Graduation Year

2024

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

Yicheng Tu, Ph.D.

Keywords

Statistical Modeling, Desirability Function, Cancer Survivorship

Abstract

Cancer is considered a health issue in the world. Many cancer research studies focus on improving the survival time of patients diagnosed with cancer, and they make an effort to find the methods that help them detect cancer and find effective treatments to increase the patient's survival time. In this study, we aim to understand the behavior of malignant tumor size in four stages. Our investigation seeks to uncover whether any statistically significant difference exists between the malignant tumor sizes of male and female patients at different cancer stages. We also investigate whether any parametric probability distribution function best fits the patient in the four stages of colon cancer. We also performed the parametric analysis using the SEER cancer database. We also have developed a data-driven statistic model to predict the malignant tumor sizes of colon cancer in the (USA). This model was developed using data from the NIH (Prostate, Lung, Colorectal, and Ovarian) cancer data, which not only satisfies all necessary assumptions but is well-validated and accurately predicts malignant tumor sizes. The model identifies significant risk factors, including interaction; we also ranked them according to their percent contribution to malignant tumor sizes. We take a step further and optimize the malignant tumor size using the desirability function approach. This approach allows us to obtain the optimal values of the risk factors needed to minimize the malignant tumor size of colon cancer. This research provides a method to determine the confidence region of the optimum value of the malignant tumor size, which can be directly applied in cancer treatment. In the second part of this dissertation, survival time is another important factor in any cancer. Most research uses common techniques for analyzing cancer survival data, such as nonparametric approaches like the Kaplan Meier and semi-parametric approaches like the Cox Proportional Hazard (Cox-PH) model. First, we tested the differences between the four stages and found that they were different; therefore, we performed a parametric analysis of the survival times that best fit the patients in the four stages of colon cancer. We also obtained the survival function for the four stages and compared them with the survival function of combining all the data. We also performed a parametric analysis of all the combined data, finding the survival function, and compared it with the Kaplan-Meier survival function.In addition, after finding differences in survival time, we developed high-quality and well-validated four Cox-PH models for four stages. Therefore, we identified the significant risk factors with their interaction and ranked them based on the hazard function. We also estimated the four survival functions and compred them with the parametric survival function of the four stages. We also built predictive models for survival time by utilizing the NIH (Prostate, Lung, Colorectal, and Ovarian) cancer data. We ranked the individuals and interaction risk factors based on their percentage contribution to survival times. This dissertation presents statistical modeling, parametric and nonparametric approaches for survival analysis and malignant tumor size. Although it focuses on colon cancer, these approaches can be applied to any cancer. This dissertation assists us to know what the risk factors that causes the colon cancer and it also helps determine the best treatment strategy for colon cancer.

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