Qiuyi Wu

Date of Award

8-2012

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Ramesh Gupta

Second Committee Member

Pushpa Gupta

Third Committee Member

Andrew Knightly

Abstract

Survival models incorporating a cure fraction, often referred to as “cure rate models” are becoming increasingly popular in analyzing data from cancer clinical trials. In this model, we assume that a fraction of the population is cured and the remaining population is uncured after the first treatment. In this thesis, we consider the uncured population where the number (N) of metastasis-competent cells (clonogens) is unknown and the event occurs as soon as one of the clonogens metastasizes. An exponential-generalized Poisson distribution (EGP) is developed, where the distribution of N is taken as generalized Poisson. The generalized Poisson distribution is a generalization of the Poisson distribution having one extra parameter. The structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated. Extensive simulation studies are carried out to study the performance of the estimates. A score test is developed to test the importance of the extra parameter. Two real data sets are examined and it is shown that the EGP model presented here fits better than the exponential Poisson distribution.

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