Graduation Year

2016

Document Type

Thesis

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

Dan Shen, Ph.D.

Committee Member

Lu Lu, Ph.D.

Keywords

Histogram Smoothing, Bayesian Statistics, Lung Cancer Mortality, Functional Data Analysis, Total Serum Cholesterol Level, Longitudinal Data

Abstract

Lung cancer has been considered one of the leading causes of deaths while cancer re- mains the second most common cause of deaths in the USA. Understanding the behavior of a disease over time could yield important information to make decisions about the disease. Statistical models could provide crucial clues and help to make a decision about the dis- ease, budget allocation, evaluation, and implement prevention. Longitudinal trend analysis of the diseases helps to understand long term effects and nature. Cholesterol level is one of the most contributing risk factors for Coronary Heart Disease. Studying cholesterol statistically helps to know more about its nature and provides crucial information to mitigate its effectiveness in diagnosing its impact to public health.

In our study, we have analyzed lung cancer mortality in the USA based on age at death, period at death, and birth cohort to investigate its nature in longitudinal effects. The attempt has been made to estimate mortality rate based on age for different age groups and to find the relative risk of mortality due to period effect and relative risk due to birth cohort for lung cancer in the United States. Our statistical analysis and modeling are based on the data obtained from Surveillance Epidemiology and End Results (SEER) program of the United States.

We have also investigated the probabilistic behavior of average cholesterol level based on gender and ethnicity. The study reveals significant differences with respect to the distribution they follow and their basic inferences which could be beneficial to draw conclusions in various ways in addressing related issues. At the same time, the change of cholesterol level over time for an individual might be a good source to study the association of cholesterol level, coronary heart disease and their effects on age. The cholesterol data is obtained from inter-university Consortium for Political and Social Research and National Health and Nutrition Examination Survey (NHANS) of the United States.

Understanding the average change in total serum cholesterol level over time as people get older could be vital to explore it. We have studied the longitudinal behavior of the association of sex and time with cholesterol level. It is observed that age, sex, and time have an individual effect and can impact differently upon collective considerations. Their adverse effect in increasing cholesterol level could promote to worsen the cholesterol re- lated issues and hence heart related diseases. We believe our study pivots knowing more about target population of cholesterol level and helps to have the useful inference about cholesterol levels for public health.

Finally, we also analyzed the average cholesterol data using a functional data analysis approach to understand its nature and effect on age. Since functional data analysis approach presents more flexibility in modeling, it could provide more insight in studying cholesterol level.

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