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Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy

School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA

Special Issues: Inverse problems in the natural and social sciences

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 uncer- tainty 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 ma- trix 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 pa- tient 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.
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Keywords mathematical modeling; prostate cancer; androgen suppression; parameter estimation; parameter identifiability; uncertainty quantification; ensemble Kalman filter

Citation: Zhimin Wu, Tin Phan, Javier Baez, Yang Kuang, Eric J. Kostelich. Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy. Mathematical Biosciences and Engineering, 2019, 16(5): 3512-3536. doi: 10.3934/mbe.2019176

References

  • 1. C. Huggins and C. V. Hodges, Studies on Prostatic Cancer: I. The Effect of Castration, of
  • 2. W. G. Nelson, Commentary on Huggins and Hodges: "Studies on Prostatic Cancer", Cancer Res., 76 (2016), 186–187.
  • 3. S. Kumas, M. Shelley, C. Harrison, et al., Neo-adjuvant and adjuvant hormone therapy for localized and locally advanced prostate cancer, The Cochrane Database Syst. Rev., 18 (2006), CD006019.
  • 4. B. J. Feldman and D. Feldman, The development of androgen-independent prostate cancer, Nat. Rev. Cancer, 1 (2001), 34–45.
  • 5. R. Siegel, E. Ward, O. Brawley, et al., Cancer statistics, 2011: The impact of eliminating socioeconomic and racial disparities on premature cancer deaths, CA: A cancer journal for clinicians, 61 (2011) , 212–236.
  • 6. N. A. Spry, L. Kristjanson, B. Hooton, et al., Adverse effects to quality of life arising from treatment can recover with intermittent androgen suppression in men with prostate cancer, Eur. J. Cancer, 42 (2006), 1083–1092.
  • 7. N. D. Shore and E. D. Crawford, Intermittent Androgen Deprivation Therapy: Redefining the Standard of Care? Rev. Urol., 12 (2010), 1–11.
  • 8. M. C. Eisenberg and H. V. Jain, A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study, J. Theor. Biol., 431 (2017), 63–78.
  • 9. T. Phan, H. Changhan, A. Martinez, et al., Dynamics and implications of models for intermit- tent androgen suppression therapy, Math. Biosci. Eng., 16 (2019).
  • 10. T. L. Jackson, A mathematical model of prostate tumor growth and androgen-independent re- lapse, Discrete Continuous Dyn. Syst. Ser. B, 4 (2003), 187–201.
  • 11. A. M. Ideta, G. Tanaka, T. Takeuchi, et al., A mathematical model of intermittent androgen suppression for prostate cancer, J. Nonlinear Sci., 18 (2008), 593–614.
  • 12. T. Portz, Y. Kuang and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, AIP Adv., 2 (2012), 0–14.
  • 13. H. Vardhan-Jain and A. Friedman, Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy, Discrete & Continuous Dynamical Systems-Series B, 18 (2013) .
  • 14. Y. Hirata, K. Akakura, C.S. Higano,et al., Quantitative mathematical modeling of PSA dy- namics of prostate cancer patients treated with intermittent androgen suppression, J. Mol. Cell. Biol., 4 (2012), 127–132.
  • 15. Y. Hirata, N. Bruchovsky and K. Aihara, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer, J. Theor. Biol., 264 (2010), 517–527.
  • 16. Y. Hirata, G. Tanaka, N. Bruchovsky, et al., Mathematically modelling and controlling prostate cancer under intermittent hormone therapy, Asian J. Androl., 14 (2012), 270–277.
  • 17. Q. Guo, Z. Lu, Y. Hirata, et al., Parameter estimation and optimal scheduling algorithm for a mathematical model of intermittent androgen suppression therapy for prostate cancer, Chaos, 23 (2013), 43125.
  • 18. Y. Hirata, S. I. Azuma and K. Aihara, Model predictive control for optimally scheduling inter- mittent androgen suppression of prostate cancer, Methods, 67 (2014), 278–281.
