Computational approaches to parameter estimation and model selection in immunology

Journal of Computational and Applied Mathematics

Volumn 184, Issue 1, 2005, Pages 50-76

  Baker, C T H ^a,b   Bocharov, G A ^a,b,c   Ford, J M ^d   Lumb, P M ^b   Norton, S J ^b   Paul, C A H ^a   Junt, T ^e   Krebs, P ^e   Ludewig, B ^e,f  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF CHESTER   (United Kingdom)

^c INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^d ALDER HEY CHILDREN'S NHS FOUNDATION TRUST   (United Kingdom)

^e UNIVERSITY OF ZURICH   (Switzerland)

^f Research Department   (Switzerland)

Author keywords

Computational modelling; Experimental LCMV infection; Immune response; Mathematical model; Maximum likelihood; Numerical accuracy; Parameter estimation; Parsimony

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; NUMERICAL METHODS; OPTIMIZATION; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; VIRUSES;

BIOMATHEMATICS; DELAY DIFFERENTIAL EQUATIONS; IMMUNE RESPONSE; INFECTION; NUMERICAL ACCURACY;

IMMUNOLOGY;

EID: 22544443751     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.02.003     Document Type: Article

References (59)

1. H. Akaike A new look at the statistical model identification IEEE Trans. Automat. Control 19 1974 716-723
2. J.D. Altman P.A.H. Moss P.J.R. Goulder D.H. Barouch M.G. McHeyzer-Williams J.I. Bell A.J. McMichael M.M. Davis Phenotypic analysis of antigen-specific T lymphocytes Science 274 1996 94-96
3. P. Armitage G. Beŕry J.N.S. Matthews Statistical Methods in Medical Research fourth ed. 2001 Blackwell Science Oxford
4. S. Audoly G. Belllu L. D'Angio M. Saccomni C. Cobelli Global identifiablity of nonlinear biological systems IEEE Trans. Biomed. Eng. 48 2001 55-65
5. C.T.H. Baker Retarded differential equations J. Comput. Appl. Math. 125 2000 309-335
6. C.T.H. Baker G.A. Bocharov C.A.H. Paul Mathematical modelling of the Interleukin-2 T-cell system: A comparative study of approaches based on ordinary and delay differential equations J. Theoret. Med. 2 1997 117-128
7. C.T.H. Baker G.A. Bocharov C.A.H. Paul F.A. Rihan Modelling and analysis of time-lags in some basic patterns of cell proliferation J. Math. Biol. 37 1998 341-371
8. C.T.H. Baker, G.A. Bocharov, C.A.H. Paul, F.A. Rihan, Computational modelling with functional differential equations: Identification, selection, and sensitivity, Appl. Numer. Math., in press. Available online 19th October 2004.
9. C.T.H. Baker, G.A. Bocharov, F.A. Rihan, A report on the use of delay differential equations in numerical modelling in the biosciences, MCCM Technical Report 343, University of Manchester, 1999, 45pp, ISSN 1360-1725.
10. C.T.H. Baker, G.A. Bocharov, F.A. Rihan, A report on the models with delays for cell population dynamics: Identification, selection and analysis-Part I. MCCM Technical Report 425, University of Manchester, 2003, 28pp, ISSN 1360-1725.
11. C.T.H. Baker, E.I. Parmuzin, Identification of the initial function for delay differential equations: Parts I, II, III, MCCM Technical Report 431, 443 & 444, University of Manchester, 2004, ISSN 1360-1725.
12. C.T.H. Baker E.I. Parmuzin Analysis via integral equations of an identification problem for delay differential equations J. Integral Equations Appl. 16 2004 111-135
13. C.T.H. Baker, E.I. Parmuzin, Identification of the initial function for nonlinear delay differential equations, Russian J. Numer. Anal. Math. Modelling, 20 (2005) to appear.
14. C.T.H. Baker C.A.H. Paul Pitfalls in parameter estimation for delay differential equations SIAM J. Sci. Comput. 18 1997 305-314
15. C.T.H. Baker, C.A.H. Paul, Discontinuous solutions of neutral delay differential equations, Appl. Numer. Math., to appear.
16. H.T. Banks, Delay systems in biological models: Approximation techniques, Nonlinear systems and applications, in: V. Lakshmikantham (Ed.), Proceedings of the International Conference, University of Texas, Arlington, TX, 1976, Academic Press, New York, 1977, pp. 21-38.
17. H.T. Banks, Approximation of delay systems with applications to control and identification. Functional differential equations and approximation of fixed points, in: H.-O. Peitgen, H.-O. Walther (Eds.), Proceedings of the Summer School and Conference, University of Bonn, Bonn, 1978, Lecture Notes in Mathematics, vol. 730, Springer, Berlin, 1979, pp. 65-76.
18. H.T. Banks K.L. Bihari Modelling and estimating uncertainty in parameter estimation Inverse Problems 17 2001 95-111
19. H.T. Banks J.A. Burns E.M. Cliff Parameter estimation and identification for systems with delay SIAM J. Control Optim. 19 6 1981 791-828
20. H.T. Banks P.K.D. Lamm Estimation of delays and other parameters in nonlinear functional differential equations SIAM J. Control Optim. 21 1983 895-915
21. Y. Bard Nonlinear Parameter Estimation 1974 Academic Press New York
