Graduation Year

2012

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos

Abstract

Abstract

The object of the present study is to apply statistical modeling and estimate the mean of optimism of breast cancer patients as function of attribute variables; delay, education and age for each race of breast cancer patients. Moreover, to investigate the nonlinear association between optimism, education, age and delay with respect to each race and both. Furthermore, to develop differential equations that will characterize the behavior of the pancreatic cancer tumor size as a function of time. Having such differential equations, the mean solution of which once plotted will identify the rate of change of tumor size as a function of age. The structures of the differential equations characterize the growth of pancreatic cancer tumor. Once we have developed the differential equations and their solutions, and the object of the present study is to probabilistically evaluate commonly used methods to perform survival analysis of medical patients to validate the quality of the differential system and discuss its usefulness.

In the last study, a comparison of parametric, semi-parametric and nonparametric analysis of probability survival time models. The first part of the evaluation of survival time by applying the statistical tests will guide us to how precede the actual cancer data and second part, identifying the parametric survival time function for each race and both. Moreover, we will evaluate the Kernel density, the popular Kaplan-Meier (KM) and the Cox Proportional Hazard (Cox PH) models by using actual pancreatic cancer data. As expected, the parametric survival analysis when applicable gives the best results followed by the not commonly used nonparametric Kernel density approach for evaluations actual cancer data.

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