abstract: 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. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2017
Identifer | oai:union.ndltd.org:asu.edu/item:46254 |
Date | January 2017 |
Contributors | Baez, Javier (Author), Kuang, Yang (Advisor), Kostelich, Eric (Committee member), Crook, Sharon (Committee member), Gardner, Carl (Committee member), Nagy, John (Committee member), Arizona State University (Publisher) |
Source Sets | Arizona State University |
Language | English |
Detected Language | English |
Type | Doctoral Dissertation |
Format | 131 pages |
Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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