TY - JOUR
T1 - Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy
AU - Wu, Zhimin
AU - Phan, Tin
AU - Baez, Javier
AU - Kuang, Yang
AU - Kostelich, Eric
N1 - Funding Information:
The research of this work was partially supported by NSF grants (to YK) DMS-1615879, DMS-1518529 and a grant (to EK and YK) by the Arizona Biomedical Research Commission. ZW was partially supported by a block grant from the Arizona State University Graduate College. We are grateful to the late Dr. Nicholas Bruchovsky for the clinical data set.
Publisher Copyright:
© 2019 the Author(s).
PY - 2019
Y1 - 2019
N2 - The past two decades have seen the development of numerous mathematical models to study various aspects of prostate cancer in clinical settings. These models often contain large sets of parameters and rely on limited data sets for validation. The quantitative analysis of the dynamics of prostate cancer under treatment may be hindered by the lack of identifiability of the parameters from the available data, which limits the predictive ability of the model. Using three ordinary differential equation models as case studies, we carry out a numerical investigation of the identifiability and uncertainty quantification of the model parameters. In most cases, the parameters are not identifiable from time series of prostate-specific antigen, which is used as a clinical proxy for tumor progression. It may not be possible to define a finite confidence bound on an unidentifiable parameter, and the relative uncertainties in even identifiable parameters may be large in some cases. The Fisher information matrix may be used to determine identifiable parameter subsets for a given model. The use of biological constraints and additional types of measurements, should they become available, may reduce these uncertainties. Ensemble Kalman filtering may provide clinically useful, short-term predictions of patient outcomes from imperfect models, though care must be taken when estimating “patient-specific” parameters. Our results demonstrate the importance of parameter identifiability in the validation and predictive ability of mathematical models of prostate tumor treatment. Observing-system simulation experiments, widely used in meteorology, may prove useful in the development of biomathematical models intended for future clinical application.
AB - The past two decades have seen the development of numerous mathematical models to study various aspects of prostate cancer in clinical settings. These models often contain large sets of parameters and rely on limited data sets for validation. The quantitative analysis of the dynamics of prostate cancer under treatment may be hindered by the lack of identifiability of the parameters from the available data, which limits the predictive ability of the model. Using three ordinary differential equation models as case studies, we carry out a numerical investigation of the identifiability and uncertainty quantification of the model parameters. In most cases, the parameters are not identifiable from time series of prostate-specific antigen, which is used as a clinical proxy for tumor progression. It may not be possible to define a finite confidence bound on an unidentifiable parameter, and the relative uncertainties in even identifiable parameters may be large in some cases. The Fisher information matrix may be used to determine identifiable parameter subsets for a given model. The use of biological constraints and additional types of measurements, should they become available, may reduce these uncertainties. Ensemble Kalman filtering may provide clinically useful, short-term predictions of patient outcomes from imperfect models, though care must be taken when estimating “patient-specific” parameters. Our results demonstrate the importance of parameter identifiability in the validation and predictive ability of mathematical models of prostate tumor treatment. Observing-system simulation experiments, widely used in meteorology, may prove useful in the development of biomathematical models intended for future clinical application.
KW - Androgen suppression
KW - Ensemble Kalman filter
KW - Mathematical modeling
KW - Parameter estimation
KW - Parameter identifiability
KW - Prostate cancer
KW - Uncertainty quantification
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U2 - 10.3934/mbe.2019176
DO - 10.3934/mbe.2019176
M3 - Article
C2 - 31499626
AN - SCOPUS:85064935975
SN - 1547-1063
VL - 16
SP - 3512
EP - 3536
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
IS - 5
ER -