Available clinical markers of treatment outcome integrated in mathematical models to guide therapy in HIV infection

Elisabeta Vergu*, Alain Mallet and Jean-Louis Golmard

INSERM U436, Mathematical and Statistical Modelling in Biology and Medicine, CHU Pitié-Salpêtrière, Paris, France


    Abstract
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
Because treatment failure in many HIV-infected persons may be due to multiple causes, including resistance to antiretroviral agents, it is important to better tailor drug therapy to individual patients. This improvement requires the prediction of treatment outcome from baseline immunological or virological factors, and from results of resistance tests. Here, we review briefly the available clinical factors that have an impact on therapy outcome, and discuss the role of a predictive modelling approach integrating these factors proposed in a previous work. Mathematical and statistical models could become essential tools to address questions that are difficult to study clinically and experimentally, thereby guiding decisions in the choice of individualized drug regimens.

Keywords: resistance tests, modelling, therapy outcome


    Introduction
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
Despite the great progress made in strategies to treat HIV infection, antiretroviral combination therapy is not effective in all patients, often failing to control viral replication. The causes of this failure are multiple, and may differ according to its timing and profile: we could cite incomplete adherence, in particular at the initiation of therapy, pharmacokinetic and pharmacodynamic factors (e.g. drug half-life, drug–drug interactions, variable drug metabolism), hepatic impairment due to co-infections1 and eventual development of drug resistance, considered as the main problem in the fight to maintain the control of viral infection. One strategy to overcome the problem of generation of resistant strains by mutation is to adapt the therapy to each infected individual. The use of individualized treatment design necessitates the prediction of its outcome by taking into account baseline immunological or virological factors (CD4 and CD8 cell counts, viral load) and characteristics of virus–patient interactions. The role of these markers in disease progression was illustrated in numerous studies based on clinical data, reviewed below. Unfortunately, all questions raised by therapy failure (such as ‘what is the potential impact of undetectable resistant strains present at treatment onset?’, ‘what are the elements to evaluate when choosing a combination of drugs?’, etc.) cannot be addressed by clinical experience only. In this context, mathematical models could be particularly useful. The modelling approach we have proposed,2 discussed in the final section here, addresses the implications of virus resistance in treatment outcome, the validation of predictive models and their use in therapeutic decision making.


    CD4 and CD8 levels as predictors of therapy outcome
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
In the evaluation of treatment response, attention initially focused on the HIV-1 RNA level, analysing only the virological response. Later, clinicians also examined the role of immunological baseline markers in clinical response to therapy. Several studies pointed out the role of CD4 cell count as an important determinant of virological and immunological outcome. Sterling et al.3 performed an observational cohort study: 530 patients initiating highly active antiretroviral therapy (HAART) were compared with 484 patients who did not receive HAART. A Cox multivariate proportional hazards model allowed the authors to demonstrate that, based on an average of 22 months of follow-up, CD4 lymphocyte counts were better than HIV-1 RNA levels at predicting disease progression. Grabar et al.4 showed in a study of a cohort of 2236 HIV-infected patients that patterns of early immunological and virological responses (after 6 months of HAART), even discordant, are predictive of clinical outcome at 24 months. Deeks5 illustrates by several examples of clinical trials the importance of baseline CD4 cell count as a predictor of HAART outcome, explaining this feature by the ability of the immune system to recognize and suppress viral replication. According to a recent report presented at the XIVth International AIDS Conference6 and to a subsequent, more detailed paper7 summarizing results of 13 cohort studies conducted in Europe and North America including 12 574 patients under triple therapy, the baseline CD4 count again emerged as the strongest predictive factor at 3 years of therapy. This last quoted prospective analysis is all the more interesting since proposed predictive models were stratified on CD4 cell count. The authors stress the fact that, in the era of HAART, CD4 cell count is an important prognostic factor for patients who start therapy with <=200 cells/mm3, but differences are small in patients with a baseline CD4 cell count above this threshold. Therefore, supplementary information needs to be taken into account to determine the optimum time for starting HAART. Another immunological marker, CD8 T lymphocyte count, is particularly involved in the control of viral replication in early HIV infection.8 CD38 expression on CD8 T cells was identified as a strong predictive marker of AIDS in patients in both early and late stages of infection.9 In a study including HIV-1-infected patients with CD4 cell count <=100 cells/mm3 and never exposed to protease inhibitors, Macias et al.10 showed that CD8 cell count was an independent predictor of survival. It is not fully established whether the number of circulating CD8 T cells is a significant independent predictor of disease progression in all cases (whatever the immunological baseline state and number of prior regimens may be), but recent progress made in quantifying HIV-specific CD8 T cells could help to clarify their role.11


