Volume 9 Supplement 1
Quantifying the treatment efficacy of reverse transcriptase inhibitors: new analyses of clinical data based on within-host modeling
© Breban et al; licensee BioMed Central Ltd. 2009
Published: 18 November 2009
Current measures of the clinical efficacy of antiretroviral therapy (ART) in the treatment of HIV include the change in HIV RNA in the plasma and the gain in CD4 cells.
We propose new measures for evaluating the efficacy of treatment that is based upon combinations of non-nucleoside and nucleoside reverse transcriptase inhibitors. Our efficacy measures are: the CD4 gain per virion eliminated, the potential of CD4 count restoration and the viral reproduction number (R 0 ). These efficacy measures are based upon a theoretical understanding of the impact of treatment on both viral dynamics and the immune reconstitution. Patient data were obtained from longitudinal HIV clinical cohorts.
We found that the CD4 cell gain per virion eliminatedranged from 10-2 to 600 CD4 cells/virion, the potential of CD4 count restorationranged from 60 to 1520 CD4 cells/μl, and the basic reproduction number was reduced from an average of 5.1 before therapy to an average of 1.2 after one year of therapy. There was substantial heterogeneity in these efficacy measures among patients with detectable viral replication. We found that many patients who achieved viral suppression did not have high CD4 cell recovery profiles. Our efficacy measures also enabled us to identify a subgroup of patients who were not virally suppressed but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen.
We show that our new efficacy measures are useful for analyzing the long-term treatment efficacy of combination reverse transcriptase inhibitors and argue that achieving a low R 0 does not imply achieving viral suppression.
With currently available combination antiretroviral therapy (ART), the majority of patients achieve viral suppression within 24 weeks of initiation . We hypothesize that further characterization of ART outcomes could differentiate among the vast majority of patients who achieve viral suppression but do not reach the immunologic reconstitution that matches their reduction in viral replication. Such characterizations may help further refine the guidelines for monitoring ART response.
Within-host HIV modeling has been a cornerstone for understanding HIV dynamics. Within this modeling paradigm, every patient is described by a set of fixed immune and viral parameters. The dynamics of HIV infection take place on two different timescales: fast viral and CD4 cell population dynamics that change on the timescale of months, and slower dynamics on the timescale of years that describe the decay of the patient's immune system. For the past decade, a vast amount of modeling work has been dedicated to understanding the interaction between the human immune system and HIV. Studies have been devoted to fitting models to within-host data and building models to provide both quantitative and qualitative answers. The principles of the within-host HIV fast dynamics are now relatively well-understood [2–6]. Further developments have focused on incorporating other elements of interaction between HIV and the immune system, such as cytotoxic T lymphocytes [4, 7–9] and latently infected T cells [10–13].
Much effort has also been devoted to modeling the impact of treatment on the within-host HIV infection [2–4, 14–26]. Major topics have been optimizing treatment for viral load reduction and CD4 increase [18–20], HIV drug resistance [15, 16, 24–26], adherence to therapy [15, 16, 20], structured treatment interruptions [21–23] and others. However, clinical applications of the understanding of fast dynamics have been limited because the necessary analyses, based upon these models, require detailed data that are difficult to obtain in large amounts from clinical trials or routine clinical care.
Here, we show how a mathematical model can be used to characterize a patient's response to a common ART regimen, the combination of nucleoside plus non-nucleoside reverse transcriptase inhibitors (NRTI/NNRTI). We use our model and novel data analysis techniques to analyze data from large longitudinal HIV clinical cohorts in order to characterize treatment efficacy. We quantify treatment efficacy by developing new surrogate markers for measuring ART outcomes. Specifically, we quantify the pace of immune destruction and the impact of therapy on the viral reproduction number. We discuss the implications of our analyses for clinical decision making.
