
Mathematical Biosciences and Engineering, 2019, 16(6): 72997326. doi: 10.3934/mbe.2019365
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Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR Tcell cancer model
1 Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, USA
2 H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USA
Received: , Accepted: , Published:
References
1. H. T. Banks, Z. R. Kenz and W. C. Thompson, A review of selected techniques in inverse problem nonparametric probability distribution estimation, CRSCTR1213, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, May 2012; J. Inverse IllPose. Probl., 20 (2012), 429–460.
2. H. T. Banks, S. Hu and W. C. Thompson, Chapter 5 of Modeling and Inverse Problems in the Presence of Uncertainty, Chapman and Hall/CRC, New York, 2014.
3. H. T. Banks, L. W.Botsford, F. Kappel, et al., Modeling and estimation in size structured population models, LCDS/CCS Rep. 8713, March, 1987, Brown Univ.; Proc. 2nd Course on Math. Ecology (Trieste, December, 1986), World Scientific Press, Singapore (1988), 521–541.
4. H. T. Banks and H. T. Tran, Chapter 9.7 of Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, Boca Raton, FL, January 2, 2009
5. H. T. Banks, J. L. Davis, S. L. Ernstberger, et al., Experimental design and estimation of growth rate distributions in sizestructured shrimp populations, CRSC TR0820, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, November, 2008; Inverse Probl., 25 (2009), 095003 (28 pp).
6. H. T. Banks, L. W. Botsford, F. Kappel, et al., Estimation of growth and survival in sizestructured cohort data: An application to larval striped bass (Morone saxatilis), CAMS Tech. Rep. 8910, University of Southern California, 1989; J. Math. Biol., 30 (1991), 125–150.
7. H. T. Banks and B. G. Fitzpatrick, Estimation of growth rate distributions in sizestructured population models, CAMS Tech. Rep. 902, University of Southern California, January, 1990; Q. Appl. Math., 49 (1991), 215–235.
8. D. AbateDaga and M. L. Davila, CAR models: nextgeneration CAR modifications for enhanced Tcell function, Mol. TherOncolytics, 3 (2016), 16014.
9. E. K. Moon, C. Carpenito, J. Sun, et al., Expression of a functional CCR2 receptor enhances tumor localization and tumor eradication by retargeted human T cells expressing a mesothelinspecific chimeric antibody receptor, Clin. Cancer Res., 17 (2011), 4719–4730.
10. H. T. Banks and N. L. Gibson, Wellposedness in Maxwell systems with distributions of polarization relaxation parameters, CRSCTR0401, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, January, 2004; Appl. Math. Lett., 18 (2005), 423–430.
11. H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters, CRSCTR0529, August, 2005; Q. Appl. Math., 64 (2006), 749–795.
12. H. T. Banks and D. M. Bortz, Inverse problems for a class of measure dependent dynamical systems, J. Inverse Illpose. Probl., 13 (2005), 103–121.
13. H. T. Banks, D. M. Bortz and S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Math. Biosci., 183 (2003), 63–91.
14. H. T. Banks, D. M. Bortz, G. A. Pinter, et al., Modeling and imaging techniques with potential for application in bioterrorism, CRSC TR0302, January 2003; Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security (H.T. Banks and C. CastilloChavez, eds.), Front. Appl. Math., FR28, SIAM, Philadelphia, 2003, 129–154.
15. H. T. Banks, J. H. Barnes, A. Eberhardt, et al., Modeling and computation of propagating waves from coronary stenosis, Comput. Appl. Math., 21 (2002), 767–788.
16. H. T. Banks, S. Hu, Z. R. Kenz, et al., Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: methodology, CRSCTR1209, April, 2012; J. Inverse Illpose. Probl., 21 (2013), 25–57.
17. H. T. Banks, S. Hu, Z. R. Kenz, et al., Model validation for a noninvasive arterial stenosis detection problem, CRSCTR1222, December, 2012; Math. Biosci. Eng., 11 (2013), 427–448.
18. H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, CRSCTR0403, January, 2004; SIAM J. Multiscale Model. Sim., 3 (2005), 395–412.
19. H. T. Banks, Chapter 14.4 of A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering, Taylor and Frances Publishing, 2012.
20. G. de Vries, T. Hillen, M. Lewis, et al., A Course in Mathematical Biology: Quantitative Modelling with Mathematical and Computational Methods, SIAM, Philadephia, 2006.
21. S. I. Rubinow, Introduction to Mathematical Biology, John Wiley & Sons, New York, 1975.
22. L. J. Allen, An Introduction to Mathematical Biology. Pearson Education, Inc., Pearson Prentice Hall, Upper Saddle River, NJ, 2007.
23. M. Braun and M. Golubitsky, Differential Equations and their Applications. Vol. 4. SpringerVerlag New York, Inc., New York, NY, 1983.
