Graduation Year


Document Type




Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos


brain tumor, functional, mortality, probability density function, quantile


Comprehensive statistical models for non-normally distributed cancerous tumor sizes are

of prime importance in epidemiological studies, whereas a long term forecasting models

can facilitate in reducing complications and uncertainties of medical progress. The statistical

forecasting models are critical for a better understanding of the disease and supply

appropriate treatments. In addition such a model can be used for the allocations of budgets,

planning, control and evaluations of ongoing efforts of prevention and early detection of

the diseases.

In the present study, we investigate the effects of age, demography, and race on primary

brain tumor sizes using quantile regression methods to obtain a better understanding of the

malignant brain tumor sizes. The study reveals that the effects of risk factors together with

the probability distributions of the malignant brain tumor sizes, and plays significant role in

understanding the rate of change of tumor sizes. The data that our analysis and modeling is

based on was obtained from Surveillance Epidemiology and End Results (SEER) program

of the United States.

We also analyze the discretely observed brain cancer mortality rates using functional

data analysis models, a novel approach in modeling time series data, to obtain more accurate

and relevant forecast of the mortality rates for the US. We relate the cancer registries,

race, age, and gender to age-adjusted brain cancer mortality rates and compare the variations

of these rates during the period of the study that data was collected.

Finally, in the present study we have developed effective statistical model for heterogenous

and high dimensional data that forecast the hazard rates with high degree of accuracy,

that will be very helpful to address subject health problems at present and in the future.