Document Type


Date of Degree

Spring 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Oleson, Jacob J.

First Committee Member

Brown, Grant D.

Second Committee Member

Cavanaugh, Joseph E.

Third Committee Member

Wall, Michael

Fourth Committee Member

Zamba, Gideon K.D.


Our interest in spatio-temporal models focuses on how a disease spreads within a body region. We use independent replications across individuals to better understand population level dynamics of disease spread. Our Bayesian hierarchical model incorporates independent spatio-temporal datasets to estimate population level parameters. A dimension reduction propagator matrix is used to identify the most variable spatial regions, which are then related to a set of latent variables and covariates. Posterior estimates of parameters allow us to create a predicted estimate of the overall disease evolution process for each individual. In addition, individual level rates of deterioration can be estimated and predictions of future spread are made. The motivating example for this model stems from a study of visual loss in participants with glaucoma. Participants’ vision was recorded across a grid covering the central part of the eye at baseline plus eight follow-up visits every 6 months. We use these spatio-temporal replications of independent participants to determine how human characteristics and demographics collectively affect the spread and progression of glaucoma. Our introduced model is available in the DROIIDS R package. We account for missing data through our model with a Bayesian imputation method.

Public Abstract

Infectious diseases spread at different rates across locations (e.g., states or cities). When we follow an outbreak, we observe a disease spread where infectious counts are collected at many locations throughout the epidemic. Current statistical methods available to model these outbreaks focus on a single monitored disease. We created a statistical method to collectively analyze replications of the same monitored disease.

The motivation for our method comes from a vision loss trial studying glaucoma progression. There are several locations within the eye where vision can be recorded. Individuals came in for multiple visits where vision loss was measured at these locations each time. The measurements collected from a single individual will be correlated (will behave similarly) which needs to be accounted for in the statistical method.

When vision loss is more severe, the variability of the measurements increases (i.e., the accuracy of the measurements decreases). We use the data collected from each individual to collectively analyze and make conclusions at the population level about glaucoma progression. These inferences will allow us to predict the disease progression within an individual accounting for the variability in the measurements. Vision loss change can be measured at each location in the eye for each person. These rates can help doctors understand what areas of the eye are affected more by the glaucoma progression.


viii, 87 pages


Includes bibliographical references (pages 85-87).


Copyright © 2016 John Matthew VanBuren

Included in

Biostatistics Commons