zbMATH — the first resource for mathematics

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials. (English) Zbl 1059.62735
Summary: We introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J02 General nonlinear regression
Full Text: DOI
[1] Anderson, Compartmental Modeling and Tracer Kinetics, Lecture Notes in Biomathematics (1983) · doi:10.1007/978-3-642-51861-4
[2] Anderson, Cell to Cell Signaling: From Experiments to Theoretical Models pp 335– (1989) · doi:10.1016/B978-0-12-287960-9.50031-9
[3] Bonhoeffer, Human immunodeficiency virus drug therapy and virus load, Journal of Virology 71 pp 3275– (1997) · Zbl 0883.92017
[4] Davidian, Nonlinear Models for Repeated Measurement Data (1995)
[5] Boer, Anti-CD4 therapy for AIDS suggested by mathematical models, Proceedings of the Royal Society of London, Series B 263 pp 899– (1996) · doi:10.1098/rspb.1996.0133
[6] Godfrey, Compartmental Models and Their Application (1983)
[7] Herz, Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay, Proceedings of the National Academy of Science USA 93 pp 7247– (1996) · doi:10.1073/pnas.93.14.7247
[8] Ho, Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection, Nature 373 pp 123– (1995) · doi:10.1038/373123a0
[9] Kirschner, Using mathematics to understand HIV immune dynamics, Notices of the American Medical Society 43 pp 191– (1996)
[10] Kirschner, Mathematical Population Dynamics: Analysis of Heterogeneity, Volume 1, Theory of Epidemics pp 295– (1995)
[11] Lindstrom, Nonlinear mixed effects models for repeated measures data, Biometrics 46 pp 673– (1990) · doi:10.2307/2532087
[12] Merrill, Theoretical Immunology pp 59– (1987)
[13] Nowak, Population dynamics of immune responses to persistent viruses, Science 272 pp 74– (1996) · doi:10.1126/science.272.5258.74
[14] Perelson, Mathematical and Statistical Approaches to AIDS Epidemiology, Volume 83, Lecture Notes in Biomathematics pp 350– (1989) · doi:10.1007/978-3-642-93454-4_17
[15] Perelson, Dynamics of HIV infection of CD4+ T cells, Mathematical Biosciences 114 pp 81– (1993) · Zbl 0796.92016 · doi:10.1016/0025-5564(93)90043-A
[16] Perelson, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science 271 pp 1582– (1996) · doi:10.1126/science.271.5255.1582
[17] Perelson, Decay characteristics of HIV-1-infected compartments during combination therapy, Nature 387 pp 188– (1997) · doi:10.1038/387188a0
[18] Phillips, Reduction of HIV concentration during acute infection: Independence from a specific immune response, Science 271 pp 497– (1996) · doi:10.1126/science.271.5248.497
[19] Pinheiro, Mixed-Effects Models Methods and Classes for S and Splus (1995)
[20] Ratkowsky, Nonlinear Regression Modeling, A Unified Practical Approach (1983)
[21] Ratkowsky, Handbook of Nonlinear Regression Models (1990) · Zbl 0705.62060
[22] Roe, Comparison of population pharmacokinetic modeling methods using simulated data: Results from the population modeling workgroup, Statistics in Medicine 16 pp 1241– (1997) · doi:10.1002/(SICI)1097-0258(19970615)16:11<1241::AID-SIM527>3.0.CO;2-C
[23] Schenzle, A model for AIDS pathogenesis, Statistics in Medicine 13 pp 2067– (1994) · doi:10.1002/sim.4780131916
[24] Tan, Stochastic modeling of the dynamics of CD4+ T cell infection by HIV and some Monte Carlo studies, Mathematical Biosciences 147 pp 173– (1998) · Zbl 0887.92021 · doi:10.1016/S0025-5564(97)00094-1
[25] Liew, Method of exponential peeling, Journal of Theoretical Biology 16 pp 43– (1967)
[26] Wei, Viral dynamics in human immunodeficiency virus type 1 infection, Nature 373 pp 117– (1995) · doi:10.1038/373117a0
[27] Wu , H. Kuritzkes , D. R. Clair , M. S. et al. 1997 Interpatient variation of viral dynamics in HIV-1 infection: Modeling results of AIDS Clinical Trials Group Protocol 315. The First International Workshop on HIV Drug Resistance, Treatment Strategies and Eradication
[28] WU, Estimation of HIV dynamic parameters, Statistics in Medicine 17 pp 2463– (1998a) · doi:10.1002/(SICI)1097-0258(19981115)17:21<2463::AID-SIM939>3.0.CO;2-A
[29] Wu, Characterizing individual and population viral dynamics in HIV-1-infected patients with potent antiretroviral therapy: Correlations with host-specific factors and virological endpoints, The 12th World AIDS Conference. Geneva (1998b)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.