Materials and methods
Patients and sampling
We analyzed data from a random group of 83 ART naïve patients receiving initial treatment with a NNRTI/NRTI regimen. Each patient had viral load and CD4 counts measured both before treatment and after approximately one year of treatment. Data were collected through the San Francisco General Hospital AIDS Program Database that was contained in the Healthcare Electronic Record Organizer (HERO) and from the UNC CFAR HIV Clinical Cohort Study. We defined the threshold of viral suppression to be 400 HIV RNA copies/ml.
where X denotes the number of uninfected CD4 cells, Y denotes the number of infected CD4 cells and V denotes the infectious viral load. The parameters are as follows: β is the infectiousness of the HIV virus, 1/δ is the average lifetime of uninfected CD4 cells, 1/α is the average lifetime of infected CD4 cells, and σ is the ratio between viral load and the infected CD4 cells that we assumed to be constant. Our assumption is justified by the fact that the average lifetime of the virus in the blood is significantly shorter than either 1/α or 1/δ . Thus, model (1) represents a good description of the within-host dynamics at timescales larger than the average lifetime of the virus, but smaller than the timescale of the destruction of the immune system. All the parameters in the model [equation (1)] given for a certain patient are expected to change only slowly with time, due to the slow destruction of the patient's immune system on the timescale of 10-15 years. We considered the model (1) for the interval of time of one to two years, so that the model's assumptions would hold. Such models of HIV dynamics have been previously used by Bonhoeffer and others [6, 27]. The model is reduced to two dimensions when the third equation is used to replace the free-virus variable in the ordinary differential equations (ODEs) and express them only in terms of infected and uninfected CD4 cell populations. This approach has helped understand the foundations of HIV within-host dynamics [6, 27]. However, the ODEs expressed in the CD4 population variables are difficult to interface with patient-specific clinical data that typically provide only the total CD4 count (C = X+Y) and the viral load (V) of the patient.
Equation (4) is independent of β, and describes the viral set-points that are reached during various NNRTI/NRTI regimens corresponding to various values of β.
Since equation (4) is linear, knowledge of the endemic equilibrium (i.e., the viral set-point) of a patient before treatment and during a particular NNRTI/NRTI treatment is enough to predict the patient's response to all NNRTI/NRTI treatments. Our model assumes that drug-naïve patients do not develop drug resistance before reaching their viral set-points during therapy. This assumption is reasonable since most patients reach their new viral set-point within one year of therapy . Figure 2 of  shows clinical trial data on how the CD4 count varies with time under various NNRTI/NRTI regimens. The featured variation approaches a plateau after approximately one year of treatment. Analysis of the HIV RNA count is less reliable, as HIV patients become virally suppressed and their viral load is hard to measure accurately. It is important to note that our model can cope with certain patterns of slight non-adherence that do not accelerate the development of drug resistance [15, 16]; non-adherence can be modeled by using an effective parameter β that is higher than the β value of the completely adherent patient.
Here, we accounted for the fact that infected and uninfected CD4 cells have different lifetimes and obtained a small correction to this formula. It may be argued that, in general, R0 AM represents the bulk of the numerical estimate of R0 for many models where additional factors (e.g., different lifetimes for infected and uninfected CD4 cells, latently infected cell populations, preferential infection of activated and HIV-specific T cells [11–13, 32–34]) bring relatively small corrections. Thus, equation (9) acquires a special status of generality and great practical importance. To estimate patient-specific R0 values, we used equation (9) where the second term in the expansion over δ/α represented an estimate of the modeling error.
(Note that s is always negative.)
Analyzing equations (10) and (12), we obtain that, depending on his/her measures of NNRTI/NRTI treatment efficacy i and s, and the potency of the regimen, a patient may achieve both viral suppression and low R0, one or neither of these conditions. In particular, when
R0* < 1/[1+V s /(i/s)]: The patient may not have a low R0, yet achieve viral suppression for some NNRTI/NRTI treatment regimens.
1/[1+V s /(i/s)] <R0*: The patient may not be virally suppressed, yet have a low R0 for some NNRTI/NRTI treatment regimens.
which divides the (i, |s|) space in the two regions specified above. (For V s = 400 HIV RNA copies/ml and R0* = 1.1, we obtain [V s /(1-1/R0*)] = 4400 HIV RNA copies/ml. Regions 1) and 2) are to the left and to the right of the dotted green curve in Figure 2, respectively.)
