departures from normality so may lead misleading or biased inference. Moreover, some covariates

such as CD4 cell count may be often measured with substantial errors. Bivariate clustered

(correlated) data are also commonly encountered in HIV dynamic studies, in which the data set particularly

exhibits skewness and heavy tails. In the literature, there has been considerable interest in,

via tangible computation methods, comparing different proposed models related to HIV dynamics,

accommodating skewness (in univariate) and covariate measurement errors, or considering skewness

in multivariate outcomes observed in longitudinal studies. However, there have been limited

studies that address these issues simultaneously.

One way to incorporate skewness is to use a more general distribution family that can provide

flexibility in distributional assumptions of random-effects and model random errors to produce robust

parameter estimates. In this research, we developed Bayesian hierarchical models in which the

skewness was incorporated by using skew-elliptical (SE) distribution and all of the inferences were

carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). Two real data set

from HIV/AIDS clinical trial were used to illustrate the proposed models and methods.

This dissertation explored three topics. First, with an SE distribution assumption, we compared

models with different time-varying viral decay rate functions. The effect of skewness on the model

fitting was also evaluated. The associations between the estimated decay rates based on the best

fitted model and clinical related variables such as baseline HIV viral load, CD4 cell count and longterm

response status were also evaluated. Second, by jointly modeling via a Bayesian approach,

we simultaneously addressed the issues of outcome with skewness and a covariate process with measurement errors. We also investigated how estimated parameters were changed under linear,

nonlinear and semiparametric mixed-effects models. Third, in order to accommodate individual

clustering within subjects as well as the correlation between bivariate measurements such as CD4

and CD8 cell count measured during the ARV therapies, bivariate linear mixed-effects models with

skewed distributions were investigated. Extended underlying normality assumption with SE distribution

assumption was proposed. The impacts of different distributions in SE family on the model

fit were also evaluated and compared.

Real data sets from AIDS clinical trial studies were used to illustrate the proposed methodologies

based on the three topics and compare various potential models with different distribution

specifications. The results may be important for HIV/AIDS studies in providing guidance to better

understand the virologic responses to antiretroviral treatment. Although this research is motivated

by HIV/AIDS studies, the basic concepts of the methods developed here can have generally broader

applications in other fields as long as the relevant technical specifications are met. In addition, the

proposed methods can be easily implemented by using the publicly available WinBUGS package,

and this makes our approach quite accessible to practicing statisticians in the fields.