    Resistance characteristics of viral strains as predictors of therapy outcome
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
The second category of markers used in the prediction of antiretroviral treatment outcome and in the further management of patients are resistance characteristics of viral strains. Drug resistance is conferred by single or several amino acid changes in antiviral target enzymes. The information (synthesized in parameters quantifying the reduced susceptibility to a drug) is obtained by resistance tests involving the identification of the genotype or the phenotype of a virus. Genotypic assays are techniques that determine the nucleotide sequence of specific genes by full-length sequencing or by point mutation assays. Phenotypic testing determines the susceptibility of virus to antivirals in culture, assays expressed as the drug concentrations inhibiting virus growth by 50% or 90% (IC50, IC90). Even though resistance testing is becoming an integral part of antiretroviral drug development and clinical practice, limitations associated with these tests, especially concerning the identification of quasispecies within each individual and thresholds of detection, necessitate the evaluation of the clinical utility of these tests. The relationship between baseline HIV drug resistance and response to antiretroviral therapy has been analysed in retrospective and prospective studies. In retrospective studies the objective is to assess the value of resistance assays in the prediction of the virological response to a new antiretroviral regimen (selected using other factors) after failure of a previous therapy. In contrast, the aim of prospective studies is to evaluate the improvement in the ability to choose the best adapted new regimen for each individual when information provided by resistance tests is added to other classic clinical factors, such as baseline CD4 cell count and viral load, antiretroviral history, etc.

Several review papers1214 summarize some of these retrospective and prospective studies. In a recent work, Torre & Tambini15 performed a meta-analysis of six published randomized controlled trials to estimate the impact of resistance-guided antiretroviral therapy on virological outcome by comparison with patients based on standard of care. Their results supported the use of genotypic testing followed by expert interpretation. Two retrospective studies quoted by Haubrich & Demeter,14 including patients receiving ritonavir/saquinavir therapy, have shown that response to antiretroviral therapy can be predicted based on genotypic patterns, baseline genotypic resistance being correlated with virological failure. In other retrospective analyses it has emerged clearly that phenotypic drug susceptibility predicts sustained viral load suppression, particularly when virus remains susceptible to two or three drugs at the initiation of therapy. All these reanalysed studies underline the importance of genotype and phenotype testing as predictors of virological failure. However, they do not evaluate the utility of resistance assays in clinical care, the appropriate method to estimate this impact being a prospective evaluation. Hence, prospective studies have been performed. VIRADAPT, a prospective, non-blinded, randomized, controlled study of patients with a first antiretroviral therapy failure, has shown greater reduction in viral load over 6 months when the treatment was guided by genotype resistance testing. The improvement in viral suppression in groups treated based on genotypic testing compared with empirical treatment assignment has also been stressed by the GART trial, another randomized study including patients after a first triple-drug therapy failure. Phenotypic testing was explored in an open-label randomized comparison with standard of care management in patients whose first drug regimen failed. After 16 weeks, change in viral load was significantly greater in the phenotype group. The suggestion inspired by this study was in agreement with those of analysis using genotypic testing: significant improvement in short-term virological outcomes may be obtained when the selection of the new regimen is guided by phenotypic testing in patients whose previous therapy failed. However, phenotypic testing is clearly more time-consuming and, in many cases, more difficult to interpret than genotypic testing.