We emphasize that all patients are able to achieve both viral suppression and a low R0, provided that the NNRTI/NRTI treatment regimen is potent enough. The situations described above may occur for NNRTI/NRTI treatment regimens of intermediate strength.
For a better illustration of the values that we found for our efficacy measures, we graphed the potential for CD4 count reconstitution versus the CD4 gain per virion eliminated; see Figure 2. A fair amount of correlation is observed between the potential for CD4 count reconstitution and the logarithm of the CD4 gain per virion eliminated (Pearson correlation coefficient ~0.675). Patients could be divided into four categories: (a) patients with a potential for both a high CD4 count reconstitution and a high CD4 gain per virion eliminated, (b) patients with a potential for only a low CD4 count reconstitution but a high CD4 gain per virion eliminated, (c) patients with a potential for a high CD4 count reconstitution but only a low CD4 gain per virion eliminated, and (d) patients with a potential for only a low CD4 count reconstitution and a low CD4 gain per virion eliminated. Surprisingly, many patients who attained viral suppression did not have high CD4 cell recovery profiles (the blue dots in the regions (b) and (d) of Figure 2). The other data (red dots) in Figure 2 also show substantial heterogeneity in our efficacy measures among the patients who were not virally suppressed. The red points are spread throughout the plane of potential of CD4 count reconstitution - CD4 gain per virion eliminated. This spread indicates that our new efficacy measures are not correlated with viral suppression. Most importantly, Figure 2 also shows that there was a subgroup of patients who were not virally suppressed but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen (the red dots in region (a)).
Our results also imply that NNRTI/NRTI treatment regimens can have substantial impact on reducing viral dynamics (i.e., the R0) and that this effect can occur even in patients who do not seem to be responding well to treatment. This paradoxical situation may occur for individuals who have low CD4 gain per virion eliminated and high potential of CD4 count reconstitution. In particular, it is possible that, due to treatment, a patient does not reach viral suppression yet his/her CD4 count very much approaches his/her potential of CD4 count reconstitution, implying an R0 close to 1. Using our model, we predict that patients with NNRTI/NRTI treatment efficacy measures in the region which is to the left of the dotted green curve in Figure 2 may have an R0 close to 1 yet will nevertheless not reach viral suppression. The patients with treatment efficacy measures in the complementary region may achieve viral suppression yet maintain a high R0 which places them far from the elimination of the infection. In our case, all patients that become virally suppressed reach a low R0 (Figure 3(a), blue dots in Figure 2). However, we identify a group of 12 patients that do not become virally suppressed although they reach a low R0 and reduced viral dynamics (Figure 3(b)). All of them are placed to the left of the dotted curve in Figure 2.
We restricted our analyses to patients receiving the common ART combination of nucleoside plus non-nucleoside reverse transcriptase inhibitors. We concentrated on this treatment regimen for two major reasons. Firstly, NRTI plus NNRTI regimens are likely to remain popular as first-line therapy because of their demonstrated efficacy, simplicity of therapy, pill number and tolerability . Secondly, NNRTI/NRTI therapy is likely to remain the dominant regimen for first-line therapy in resource-constrained countries. Among the 42 antiretroviral products whose price the Clinton foundation negotiated for resource-constrained countries only two contain PIs . There are 71 countries (including the vast majority of sub-Saharan countries) that can now benefit from this negotiation, representing more than 92% of the people living with HIV globally [36, 37]. It is important to note that, as a general trend, PIs are likely to remain prohibitively expensive for resource-constrained countries in the short term . In fact, in their third annual report on the current rollout of treatment in Africa, PEPFAR cautions against poor management of first-line NNRTI/NRTI treatment regimens that would require an early introduction of more costly PI-based second-line regimens . PEPFAR reports that only 10% of the treatment regimens that they currently sponsor in Africa are second line . Therefore, it is expected that NNRTI/NRTI treatment regimens will remain the first and most important line of defense against the HIV pandemic in resource-constrained settings.
