Bulletin of Mathematical Biology

, Volume 69, Issue 2, pp 563–584

Estimation and Prediction With HIV-Treatment Interruption Data

  • B. M. Adams
  • H. T. Banks
  • M. Davidian
  • E. S. Rosenberg
Original Article

Abstract

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.

Keywords

HIV models Treatment interruptions Censored data Parameter estimation Prediction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, B.M., 2005. Non-parametric parameter estimation and clinical data fitting with a model of HIV Infection. PhD Thesis, NC State University, Raleigh.Google Scholar
  2. Adams, B.M., Banks, H.T., Davidian, M., Kwon, H.D., Tran, H.T., Wynne, S.N., Rosenberg, E.S., 2005. HIV dynamics: Modeling, data analysis, and optimal treatment protocols. J. Comput. Appl. Math. 184(1), 10–49.Google Scholar
  3. Adams, B.M., Banks, H.T., Davidian, M., Rosenberg, E.S., 2005. Model fitting and prediction with HIV treatment interruption data, Center for Research in Scientific Computation Technical Report CRSC-TR05-40, NC State University, Raleigh, October. Online:http://www.ncsu.edu/crsc/reports.
  4. Adams, B.M., Banks, H.T., Tran, H.T., Kwon, H., 2004. Dynamic multidrug therapies for HIV: Optimal and STI control approaches. Math. Biosci. Eng. 1(2), 223–241.MATHGoogle Scholar
  5. Aitkin, M., 1981. A note on the regression analysis of censored data. Technometrics 23, 161–163.CrossRefGoogle Scholar
  6. Armstrong, S., Fontaine, C., Wilson, A., 2004. 2004 Report on the Global AIDS Epidemic. UNAIDS/Joint United Nations Programme on HIV/AIDS, Geneva, Switzerland. Online:http://www.unaids.org.
  7. Banks, H.T., Kunisch, K., 1989. Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston.MATHGoogle Scholar
  8. Banks, H.T., Kwon, H., Toivanen, J.A., Tran, H.T., 2006. An SDRE-based estimator approach for HIV feedback control [Technical Report CRSC-TR05-20, NC State University, Raleigh, April]. Optim. Control Appl. Methods 27, 93–121.CrossRefGoogle Scholar
  9. Bonhoeffer, S., Rembiszewski, M., Ortiz, G.M., Nixon, D.F., 2000. Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection. AIDS 14, 2313–2322.CrossRefGoogle Scholar
  10. Callaway, D.S., Perelson, A.S., 2002. HIV-1 infection and low steady state viral loads. Bull. Math. Biol. 64(1), 29–64.CrossRefGoogle Scholar
  11. Dempster, A.P., Laird, N.M., Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc., Ser. B 39(1), 1–38.MATHGoogle Scholar
  12. Finkel, D.E., 2005. Global optimization with the DIRECT algorithm. PhD Thesis, NC State University, Raleigh. Online:http://www4.ncsu.edu/definkel/research/Direct.m.
  13. Hindmarsh, A.C., 1983. Scientific Computing. Chapter ODEPACK, A Systematized Collection of ODE Solvers, North-Holland, Amsterdam, pp. 55–64. Online:http://www.llnl.gov/CASC/odepack/. Google Scholar
  14. Kalbfleisch, J.P., Prentice, R.L., 2002. The Statistical Analysis of Failure Time Data. Wiley, New York.MATHGoogle Scholar
  15. Kassutto, S., Maghsoudi, K., Johnston, M.N., Robbins, G.K., Burgett, N.C., Sax, P.E., Cohen, D., Pae, E., Davis, B., Zachary, K., Basgoz, N., D'agata, E.M.C., DeGruttola, V., Walker, B.D., Rosenberg, E.S., 2006. Longitudinal analysis of clinical markers following antiretroviral therapy initiated during acute or early HIV-1 infection. Clin. Infect. Dis. 42, 1024–1031.Google Scholar
  16. Kelley, C.T., 1999. Iterative methods for optimization. In: Frontiers in Applied Mathematics FR18. SIAM, Philadelphia.Google Scholar
  17. Klein, J.P., Moeschberger, M.L., 2003. Survival Analysis: Techniques for Censored and Truncated Data. Springer, New York.MATHGoogle Scholar
  18. Lichterfeld, M., Kaufman, D.E., Yu, G., Mui, S.K., Addo, M.M., Johnston, M.N., Cohen, D., Robbins, G.K., Pae, E., Alter, G., Wurcel, A., Stone, D., Rosenberg, E.S., Walker, B.D., Altfield, M., 2004. Loss of HIV-1-specific CD8+ T-cell proliferation after acute HIV-1 infection and restoration by vaccine-induced HIV-1-specific CD4+ T-cells. J. Exp. Med. 200(6), 701–712.Google Scholar
  19. Lori, F., Lisziewicz, J., 2001. Structured treatment interruptions for the management of HIV infection. J. Am. Med. Assoc. 4286(23), 2981–2987.CrossRefGoogle Scholar
  20. McLachlan, G.J., Krishnan, T., 1997. The EM Algorithm and Extensions. Wiley, New York.MATHGoogle Scholar
  21. Norris, P.J., Rosenberg, E.S., 2002. CD4+ T-helper cells and the role they play in viral control. J. Mol. Med. 80, 397–405.CrossRefGoogle Scholar
  22. Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics of immune responses to persistent viruses. Science 272, 74–79.CrossRefGoogle Scholar
  23. Perelson, A.S., Nelson, P.W., 1999. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41(1), 3–44.MATHCrossRefGoogle Scholar
  24. Rosenberg, E.S., Altfield, M., Poon, S.H., Phillips, M.N., Wilkes, B., Eldridge, R.L., Robbins, G.K., D'Aquila, R.D., Goulder, P.J.R., Walker, B.D., 2000. Immune control of HIV-1 after early treatment of acute infection. Nature 407, 523–526.Google Scholar
  25. Schneider, H., 1986. Truncated and Censored Samples from Normal Populations. Marcel Dekker, New York.MATHGoogle Scholar
  26. Wodarz, D., Nowak, M.A., 1999. Specific therapy regimes could lead to long-term immunological control of HIV. Proc. Natl. Acad. Sci. 96(25), 14464–14469.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • B. M. Adams
    • 1
  • H. T. Banks
    • 1
  • M. Davidian
    • 1
  • E. S. Rosenberg
    • 2
  1. 1.Center for Research in Scientific ComputationNorth Carolina State UniversityRaleighUSA
  2. 2.I.D. Unit—Gray 5Massachusetts General Hospital and Harvard Medical SchoolBostonUSA

Personalised recommendations