Retrospective and prospective studies re-analysed by DeGruttola et al.12 using a standardized data analysis plan pointed out the fact that cumulative susceptibility scores (such as GSS, genotypic susceptibility score, and PSS, phenotypic susceptibility score) containing summarized complex information could be used in clinical management of patients. However, the authors stress the importance of improving the accuracy of these scores and the need to use standard analytical methods when analysing data. Indeed, all the studies quoted above claim the interest of using resistance tests, but further investigations are necessary in order to eliminate their intervariability due to the quality of interpretation, the number of prior regimens and the quality of standard of care decisions.

Several questions persist (currently submitted to expert interpretation) regarding the clinical use of resistance testing to monitor antiretroviral therapy. Do strains present at undetectable levels at the initiation of the therapy contribute to therapy outcome? How can the use of resistance test results be optimized when making a therapeutic decision?


    A model-based approach for the prediction of therapy outcome
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
Our previous study2 proposed a regression model that can be useful in the management of individual treatment tailoring. In this work we have focused on the aspect of viral resistance as cause of therapy failure.

First, we simulated a cohort of HIV-infected patients using a dynamic model describing the interactions illustrated in Figure 1. Its deterministic part includes equations defining the time course of T cell subpopulations and virus strains under a combination therapy including one or more reverse transcriptase inhibitors (RTIs, nucleoside or non-nucleoside) and one protease inhibitor (PI). Lack of efficacy of treatment, interpreted as resistance levels, are symbolized by b (a composite parameter, expressed as the product of treatment-specific resistance levels and acting on interaction between target cells and virus, K1VT term, according to Figure 1) and h [an infected T cell producing Nh infectious virus particles and N(1 – h) non-infectious ones, as represented in Figure 1], respectively. These parameters (b and h) only characterize global susceptibility of a strain to drugs, without explicit distinction between resistance conferred by one major mutation and resistance generated by several minor mutations, their values varying between 0 (complete susceptibility) and 1 (total resistance). The state variables are: target cells, latently infected cells, productively infected cells, infectious virus, non-infectious virus and immune responses (cytotoxic T lymphocytes) specific to two epitopes. This model also comprises a stochastic component that specifies the emergence of viral strains by mutation on one of the two epitopes chosen randomly, and associates characteristics (virulence, immunogenicity and specific drug efficacy) to each viral mutant, drawn from predefined distributions. HAART was initiated at different times in disease evolution, chosen randomly. All parameters of the model were chosen consistent with biological plausibility within ranges allowing realistic dynamics.



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Figure 1. A model of multispecies HIV-1 infection under therapy. Cell populations implied in infection dynamics are CD4 cells with three subpopulations, target cells (T), latently infected cells (L) and productively infected cells (T*), and CD8 cells with two subpopulations (X and Y) specific to two different epitopes. Virus are infectious (VI) or non-infectious (VNI). All the variables (except target cells, T, and non-infectious virus, VNI) are indexed and correspond to a strain ij, containing sequence i on one epitope and sequence j on the other. Mutations appear at random in one of the two epitopes, viral strains being continuously created by a stochastic process. Parameters of the model are: s, source; r, proliferation; µ, death or clearance; K1, affinity; K2, proportion of latently infected cells that become productively infected; N, number of virions produced by one productively infected cell; {zeta}, activation rate of CD8; c, k, immunogenicities; p, elimination; b, h, lack of efficacy of RTIs and PIs respectively, interpreted also as strain-specific resistance levels. Strain-specific parameters are indexed.