The need for developing new accurate and reliable surrogate markers for evaluating the clinical efficacy of antiretroviral agents has become a major focus of HIV clinical care. Surrogate markers have been used by regulatory agencies to approve new agents, by consensus panels to develop clinical guidelines and by investigators to determine clinical efficacy. In this paper, we have presented new methodologies for generating surrogate marker data in order to quantify new measures of treatment efficacy. Unlike previous efficacy measures, our efficacy measures are based upon a theoretical understanding of the impact of treatment on both viral dynamics and the immune response. We have shown that our methodology can be used to analyze data collected during routine clinical care. The advantage of our surrogate markers for measuring treatment efficacy is that they are patient-specific in contrast to the surrogate markers that have been developed previously from aggregate clinical trial data. Thus, we found that two of our surrogate markers have a moderate degree of correlation indicating that a low CD4 gain per virion eliminated may be associated with a low potential for CD4 count reconstitution. We have also developed for the first time a methodology for calculating patient-specific R0 estimates and used these values to quantify the efficacy of the NNRTI/NRTI treatment therapy. Thus, we showed that achieving a low R0 does not imply achieving viral suppression. Our new efficacy measures have also shown two important new results that have significant clinical implications. Our efficacy measures enabled us to identify a subgroup of patients who achieved viral suppression, but did not have a high likelihood of achieving a high CD4 cell count. Most importantly, our efficacy measures enabled us to identify a subgroup of patients who were not virally suppressed, but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen.
Based upon a theoretical understanding of the impact of HIV treatment on viral dynamics and immune reconstitution, we propose new measures for evaluating the efficacy of treatment with reverse transcriptase inhibitors. Our efficacy measures are: the CD4 gain per virion eliminated, the potential of CD4 count restoration and the viral reproduction number (R0). We show that our new efficacy measures are useful for analyzing the long-term treatment efficacy of combination reverse transcriptase inhibitors and argue that achieving a low R0 does not imply achieving viral suppression.
The authors thank Bernard Shields for assistance with the data. SB and RB gratefully acknowledge financial support from NIH/NIAID (RO1 AI041935). SN gratefully acknowledges financial support from the UNC-CFAR program sponsored by NIH (P30 AI50410). JK gratefully acknowledges financial support from NIH (K24MH064384). SB, SN and RB thank Myron Cohen for discussions during the course of this research. SB thanks Timothy Pylko for discussions during the course of this research. The authors are grateful to two anonymous referees for helpful comments.
This article has been published as part of BMC Public Health Volume 9 Supplement 1, 2009: The OptAIDS project: towards global halting of HIV/AIDS. The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2458/9?issue=S1.
- Hammer SM, Eron JJ, Reiss P, Schooley RT, Thompson MA, Walmsley S, Cahn P, Fischl MA, Gatell JM, Hirsch MS, et al: Antiretroviral treatment of adult HIV infection: 2008 recommendations of the International AIDS Society-USA panel. JAMA. 2008, 300 (5): 555-570. 10.1001/jama.300.5.555.View ArticlePubMedGoogle Scholar
