Date of Award

Spring 4-30-2018

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Ruiyan Luo, PhD

Second Advisor

Xin Qi, PhD

Third Advisor

Gengsheng Qin, PhD

Fourth Advisor

James A. Singleton, PhD


This dissertation applies Bayesian Hierarchical (BH) methods and Spatial effects at both the state and county levels to estimate Human papillomavirus (HPV) vaccination initiation coverage at the county level in the ten Southeastern U.S. states (925 counties) using 2016 National Immunization Survey-Teen (NIS-Teen) adequate provider data. Small sample sizes yield inadequate precision for direct domain estimators. Bayesian methods allows indirect estimation with small sample size, missing values and covariates via the Markov Chain Monte Carlo (MCMC) method. The BH method, which allows the parameters of a prior distribution or a population distribution themselves to be estimated from data, is one of the appropriate ways in handling small areas with sparse data because posterior inference is exact which does not rely on asymptotic arguments. We use the conditional autoregressive (CAR) model to capture the spatial correlation and study its role in modeling the HPV vaccination initiation coverage. Additionally, we applied Bayesian modeling of temporal trends of HPV vaccination initiation coverage over time (quarter of survey year) and space (in the 10 southeastern states in US) using NIS-Teen survey years 2011 to 2016 adequate provider data. These methods can be used in further analysis for the temporal trend of HPV vaccination initiation coverage at the county level.