 
Secondly, we used the set of histories of infected patients, generated by the dynamic model described above, to specify, by multiple linear regression, a prediction model of the immunological (increase in CD4 cell count from baseline) and virological (decrease in HIV level from baseline) responses to therapy at 6 months. Candidate prognostic variables were baseline viral load, baseline CD4 and CD8 cell counts, number of viral strains and their specific resistance levels (bs and hs) at the initiation of therapy.

Finally, we have obtained a regressive model predicting the variation in CD4 count and in log10 of viral load from baseline:

{Delta}CD4 = f [baseline viral load, baseline CD8 count, number of detectable strains, sum of (resistance levels to RTIs), sum of (resistance levels to PI), max of (resistance levels to PI), min of (resistance levels to PI)] (1)

{Delta}log10(viral load) = f [baseline viral load, baseline CD4 count, baseline CD8 count, sum of (resistance levels to PI), max of (resistance levels to PI), min of (resistance levels to PI), max (resistance levels to RTIs)] (2)

In expressions above, sum, max and min of resistance levels (parameters b and h) were calculated on detectable strains present at commencement of HAART.

These findings, consistent with the experimental data recalled in previous sections, may be considered as a validation of the underlying dynamic model and of the regressive model (that could be used further to deal with the experimentally out of reach question and to predict the therapy outcome). For example, the best predictive model of the viral load decrease includes both baseline CD8 and CD4 cell counts, while the model with the best predictive power explaining the increase in CD4 cell count contains baseline CD8 cell count. Our predictive regression model underlines a continuous effect (without any threshold) of baseline CD4 count on disease progression.

The first point highlighted by our modelling approach is related to viral diversity and its role in treatment outcome. Our results indicate that ignoring strains present at undetectable levels does not influence the quality of the prediction; moreover, they degrade it, the best predictive model does not rely on the characteristics of less frequent strains, nor even on their existence. This could be explained by the fact that, even if highly resistant, a strain present at low level at therapy initiation will not grow enough to become preponderant in a short time. Hence, our findings suggest that resistance assays could provide worthwhile complete information concerning the choice of the best-tailored drug combination. Since long-term results are the goal of the treatment, resistance tests have to be regularly updated.

The next aspect that results from our study is the use of the regressive model defined by Equations 1 and 2 when choosing adapted treatment regimens in HIV-infected patients. Indeed, all aforementioned studies stress the importance of resistance testing, especially when previous therapy has failed. We propose an efficient tool that incorporates knowledge provided by these tests in addition to classic predictive factors (such as baseline viral load, and CD4 and CD8 counts). However, in our approach, these classic markers are not likely to govern the choice of the best therapy combination, since the regressive model does not include interaction terms between them and treatments. Therefore, the choice will be based on resistance levels to drugs.

For example, consider a case where a combination of new drugs must be chosen for an HIV-infected person after treatment has failed. Suppose that the resistance characteristics of viral strains from this person are also known, the efficacy of each potential new therapy on patient quasispecies having been quantified by genotypic or phenotypic assays. In the context of our modelling approach this means that values for parameters b and h are given for each tested combination of drugs and for each viral strain identified in patient’s blood. In fact, it could be sufficient to identify parameters corresponding to the most susceptible and the most resistant strains (min and max of bs and hs in our regressive model) and global resistance levels to tested treatments (sum of bs and sum of hs here), since the predictive model (Equations 1 and 2) only includes this information. Therefore, candidate therapies can be classified according to the expected variations in viral load and CD4 count they induce, based on the regressive model. The interest of using a predictive model is enhanced when the viral quasispecies of the patient is not completely susceptible to any of the treatments available to select; in such a case the optimal therapy is not obvious. For instance, consider a simple configuration: the plasma sample of our patient contains three viral strains and we have to choose between two combinations of RTIs (treatments 1 and 2, T1 + T2, versus treatments 1 and 3, T1 + T3) to include in the best-adapted multidrugs regimen. Strains 1 and 2 are susceptible to T1 and T3 (treatment-specific resistance levels all equal to 0.1) and moderately resistant to T2 (treatment-specific resistance levels equal to 0.3), while strain 3 is completely susceptible to T1, susceptible to T2 and totally resistant to T3 (treatment-specific resistance levels equal to 0, 0.1 and 1, respectively). Specifically for these values, the intuitive choice (based on the minimum sum of treatment-specific resistance levels for each combination of drugs) would be T1 + T2, whereas the optimal choice based on our regressive model (more precisely on the minimum sum of composite resistance levels bs, participating in the prediction in Equation 1) is T1 + T3. The explanation is that total resistance of strain 3 to T3 is annihilated by its complete susceptibility to T1 (as detailed in dynamic model description, for each viral strain, parameter b is expressed as a product of treatment-specific resistance levels).