- Perelson AS: Modelling viral and immune system dynamics. Nat Rev Immuniol. 2002, 2: 28-36. 10.1038/nri700.View ArticleGoogle Scholar
- Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD: HIV-1 Dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science. 1996, 271: 1582-1586. 10.1126/science.271.5255.1582.View ArticlePubMedGoogle Scholar
- Nowak MA, Robert MM: Virus dynamics: mathematical principles of immunology and virology. 2000, Oxford: Oxford University PressGoogle Scholar
- Bonhoeffer S, May RM, Shaw GM, Nowak MA: Virus dynamics of immune responses to persistent viruses. Proc Natl Acad Sci USA. 1997, 94: 6971-6976. 10.1073/pnas.94.13.6971.PubMed CentralView ArticlePubMedGoogle Scholar
- Bonhoeffer S, Coffin J, Nowak MA: Human immunodeficiency virus drug therapy and viral load. J Virol. 1997, 71 (4): 3275-3278.PubMed CentralPubMedGoogle Scholar
- Althaus CL, De Boer RJ: Dynamics of immune escape during HIV/SIV infection. PLoS Comput Biol. 2008, 4 (7): e1000103-10.1371/journal.pcbi.1000103.PubMed CentralView ArticlePubMedGoogle Scholar
- Wodarz D: Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology. 2006, New York: Springer VerlagGoogle Scholar
- Yao W, Hertel L, Wahl LM: Dynamics of recurrent viral infection. Proc Biol Sci. 2006, 273 (1598): 2193-2199. 10.1098/rspb.2006.3563.PubMed CentralView ArticlePubMedGoogle Scholar
- Rong L, Perelson AS: Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips. Math Biosci. 2008Google Scholar
- Perelson AS, Kirschner DE, Deboer R: Dynamics of HIV-Infection of Cd4+ T-cells. Math Biosci. 1993, 114 (1): 81-125. 10.1016/0025-5564(93)90043-A.View ArticlePubMedGoogle Scholar
- Krakauer DC, Nowak M: T-cell induced pathogenesis in HIV: bystander effects and latent infection. Proc R Soc Lond B Biol Sci. 1999, 266 (1423): 1069-1075. 10.1098/rspb.1999.0745.View ArticleGoogle Scholar
- Culshaw RV, Ruan SG: A delay-differential equation model of HIV infection of CD4(+) T-cells. Math Biosci. 2000, 165 (1): 27-39. 10.1016/S0025-5564(00)00006-7.View ArticlePubMedGoogle Scholar
- Bonhoeffer S, May RM, Shaw GM, Nowak MA: Virus dynamics and drug therapy. Proc Natl Acad Sci USA. 1997, 94: 6971-6976. 10.1073/pnas.94.13.6971.PubMed CentralView ArticlePubMedGoogle Scholar
- Smith RJ: Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges?. Proc R Soc B. 2006, 273 (1586): 617-624. 10.1098/rspb.2005.3352.PubMed CentralView ArticlePubMedGoogle Scholar
- Wahl LM, Nowak MA: Adherence and drug resistance: predictions for therapy outcome. Proc R Soc Lond B Biol Sci. 2000, 267 (1445): 835-843. 10.1098/rspb.2000.1079.View ArticleGoogle Scholar
- Austin DJ, White NJ, Anderson RM: The dynamics of drug action on the within-host population growth of infectious agents: melding pharmacokinetics with pathogen population dynamics. J Theor Biol. 1998, 194: 313-339. 10.1006/jtbi.1997.0438.View ArticlePubMedGoogle Scholar
- Caetano MA, Yoneyama T: Short and long period optimization of drug doses in the treatment of AIDS. An Acad Bras Cienc. 2002, 74 (3): 379-392.View ArticlePubMedGoogle Scholar
- Castiglione F, Pappalardo F, Bernaschi M, Motta S: Optimization of HAART with genetic algorithms and agent-based models of HIV infection. Bioinformatics. 2007, 23 (24): 3350-3355. 10.1093/bioinformatics/btm408.View ArticlePubMedGoogle Scholar
- Krakovska O, Wahl LM: Optimal drug treatment regimens for HIV depend on adherence. J Theor Biol. 2007, 246 (3): 499-509. 10.1016/j.jtbi.2006.12.038.View ArticlePubMedGoogle Scholar
- Breban R, Blower S: Role of parametric resonance in virological failure during HIV treatment interruption therapy. Lancet. 2006, 367 (9518): 1285-1289. 10.1016/S0140-6736(06)68543-7.View ArticlePubMedGoogle Scholar
