Bulletin of Mathematical Biology

, Volume 65, Issue 6, pp 1131–1139 | Cite as

Maximum likelihood estimator and likelihood ratio test in complex models: An application to B lymphocyte development

  • Malka Gorfine
  • Laurence Freedman
  • Gitit Shahaf
  • Ramit Mehr
Article

Abstract

In this paper we introduce a simple framework which provides a basis for estimating parameters and testing statistical hypotheses in complex models. The only assumption that is made in the model describing the process under study, is that the deviations of the observations from the model have a multivariate normal distribution. The application of the statistical techniques presented in this paper may have considerable utility in the analysis of a wide variety of complex biological and epidemiological models. To our knowledge, the model and methods described here have not previously been published in the area of theoretical immunology.

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References

  1. Agur, Z. and R. Mehr (1997). Modeling Trypanosoma congolense parasitaemia patterns during the chronic phase of infection in N’Dama cattle. Parasite Immunol. 19, 171–182.CrossRefGoogle Scholar
  2. Blower, S. M. and G. F. Medley (1992). Epidemiology, HIV & drugs: mathematical models & data. Br. J. Addict. 87, 31–39.CrossRefGoogle Scholar
  3. Detours, V., R. Mehr and A. Perelson (1999). A quantitative theory of affinity-driven T cell repertoire selection. J. Theor. Biol. 200, 389–403.CrossRefGoogle Scholar
  4. Detours, V., R. Mehr and A. Perelson (2000). Deriving quantitative constrains under which T cell selection operates from data on the mature T cell repertoire. J. Immunol. 164, 121–128.Google Scholar
  5. Ferguson, S. F. (1996). A Course in Large Sample Theory, London, UK: Chapman and Hall.Google Scholar
  6. Hardy, R. R., Y. S. Li, D. Allman, M. Asano, M. Gui and K. Hayakawa (2002). B-cell commitment, development and selection. Immunol. Rev. 175, 23–32.CrossRefGoogle Scholar
  7. Kirschner, D. (2001). Reconstructing microbial pathogenesis. ASM News 67, 567–573.Google Scholar
  8. Kirschner, D., R. Mehr and A. Perelson (1998). The role of the thymus in HIV infection. J. AIDS Hum. Retrovirol. 18, 95–109.Google Scholar
  9. Lehmann, E. L. and G. Casella (1998). Theory of Point Estimation, 2nd edn, NY: Springer.Google Scholar
  10. Mehr, R. and A. Perelson (1997). Blind homeostasis and the CD4:CD8 ratio in the thymus and peripheral blood. J. AIDS Hum. Retrovirol. 14, 387–398.Google Scholar
  11. Mehr, R., G. Shahaf, A. Sah and M. Cancro (2003). Asynchronous differentiation models explain bone marrow labeling kinetics and predict reflux between the pre-and immature B cell pools. Intl. Immunol. 15, 301–312.CrossRefGoogle Scholar
  12. Shannon, M. and R. Mehr (1999). Reconciling repertoire shift with affinity maturation: the role of deleterious mutations. J. Immunol. 162, 3950–3956.Google Scholar
  13. Shlomchik, M., P. Watts, M. Weigert and S. Litwin (1998). Clone: a Monte-Carlo computer simulation of B cell clonal expansion, somatic mutation, and antigen-driven selection. Curr. Top. Microbiol. Immunol. 229, 173–197.Google Scholar

Copyright information

© Society for Mathematical Biology 2003

Authors and Affiliations

  • Malka Gorfine
    • 1
  • Laurence Freedman
    • 1
  • Gitit Shahaf
    • 2
  • Ramit Mehr
    • 2
  1. 1.Department of Mathematics and StatisticsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Faculty of Life SciencesBar-Ilan UniversityRamat-GanIsrael

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