24. G. E. Collins and A. G. Akritas, Polynomial real root isolation using Descarte's rule of signs, Proceedings of the third ACM symposium on Symbolic and algebraic computation, ACM, 1976.
25. H. T. Banks, L. BekeleMaxwell, L. Bociu, et al., The complexstep method for sensitivity analysis of nonsmooth problems arising in biology, CRSCTR1511, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2015; Eurasia. J. Math. Comput. Appl., 3 (2015), 16–68.
26. H. T. Banks, K. BekeleMaxwell, R. A. Everett, et al., Dynamic modeling of problem drinkers undergoing behavioral treatment, CRSCTR1612, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, October, 2016; Bull. Math. Biol., 79 (2017), 1254–1273.
27. H. T. Banks and K. L. Bihari, Modeling and estimating uncertainty in parameter estimation, CRSCTR9940, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2016; December, 1999; Inverse Probl., 17 (2001), 95–111.
28. H. T. Banks, K. B. Flores, I. G. Rosen, et al., The Prohorov Metric Framework and aggregate data inverse problems for random PDEs, CRSCTR1805, Center for Research in Scientific Computa tion, N. C. State University, Raleigh, NC, June, 2018; Commun. Appl. Anal., 22 (2018), 415–446.
29. H. T. Banks, J. Catenacci and S. Hu, Use of differencebased methods to explore statistical and mathematical model discrepancy in inverse problems, CRSCTR1505, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, May, 2015. J. Inverse Illpose. P., 24 (2016), 413–433.
30. H. T. Banks, J. E. Banks, N. G. Cody, et al., Population model for the decline of Homalodisca vitripennis (HEMIPTERA: CICADELLIDAE) over a tenyear period, CRSCTR1806, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, June, 2018; J. Biol. Dyn., 13 (2019), 422–446.
31. H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhasser, Boston, 1989.
32. H. T. Banks and P. Kareiva, Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models, J. Math. Biol., 17 (1983), 253–273.
33. A. C. Atkinson and R. A. Bailey, One hundred years of the design of experiments on and off the pages of Biometrika, Biometrika, 88 (2001), 53–97.
34. A. C. Atkinson and A. N. Donev, Optimum Experimental Designs, Oxford University Press, New York, 1992.
35. M. P. F. Berger and W. K. Wong (Editors), Applied Optimal Designs, John Wiley & Sons, Chichester, UK, 2005.
36. V. V. Fedorov, Theory of Optimal Experiments, Academic Press, New York and London, 1972.
37. V. V. Fedorov and P. Hackel, ModelOriented Design of Experiments, SpringerVerlag, New York, 1997.
38. W. Mueller and M. Stehlik, Issues in the optimal design of computer simulation experiments, Appl. Stoch. Model. Bus., 25 (2009), 163–177.
39. M. Patan and B. Bogacka, Optimum experimental designs for dynamic systems in the presence of correlated errors, Comput. Stat. Data An., 51 (2007), 5644–5661.
40. D. Ucinski and A. C. Atkinson, Experimental design for timedependent models with correlated observations, Stud. Nonlinear Dyn. E., 8 (2004), Article 13: The Berkeley Electronic Press.
41. H. T. Banks, K. Holm and F. Kappel, Comparison of optimal design methods in inverse problems, CRSCTR1011, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, July, 2010; Inverse Probl., 27 (2011), 075002.
42. H. T. Banks, A. Cintr'onArias and F. Kappel, Parameter selection methods in inverse problem formulation, CRSCTR1003, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, revised November 2010; Mathematical Model Development and Validation in Physiology: Application to the Cardiovascular and Respiratory Systems, Lecture Notes in Mathematics, Vol. 2064, Mathematical Biosciences Subseries; SpringerVerlag, Berlin, 2013.
43. M. Avery, H. T. Banks, K. Basu, et al., Experimental design and inverse problems in plant biological modeling, CRSCTR1112, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2011; J. Inverse Illpose. P., 20 (2012), 169–191.
44. H. T. Banks and K. L. Rehm, Experimental design for vector output systems, CRSCTR1211, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, April, 2012; Inverse Probl. Sci. En., 22 (2014), 557–590.
45. H. T. Banks and K. L. Rehm, Experimental design for distributed parameter vector systems, CRSCTR1217, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, August, 2012; Appl. Math. Lett., 26 (2013), 10–14.
46. H. T. Banks, S. Dediu, S. L. Ernstberger, et al., Generalized sensitivities and optimal experimental design, CRSCTR0812, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, September, 2008, revised November, 2009; J. Inverse Illpose. P., 18 (2010), 25–83.
47. B. M. Adams, H. T. Banks, M. Davidian, et al., Model fitting and prediction with HIV treatment interruption data, CRSC TR0540, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October, 2005; Bull. Math. Biol., 69 (2007), 563–584.
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