2024-03-28T16:57:57Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1559842021-08-27T02:47:01Zoai_pmh:all155984
https://hdl.handle.net/2286/R.I.46254
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2017
131 pages
Doctoral Dissertation
Academic theses
Text
eng
Baez, Javier
Kuang, Yang
Kostelich, Eric
Crook, Sharon
Gardner, Carl
Nagy, John
Arizona State University
Doctoral Dissertation Applied Mathematics 2017
Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.
Applied Mathematics
Statistics
Biology
Differential Equations
Kalman filtering
Mathematical Modeling
Parameter estimation
Regression
time series
Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy