ORCID Identifier(s)

0000-0003-3606-0921

Graduation Semester and Year

2016

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Suvra Pal

Abstract

A cure rate or long-term survival model is a model for survival data with the presence of a cure fraction. In this study, we consider the analysis of a cure rate model with interval-censored data, which is one of the most practical censoring scheme in survival study. A competing cause scenario has been considered and the number of competing causes is assumed to follow a flexible Conway-Maxwell Poisson (COM-Poisson) distribution which can handle both over- and under-dispersion that is usually encountered in discrete data and also includes some of the well-known discrete distributions as special cases. In addition, a logistic link function is used to relate the cure rate to a set of covariates so as to examine the effect of covariates on the cure rate. A missing data caused due to this interval censoring mechanism motivates an application of the expectation maximization (EM) algorithm for the estimation of the model parameters. The main contribution is in developing the steps of the EM algorithm for the determination of the maximum likelihood estimates of the model parameters for the COM-Poisson model and some of its special cases. Considering a parametric setup, the distribution of the time-to-event is assumed to be lognormal and gamma, which are some of parametric distributions commonly used in survival studies. The performance of the proposed estimation method is demonstrated through an extensive Monte Carlo simulation study. Model discrimination within the COM-Poisson family is addressed using both likelihood ratio test and information-based criteria. The effect of model mis-specification on the cure rate is also studied through calculated bias and relative efficiency. Finally, a real data on smoking cessation is analyzed for illustrative purpose.

Keywords

Competing cause scenario, EM-algorithm, Maximum likelihood estimation, Long-term survivor, Profile likelihood

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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