- Dorman KS, Kaplan AH, Lange K, Sinsheimer JS: Mutation takes no vacation: can structured treatment interruptions increase the risk of drug-resistant HIV-1?. J Acquir Immune Defic Syndr. 2000, 25 (5): 398-402. 10.1097/00042560-200012150-00003.View ArticlePubMedGoogle Scholar
- Krakovska O, Wahl LM: Drug-sparing regimens for HIV combination therapy: benefits predicted for "drug coasting". Bull Math Biol. 2007, 69 (8): 2627-2647. 10.1007/s11538-007-9234-9.View ArticlePubMedGoogle Scholar
- Wodarz D, Lloyd AL: Immune responses and the emergence of drug-resistant virus strains in vivo. Proc Biol Sci. 2004, 271 (1544): 1101-1109. 10.1098/rspb.2003.2664.PubMed CentralView ArticlePubMedGoogle Scholar
- Smith RJ, Wahl LM: Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects. Bull Math Biol. 2005, 67 (4): 783-813. 10.1016/j.bulm.2004.10.004.View ArticlePubMedGoogle Scholar
- Wu H, Huang Y, Acosta EP, Rosenkranz SL, Kuritzkes DR, Eron JJ, Perelson AS, Gerber JG: Modeling long-term HIV dynamics and antiretroviral response: effects of drug potency, pharmacokinetics, adherence, and drugresistance. J Acquir Immune Defic Syndr. 2005, 39 (3): 272-283. 10.1097/01.qai.0000165907.04710.da.View ArticlePubMedGoogle Scholar
- Bonhoeffer S, Funk G, Gunthard H, Fischer M, Muller V: Glancing behind virus load variation in HIV-1 infection. TRENDS in Microbiology. 2003, 11 (11): 499-504. 10.1016/j.tim.2003.09.002.View ArticlePubMedGoogle Scholar
- Staszewski S, Morales-Ramirez J, Tashima KT, Rachlis A, Skies D, Stanford J, Stryker R, Johnson P, Labriola DF, Farina D, et al: Efavirenz plus zidovudine and lamivudine, evafirenz plus indinavir, and indinavir plus zidovudine and lamivudine in the treatment of HIV-1 infection in adults. N Engl J Med. 1999, 341 (25): 1865-1872. 10.1056/NEJM199912163412501.View ArticlePubMedGoogle Scholar
- Anderson RM, May RM: Infectious diseases of humans. 1992, Oxford: Oxford University PressGoogle Scholar
- Ball F, Donnelly P: Strong approximations for epidemic models. Stochastic Processes and Applications. 1995, 55: 1-21. 10.1016/0304-4149(94)00034-Q.View ArticleGoogle Scholar
- Mode C, Sleeman C: Stochastic Processes in Epidemiology. 2003, Singapore: World ScientificGoogle Scholar
- Tuckwell HC, Wan FYM: Nature of equilibria and effects of drug treatments in some simple viral population dynamical models. IMA J Math Appl Med Biol. 2000, 17 (4): 311-327. 10.1093/imammb/17.4.311.View ArticlePubMedGoogle Scholar
- Funk GA, Fischer M, Joos B, Opravil M, Gunthard HF, Ledergerber B, Bonhoeffer S: Quantification of in vivo replicative capacity of HIV-1 in different compartments of infected cells. J Acquir Immune Defic Syndr. 2001, 26 (5): 397-404.View ArticlePubMedGoogle Scholar
- Heffernan JM, Wahl LM: Improving estimates of the basic reproductive ratio: Using both the mean and the dispersal of transition times. Theor Pop Biol. 2006, 70 (2): 135-145. 10.1016/j.tpb.2006.03.003.View ArticleGoogle Scholar
- Antiretroviral price list. 2008, Clinton Foundation HIV/AIDS Initiative
- Clinton Foundation HIV/AIDS Initiative. [http://www.clintonfoundation.org/what-we-do/clinton-hiv-aids-initiative]
- Procurement Consortium List (September 2008). Clinton HIV/AIDS Initiative. 2008
- Untangling the web of antiretroviral price reductions, 11 edn. Médecins Sans Frontières. 2008
- The power of partnerships: The president's emergency plan for AIDS relief (PEPFAR). Office of the United States Global AIDS Coordinator. 2007
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