Graduation Year

2021

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody M. Ramachandran, Ph.D.

Committee Member

Lu Lu, Ph.D.

Committee Member

Barbos Andrei, Ph.D.

Keywords

Cancer Survivorship, Desirability Function, NHPP, Production Evaluation, Statistical Modeling

Abstract

Globally, cancer disease is a major health issue causing a lot of deaths. The duration of time an individual diagnosed with a particular type of cancer survives has become a major area of research concern. The Kaplan Meier and Cox Proportional Hazard (Cox-PH) model have been a traditionally used method for survival analysis of cancer data. These techniques of cancer survival analysis are developed from nonparametric and semi-parametric approaches, respectively, which are not as robust as a parametric approach. In this dissertation, we proposed a new method of cancer survival analysis based on a parametric approach using multiple myeloma cancer (MMC) data. Firstly, we performed a parametric analysis of only the survival times without taking into account the risk factors, obtaining the survival function, and comparing it with the Kaplan Meier survival function.

Next, we assessed the survival times taking into consideration the risk factors contributing to the survival times. We developed a high-quality and well-validated Cox-PH model, identifying the significant risk factors and estimating the survival function. Further, a parametric analysis was conducted, obtaining the survival function from highly accurately predicted survival times from a well-developed and validated nonlinear statistical model that identifies the significant risk factors and ranks them according to the percentage contribution to the survival times. We compared the quality of the two models and their robustness in estimating the survival function. Our parametric approaches of cancer survival analysis outperformed both the Kaplan Meier and Cox-PH model of cancer survival analysis, given better estimates of the survival times. The proposed statistical modeling and parametric approach for cancer survival analysis used in this dissertation for multiple myeloma cancer can be generalized and applied to the various cancer diseases in the world. This study offers a more improved, effective, and efficient therapeutic/treatment strategy for cancer diseases.

Another research study in this dissertation is corn production. Corn is globally known to be the most economically viable and versatile agricultural product. The United States (U.S.) is noticeable the world’s leading producer of corn. In this study, we proposed a real data-driven analytical model for the returns of corn production in the U.S. utilizing data obtained from the U.S. Department of Agriculture (USDA) from 1975 to 2018. The developed model is of high quality, satisfies all necessary assumptions, well-validated, and predicts the returns with a high degree of accuracy. It identifies significant risk factors, including interaction, and ranks them according to percent contribution to the returns. We further performed an optimization analysis of the returns using the desirability function approach, obtaining the optimum return and the optimal values of the risk factors needed to maximize the returns of corn production in the U.S. We also obtained the confidence region of the optimum value of the return for the purpose of statistical inferences, as well as surface response plots to assess the combination of risk factors contribution to the returns. Finally, we proposed a time-dependent analytical model to evaluate and monitor the returns based on whether it is increasing, decreasing, or remaining unchanged. The evaluation and monitoring process utilizes beta-factor obtained from the intensity function of the nonhomogeneous Poisson process (NHPP) / Power Law Process (PLP). This study offers a more robust and efficient approach for maximizing the returns of crop production.

The approach and methodology of evaluating and monitoring the returns of corn production used in this study can be extended to multidisciplinary fields studies, including different settings of production, finance in monitoring the stock returns, health science in monitoring the number of deaths and reported cases from disease, environmental science in monitoring the emission of carbon dioxide, cybersecurity in monitoring the vulnerability scores of software system, transportation in monitoring the number of accident, etc.

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