Electronic Theses and Dissertations




Wenyan Zhao



Document Type

Dissertation (Access Restricted)

Degree Name

Doctor of Philosophy


Mathematical Sciences


Applied Statistics

Committee Chair

Wai-Yuan Tan

Committee Member

Lih-Yuan Deng

Committee Member

Seok P. Wong


Cancer is ranked the second leading cause of death in the USand accounts for 23% of total deaths annually afterheart disease (25%) and before stroke (6%). Carcinogenesis is the transformation of normal cells intocancer cells and has beenshown to be of a multistage nature with stemcells going through the sequential accumulationof alterations in genes responsible for the control of cell proliferation,cell death and the maintenance of genetic integrity. Basedon the multistage nature of carcinogenesis, biologically based mathematical modelinghas played an important role in theanalysis of the plausible mechanisms of carcinogenesis. In this dissertation, we summarized and developed two numerical methods to predict cancer incidence rates. We used 2-, 3-, and 4-stage stochastic and state space models of carcinogenesis to analyze the continuous administration of AAF liver and bladder data in the ED01 study. Weapplied the fittedmodels and comparedthe model predictionsto the observed tumor incidence rates in thediscontinuous administration of AAF treatment groups.We concluded thatthe 2-stage modelis the best fitfor the continuous administration ofAAF liver data, whereas the 3-stage modelcan better explain the mechanism of carcinogenesis in mouse bladder. The dose-responsecurves indicateddifferentmechanisms of carcinogenesisinduced by AAF inthe mouse liver and bladder. Based on our model fitting experience, wefeel thatit is necessary to incorporate biological and experimental facts into mathematical model fitting and selection, and it isimportant to work closelywith biomedical scientists to come upwith a scientific interpretation of the plausible mechanisms of carcinogenesis for each type of cancers.


Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.