Differential equation modeling of HIV viral fitness experiments: Model identification, model selection, and multimodel inference

Biometrics

Volumn 65, Issue 1, 2009, Pages 292-300

  Miao, Hongyu ^a   Dykes, Carrie ^a   Demeter, Lisa M ^a   Wu, Hulin ^a  

^a UNIVERSITY OF ROCHESTER SCHOOL OF MEDICINE AND DENTISTRY   (United States)

Author keywords

Differential equation modeling; Global optimization; HIV dual infection; Identifiability analysis; Model selection; Multimodel inference; Viral fitness

Indexed keywords

NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; STATISTICAL METHODS;

DIFFERENTIAL EQUATION MODEL; EXPERIMENT MODELING; GLOBAL OPTIMISATION; HIV DUAL INFECTION; IDENTIFIABILITY ANALYSIS; IDENTIFICATION MODELING; MODEL IDENTIFICATION; MODEL SELECTION; MULTI-MODEL INFERENCE; VIRAL FITNESS;

GLOBAL OPTIMIZATION;

HUMAN IMMUNODEFICIENCY VIRUS; INFECTIOUS DISEASE; NUMERICAL METHOD; NUMERICAL MODEL; OPTIMIZATION; STATISTICAL ANALYSIS; VIRUS;

ARTICLE; HUMAN IMMUNODEFICIENCY VIRUS 1; IN VITRO STUDY; NONLINEAR SYSTEM; STATISTICAL MODEL; STATISTICAL PARAMETERS; VIRUS MUTANT; VIRUS REPLICATION;

HUMAN IMMUNODEFICIENCY VIRUS 1;

EID: 62749173565     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2008.01059.x     Document Type: Article

References (40)

1. Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle. In Second International Symposiumon Information Theory, B. N. Petrov and F. Csaki (eds 267 281. Budapest : Akademiai Kiado.
2. Audoly, S., D'angio, L., Saccomani, M. P., and Cobelli, C. (1998). Global identifiability of linear compartmental models. IEEE Transactions on Biomedical Engineering 45, 36 47.
3. Audoly, S., Bellu, G., D'Angio, L., Saccomani, M. P., and Cobelli, C. (2001). Global identifiability of nonlinear models of biological systems. IEEE Transactions on Biomedical Engineering 48, 55 65.
4. Bickel, P. J. and Doksum, K. A. (2001). Mathematical Statistics Basic Ideas and Selected Topics, 2nd edition. Englewood Cliffs, NJ : Prentice Hall.
5. Bonhoeffer, S., Barbour, A. D., and De Boer, R. J. (2002). Procedures for reliable estimation of viral fitness from time-series data. Proceedings of the Royal Society of London, Series B 269, 1887 1893.
6. Burnham, K. P. and Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods Research 33, 261 304.
7. Conte, G., Moog, C. H., and Perdon, A. M. (1999). Nonlinear Control Systems: An Algebraic Setting. London : Springer.
8. Dang, Q., Chen, J., Unutmaz, D., Coffin, J. M., Pathak, V. K., Powell, D., KewalRamani, V. N., Maldarelli, F., and Hu, W. S. (2004). Nonrandom HIV-1 infection and double infection via direct and cell-mediated pathways. Proceedings of the National Academy of Sciences USA 101, 632 637.
9. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge, U.K. : Cambridge University Press.
10. Diop, S. and Fliess, M. (1991). On nonlinear observability. In Proceedings of the First European Control Conference, Paris, Hermes, 152 157.
11. Dykes, C., Wang, J., Jin, X., Planelles, V., An, D. S., Tallo, A., Huang, Y., Wu, H., and Demeter, L. M. (2006). Evaluation of a multiple-cycle, recombinant virus, growth competition assay that uses flow cytometry to measure replication efficiency of HIV-1 in cell culture. Journal of Clinical Microbiology 44, 1930 1943.
12. Englezos, P. and Kalogerakis, N. (2001). Applied Parameter Estimation for Chemical Engineers. New York : Marcel-Dekker.
13. Goudsmit, J., De Ronde, A., De Rooij, E., and De Boer, R. J. (1997). Broad spectrum of in vivo fitness of human immunodeficiency virus type 1 subpopulations differing at reverse transcriptase codons 41 and 215. Journal of Virology 71, 4479 4484.
14. Glad, S. T. (1997). Solvability of differential algebraic equations and inequalities: An algorithm. European Control Conference, Brussels, ECC97.
15. Jeffrey, A. M. and Xia, X. (2005). Identifiability of HIV/AIDS models. In Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, W. Y. Tan and H. Wu (eds 255 286. Singapore : World Scientific.
16. Jung, A., Maier, R., Vartanian, J. P., Bocharov, G., Jung, V., Fischer, U., Meese, E., Wain-Hobson, S., and Mayerhans, A. (2002). Multiply infected spleen cells in HIV patients. Nature 418, 144.
17. Levy, D. N., Aldrovandi, G. M., Kutsch, O., and Shaw, G. M. (2005). Dynamics of HIV-1 recombination in its natural target cells. Proceedings of the National Academy of Sciences USA 101, 4204 4209, and correction (2005) 102, 1808.
18. Linga, P., Al-Saifi, N., and Englezos, P. (2006). Comparison of the Luus-Jaakola optimization and Gauss-Newton methods for parameter estimation in ordinary differential equation models. Industrial & Engineering Chemistry Research 45, 4716 4725.
19. Ljung, L. and Glad, S. T. (1994). On global identifiability for arbitrary model parameterizations. Automatica 30, 265 276.
20. Luus, R. and Jaakola, T. H. I. (1973). Optimization by direct search and systematic reduction of size of search region. AIChE Journal 19, 760 766.
21. Martinez-Picado, J., Savara, A. V., Sutton, L., and D'Aquila, R. T. (1999). Replicative fitness of protease inhibitor-resistant mutants of human immunodeficiency virus type 1. Journal of Virology 73, 3744 3752.
22. Marée, A. F. M., Keulen, W., Boucher, C. A. B., and De Boer, R. J. (2000). Estimating relative fitness in viral competition experiments. Journal of Virology 74, 11067 11072.
23. Metropolis, N. and Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association 44, 335 341.
24. Miao, H., Dykes, C., Demeter, L. M., Cavenaugha, J., Parka, S. Y., Perelson, A. S., and Wu H. (2008). Modeling and estimation of kinetic parameters and replication fitness of HIV-1 from flow-cytometry-based growth competition experiments. Bulletin of Mathematical Biology, in press.
25. Moles, C. G., Bangaa, J. R., and Keller, K. (2004). Solving nonconvex climate control problems: Pitfalls and algorithm performances. Applied Soft Computing 5, 35 44.
26. Mood, A. M., Graybill, F. A., and Boes, D. C. (1974). Introduction to the Theory of Statistics, 3rd edition. New York : McGraw-Hill.
27. Nocedal, J. and Wright, S. J. (1999). Numerical Optimization. New York : Springer Verlag.
28. Ollivier, F. (1990). Le problème de l'identifiabilité structurelle globale: étude théorique, méthodes effectives et bornes de complexité. Thèsis de Doctorat en Science, École Polytéchnique, Paris, France.
29. Pohjanpalo, H. (1978). System identifiability based on the power series expansion of the solution. Mathematical Biosciences 41, 1 32.
30. Ritt, J. (1950). Differential Algebra. Providence, RI : American Mathematical Society.
31. Rodriguez-Fernandez, M., Egea, J. A., and Banga, J. R. (2006). Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics 7, 483 500.
32. Schwarz, G. (1978). Estimating the dimensions of a model. Annals of Statistics 6, 461 464.
33. Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap. New York : Springer.
34. Storn, R. and Price, K. (1997). Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341 359.
35. Tunali, T. and Tarn, T. J. (1987). New results for identifiability of nonlinear systems. IEEE Transactions on Automatic Control 32, 146 154.
36. Vajda, S., Godfrey, K., and Rabitz, H. (1989). Similarity transformation approach to identifiability analysis of nonlinear compartmental models. Mathematical Biosciences 93, 217 248.
37. Wu, H., Huang, Y., Dykes, C., Liu, D., Ma, J., Perelson, A. S., and Demeter, L. (2006). Modeling and estimation of replication fitness of HIV-1 in vitro experiments using a growth competition assay. Journal of Virology 80, 2380 2389.
38. Wu, H., Zhu, H., Miao, H., and Perelson, A. S. (2008). Parameter identifiability and estimation of HIV/AIDS dynamic models. Bulletin of Mathematical Biology, 70, 785 799.
39. Xia, X. (2003). Estimation of HIV/AIDS parameters. Automatica 39, 1983 1988.
40. Xia, X. and Moog, C. H. (2003). Identifiability of nonlinear systems with applications to HIV/AIDS models. IEEE Transactions on Automatic Control 48, 330 336.