Title page for ETD etd-0501102-110350

Document Type thesis

Author Name Liu, Jie

URN etd-0501102-110350

Title Novel Bayesian Methods for Disease Mapping: An Application to Chronic Obstructive Pulmonary Disease

Degree MS

Department Mathematical Sciences

Advisors
Balgobin Nandram, Advisor
Homer Walker, Department Head

Keywords
latent class model
poisson regression model
Metropolis-Hastings sampler
order restriction
disease mapping

Date of Presentation/Defense 2002-04-24

Availability unrestricted

Abstract
Mapping of mortality rates has been a valuable public health tool.
We describe novel Bayesian methods for constructing maps which do
not depend on a post stratification of the estimated rates. We also
construct posterior modal maps rather than posterior mean maps. Our
methods are illustrated using mortality data from chronic obstructive
pulmonary diseases (COPD) in the continental United States.

Poisson regression models have attracted much attention in the
scientific community for their superiority in modeling rare events
(including mortality counts from COPD). Christiansen and Morris (JASA 1997)
described a hierarchical Bayesian model for heterogeneous Poisson
counts under the exchangeability assumption. We extend this model
to include latent classes (groups of similar Poisson rates
unknown to an investigator).

Also, it is standard practice
to construct maps using quantiles (e.g., quintiles) of the estimated
mortality rates. For example, based on quintiles, the mortality rates
are cut into 5 equal size groups, each
containing $20\%$ of the data, and a different color is applied
to each of them
on the map. A potential problem is that, this method assumes an equal
number of data in each group, but this is often not the case.
The latent class model produces a method to construct
maps without using quantiles, providing a more natural
representation of the colors.

Typically, for rare events, the posterior densities of the rates are
skewed, making the posterior mean map inappropriate and inaccurate.
Thus, although it is standard practice
to present the posterior mean maps, we also develop a method to
provide the joint posterior modal map (i.e., the map with the highest
posterior probability over the ensemble).

For the COPD data, collected 1988-1992 over 798 health service areas,
we use Markov chain Monte Carlo methods to fit the model, and
an output analysis is used to construct the new maps.

Files
jliu.pdf

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Document Type	thesis
Author Name	Liu, Jie
URN	etd-0501102-110350
Title	Novel Bayesian Methods for Disease Mapping: An Application to Chronic Obstructive Pulmonary Disease
Degree	MS
Department	Mathematical Sciences
Advisors	Balgobin Nandram, Advisor Homer Walker, Department Head
Keywords	latent class model poisson regression model Metropolis-Hastings sampler order restriction disease mapping
Date of Presentation/Defense	2002-04-24
Availability	unrestricted
Abstract Mapping of mortality rates has been a valuable public health tool. We describe novel Bayesian methods for constructing maps which do not depend on a post stratification of the estimated rates. We also construct posterior modal maps rather than posterior mean maps. Our methods are illustrated using mortality data from chronic obstructive pulmonary diseases (COPD) in the continental United States. Poisson regression models have attracted much attention in the scientific community for their superiority in modeling rare events (including mortality counts from COPD). Christiansen and Morris (JASA 1997) described a hierarchical Bayesian model for heterogeneous Poisson counts under the exchangeability assumption. We extend this model to include latent classes (groups of similar Poisson rates unknown to an investigator). Also, it is standard practice to construct maps using quantiles (e.g., quintiles) of the estimated mortality rates. For example, based on quintiles, the mortality rates are cut into 5 equal size groups, each containing $20\%$ of the data, and a different color is applied to each of them on the map. A potential problem is that, this method assumes an equal number of data in each group, but this is often not the case. The latent class model produces a method to construct maps without using quantiles, providing a more natural representation of the colors. Typically, for rare events, the posterior densities of the rates are skewed, making the posterior mean map inappropriate and inaccurate. Thus, although it is standard practice to present the posterior mean maps, we also develop a method to provide the joint posterior modal map (i.e., the map with the highest posterior probability over the ensemble). For the COPD data, collected 1988-1992 over 798 health service areas, we use Markov chain Monte Carlo methods to fit the model, and an output analysis is used to construct the new maps.
Files	jliu.pdf