22. M. Battegay S. Cooper A. Althage H. Banziger H. Hengartner R.M. Zinkernagel Quantification of lymphocytic choriomeningitis virus with an immunological focus assay in 24- or 96-well plates J. Virol. Methods 33 1991 191-198
23. A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford University Press, New York, 2003.
24. A. Bertuzzi A. Gandolfi R. Vitelli A regularization procedure for estimating cell kinetic parameters from flow-cytometry data Math. Biosci. 82 1986 63-85
25. G.A. Bocharov Modelling the dynamics of LCMV infection in mice: conventional and exhaustive CTL responses J. Theoret. Biol. 192 1998 283-308
26. +-T-lymphocyte responses J. Virol. 78 2004 2247-2254
27. G.A. Bocharov F.A. Rihan Numerical modelling in biosciences using delay differential equations J. Comput. Appl. Math. 125 2000 183-199
28. J.A. Borghans L.S. Taams M.H.M. Wauben R.J. De Boer Competition for antigenic sites during T cell proliferation: A mathematical interpretation of in vitro data Proc. Natl. Acad. Sci. USA 96 1999 10782-10787
29. F.M. Burnet The Clonal Selection Theory of Acquired Immunity 1959 Cambridge University Press Cambridge
30. K.P. Burnham D.R. Anderson Model Selection and Inference - a Practical Information-Theoretic Approach 1998 Springer New York
31. A.K. Chakraborty M.L. Dustin A.S. Shaw In silico models for cellular and molecular immunology: Successes, promises and challenges Nat. Immunol. 4 2003 933-936
32. A.R. Conn N. Gould P.L. Toint LANCELOT: A Fortran Package for Large-scale Nonlinear Optimization 1992 Springer New York
33. + T-cell response to lymphocytic choriomeningitis virus J. Virol. 75 2001 10663-10669
34. B. Efron R. Tibshirani Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy Statist. Sci. 1 1986 54-77
35. + T-cell precursors on the outcome of virus infection Cell. Immunol. 189 1998 67-73
36. N.A. Gershenfeld The Nature of Mathematical Modelling 2000 Cambridge University Press Cambridge
37. P.D. Gingerich Arithmetic or geometric normality of biological variation: An empirical test of theory J. Theoret. Biol. 204 2000 201-221
38. E. Hairer S.P. Nørsett G. Wanner Solving Ordinary Differential Equations, I, Nonstiff Problems second ed. 1993 Springer Berlin
39. W. Horbelt J. Timmer H.U. Voss Parameter estimation in nonlinear delayed feedback systems from noisy data Phys. Lett. A 299 2002 513-521
40. C. Kesmir R. De Boer Clonal exhaustion as a result of immune deviation Bull. Math. Biol. 65 2003 359-374
41. S. Kullback R.A. Leibler On information and sufficiency Ann. Math. Statist. 22 1951 79-86
42. G.I. Marchuk Mathematical Modelling of Immune Response in Infectious Diseases 1997 Kluwer Academic Publishers Dordrecht
43. A.R. McLean M.M. Rosado F. Agenes R. Vascocellos A.A. Freitas Resource competition as a mechanism for B cell homeostasis Proc. Natl. Acad. Sci. USA 94 1997 5792-5797
44. I.J. Myung Tutorial on maximum likelihood estimation J. Math. Physiol. 47 2003 90-100
45. U. Nowak, A. Grah, M. Schreier, Parameter estimation and accuracy matching strategies for 2-D reactor models, ZIB-Report 03-52, 2003, 13pp.
46. Numerical Algorithms Group The NAg FORTRAN Library http://www.nag.co.uk/ numeric/Fortran_Libraries.asp.
47. M.A. Pascual P. Kareiva Predicting the outcome of competition using experimental data: Maximum likelihood and Bayesian approaches Ecology 77 1996 337-349
48. C.A.H. Paul, A User Guide to Archi, MCCM Report 283, University of Manchester. http://www.maths.man.ac.uk/chris/reports/rep283.pdf.
49. H. Rabitz Chemical sensitivity analysis theory with applications to molecular dynamics and kinetics Comput. Chem. 5 1981 167-180
50. E. Renshaw Modelling Biological Populations in Space and Time 1993 Cambridge University Press Cambridge
51. G. Schwarz Estimating the dimension of a model Ann. Statist. 6 1978 461-464
52. D.J. Venzon S.H. Mooogavkor A method for computing profile-likelihood-based confidence intervals Appl. Statist. 37 1988 87-94
53. D. Verotta F. Schaedeli Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials Math. Biosci. 176 2002 163-183
54. D.R. Willé C.T.H. Baker The tracking of derivative discontinuities in systems of delay-differential equations Appl. Numer. Math. 9 1992 209-222
55. D. Wodarz P. Klenerman M.A. Nowak Dynamics of cytotoxic T-lymphocyte exhaustion Proc. R. Soc. (London) Ser. B 265 1998 191-203
56. D.H. Wolpert The bootstrap is inconsistent with probability theory, in: K. Hanson R. Silver (Eds.) Maximum Entropy and Bayesian Methods 1995
57. L.M.M. Wolters B.E. Hansen H.G.M. Niesters R.S.L. Levi-Drummer A.U. Neumann S.W. Schalm R.A. de Man The influence of baseline characteristics on viral dynamic parameters in chronic hepatitis B patients treated with lamivudine J. Hepatol. 37 2002 253-258
58. R.M. Zinkernagel Lymphocytic choriomeningitis virus and immunology Curr. Top. Microbiol. Immunol. 263 2002 1-5
59. C.A.H. Paul, Archi FORTRAN listing, University of Manchester, http://www.maths.man.ac.uk/~chris/software/.