  • 19. Y. Hirata, K. Morino, K. Akakura, et al., Personalizing Androgen Suppression for Prostate Cancer Using Mathematical Modeling, Sci. Rep., 8 (2018), 2673.
  • 20. R. A. Everett, A. M. Packer and Y. Kuang, Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy? Biophys. Rev. Lett., 9 (2014), 173–191.
  • 21. M. Droop, Some thoughts on nutrient limitation in algae. J. Phycol., 9 (1973), 264–272.
  • 22. J. Baez and Y. Kuang, Mathematical Models of Androgen Resistance in Prostate Cancer Pa- tients under Intermittent Androgen Suppression Therapy. Appl. Sci., 6 (2016), 352.
  • 23. J. D. Morken, A. Packer, R. A. Everett, et al., Mechanisms of resistance to intermittent andro- gen deprivation in patients with prostate cancer identified by a novel computational method, Cancer Res., (2014).
  • 24. T. Phan, K. Nguyen, P. Sharma, et al., The Impact of Intermittent Androgen Suppression Ther- apy in Prostate Cancer Modeling, Appl. Sci., 9 (2019), 36.
  • 25. A. Zazoua and W. Wang, Analysis of mathematical model of prostate cancer with androgen deprivation therapy, Commun. Nonlinear Sci. Numer. Simul., 66 (2019), 41–60.
  • 26. T. Hatano, Y. Hirata, H. Suzuki, et al., Comparison between mathematical models of intermit- tent androgen suppression for prostate cancer, J. Theor. Biol., 366 (2015), 33–45.
  • 27. N. Bruchovsky, L. Klotz, J. Crook, et al., Final results of the Canadian prospective Phase II trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer: Clinical parameters, Cancer, 107 (2006), 389–395.
  • 28. C. Cobelli and J. J .DiStefano-III, Parameter and structural identifiability concepts and ambigu- ities: a critical review and analysis, Am. J. Physiol. Regul. Integr. Comp. Physiol., 239 (1980), R7–24.
  • 29. A. Raue, C. Kreutz, T. Maiwald, et al., Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood, Bioinformatics, 25 (2009), 1923–1929.
  • 30. S. Audoly, G. Bellu, L. D'Angio, et al., Global identifiability of nonlinear models of biological systems, IEEE Trans. Biomed. Eng., 48 (2001), 55–65.
  • 31. M. C. Eisenberg, S. L. Robertson and J. H. Tien, Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease. J. Theor. Biol., 324 (2013), 84–102.
  • 32. M. P. Saccomani and L. D'angiò, Examples of testing global identifiability with the DAISY software, IFAC Proc. Vol., 42 (2009), 48–53.
  • 33. H. Wu, H. Zhu, H. Miao, et al., Parameter identifiability and estimation of HIV/AIDS dynamic models, Bull. Math. Biol., 70 (2008), 785–799.
  • 34. M. C. Eisenberg and M. A. L. Hayashi, Determining identifiable parameter combinations using subset profiling, Math. Biosci., 256 (2014), 116–126.
  • 35. H. Miao, X. Xia, A. S. Perelson, et al., On Identifiability of Nonlinear ODE Models and Ap- plications in Viral Dynamics, SIAM Rev. Soc. Ind. Appl. Math., 53 (2011), 3–39.
  • 36. T. Quaiser and M. Monnigmann, Systematic identifiability testing for unambiguous mechanis- tic modeling - application to JAK-STAT, MAP kinase, and NF-κB signaling pathway models, BMC Syst. Biol., 3 (2009), 50.
  • 37. C. Kreutz, A. Raue, D. Kaschek, et al., Profile likelihood in systems biology, FEBS J., 280 (2013), 2564–2571.
  • 38. G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res. Oceans, 99 (1994), 10143– 10162.
  • 39. G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementa- tion, Ocean Dyn., 53 (2003), 343–367.
  • 40. B. R. Hunt, E. J. Kostelich and I. Szunyogh, Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230 (2007), 112–126,
  • 41. S. J. Baek, B. R. Hunt, E. Kalnay, et al., Local ensemble Kalman filtering in the presence of model bias, Tellus A, 58 (2006), 293–306.
  • 42. C. P. Arnold and C. H. Day, Observing-Systems Simulation Experiments: Past, Present, and Future. Bull. Am. Meteorol. Soc., 67 (1986), 687–695.
  • 43. R. M. Errico, R. Yang, N. C. Privé, et al., Development and validation of observing-system simulation experiments at NASA's Global Modeling and Assimilation Office, Q. J. R. Meteorol. Soc., 139 (2013), 1162–1178.

 

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