Skip to main content

Advertisement

Log in

Estimation and Prediction With HIV-Treatment Interruption Data

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adams, B.M., 2005. Non-parametric parameter estimation and clinical data fitting with a model of HIV Infection. PhD Thesis, NC State University, Raleigh.

  • 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 

  • 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.

  • 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.

    MATH  Google Scholar 

  • Aitkin, M., 1981. A note on the regression analysis of censored data. Technometrics 23, 161–163.

    Article  Google Scholar 

  • 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.

  • Banks, H.T., Kunisch, K., 1989. Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Callaway, D.S., Perelson, A.S., 2002. HIV-1 infection and low steady state viral loads. Bull. Math. Biol. 64(1), 29–64.

    Article  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • 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.

  • 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 

  • Kalbfleisch, J.P., Prentice, R.L., 2002. The Statistical Analysis of Failure Time Data. Wiley, New York.

    MATH  Google Scholar 

  • 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 

  • Kelley, C.T., 1999. Iterative methods for optimization. In: Frontiers in Applied Mathematics FR18. SIAM, Philadelphia.

  • Klein, J.P., Moeschberger, M.L., 2003. Survival Analysis: Techniques for Censored and Truncated Data. Springer, New York.

    MATH  Google Scholar 

  • 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 

  • Lori, F., Lisziewicz, J., 2001. Structured treatment interruptions for the management of HIV infection. J. Am. Med. Assoc. 4286(23), 2981–2987.

    Article  Google Scholar 

  • McLachlan, G.J., Krishnan, T., 1997. The EM Algorithm and Extensions. Wiley, New York.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics of immune responses to persistent viruses. Science 272, 74–79.

    Article  Google Scholar 

  • Perelson, A.S., Nelson, P.W., 1999. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41(1), 3–44.

    Article  MATH  Google Scholar 

  • 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 

  • Schneider, H., 1986. Truncated and Censored Samples from Normal Populations. Marcel Dekker, New York.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. T. Banks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adams, B.M., Banks, H.T., Davidian, M. et al. Estimation and Prediction With HIV-Treatment Interruption Data. Bull. Math. Biol. 69, 563–584 (2007). https://doi.org/10.1007/s11538-006-9140-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-006-9140-6

Keywords

Navigation