Graduation Semester and Year

2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Suvra Pal

Abstract

Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2007, Tournoud and Ecochard rst proposed a mechanistic formulation of cure rate model in the context of infectious diseases with multiple exposures to infection. However, they assumed a simple Poisson distribution to capture the unobserved number of pathogens at each exposure time. In this thesis, we propose a new exible cure rate model to study infectious diseases with discrete multiple exposures to infection. This new model uses the Conway-Maxwell Poisson (COM-Poisson) distribution to model the number of competing pathogens at each moment of exposure. This new formulation takes into account both over-dispersion and under-dispersion with respect to the count on pathogens at each time of exposure and includes the model proposed by Tournoud and Ecochard as a special case. We also propose a new estimation algorithm based on the expectation maximization (EM) algorithm to calculate the maximum likelihood estimates of the model parameters. Infectious diseases data are often right censored, and the EM algorithm can be utilized to e ciently determine the maximum likelihood iv estimates of the underlying model. We carry out a detailed Monte Carlo simulation study to demonstrate the performance of the proposed estimation algorithm. The exibility of our proposed model also allows us to carry out a model discrimination, which we do using both likelihood ratio test and information-based criteria. Finally, to illustrate our proposed model, we analyze a recently collected infectious data.

Keywords

Multiple exposures, Conway-Maxwell-Poisson (COM-Poisson) distribution, Expectation maximization algorithm, Nosocomial infection, Weibull distribution, HIV

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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