The regressive model described by Equations 1 and 2 could be replaced by logistic models if the response to predict is binary (treatment failure or not, viral load below or above a given threshold, etc.), or by survival regression models if the progression to a new AIDS-defining event or death is analysed. The dynamic model that generated the set of infected patients on which the regressive model was built could also be used as a predictive model (all the more because it provides long-term results) if specific information (infected CD4 count, CD8 count and viral load for each strain) were available.


    Conclusions
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
In conclusion, mathematical models could become essential tools in decisions concerning individualized treatment combinations, and represent a promising future in HIV therapy until the discovery of an effective vaccine. However, this approach is not yet feasible for decision-making by AIDS care providers. Indeed, to provide useful predictions, these models need to include strain-specific resistance parameters, obtained by identification from quantitative strain-specific viral data. Progress has to be made in viral strain typing techniques in order to increase their sensitivity, improve standardization and better correlate their results with clinical outcome.


    Acknowledgements
 
We thank Henri Agut for valuable comments on the manuscript. This work was supported by the French Ministère de l’Education Nationale et de la Recherche and by the French Agence Nationale de la Recherche sur le SIDA.


    Footnotes
 
* Correspondence address. INSERM U436, 91 boulevard de l’Hôpital, Paris cedex 13, France. Tel: +33-1-40-77-98-54; Fax: +33-1-45-85-15-29; E-mail: eve{at}biomath.jussieu.fr Back


    References
 Top
 Abstract
 Introduction
 CD4 and CD8 levels...
 Resistance characteristics of...
 A model-based approach for...
 Conclusions
 References
 
1 . Back, D., Gatti, G., Fletcher C. et al. (2002). Therapeutic drug monitoring in HIV infection: current status and future directions. AIDS 16, Suppl. 1, 5–37.[CrossRef][ISI][Medline]

2 . Vergu, E., Mallet, A. & Golmard, J. L. (2002). The role of resistance characteristics of viral strains in the prediction of the response to antiretroviral therapy in HIV infection. Journal of Acquired Immune Deficiency Syndromes 30, 263–70.[ISI][Medline]

3 . Sterling, T. R., Chaisson, R. E. & Moore, R. D. (2001). HIV-1 RNA, CD4 T-lymphocytes, and clinical response to highly active antiretroviral therapy. AIDS 15, 2251–7.[CrossRef][ISI][Medline]

4 . Grabar, S., Le Moing, V., Goujard, C. et al. (2000). Clinical outcome of patients with HIV-1 infection according to immunologic and virologic response after 6 months of highly active antiretroviral therapy. Annals of Internal Medicine 133, 401–10.[Abstract/Free Full Text]

5 . Deeks, S. G. (2000). Determinants of virological response to antiretroviral therapy: implications for long-term strategies. Clinical Infectious Diseases 30, S177–84.[CrossRef][ISI][Medline]

6 . Chêne, G., May, R., Costagliola, D. et al. (2002). Prognosis of HIV-1 infected drug naïve patients starting potent antiretroviral therapy. ART Cohort Collaboration. In Program and Abstracts of the XIV International AIDS Conference, Barcelona, Spain, 2002. Abstract TuOrB1140, p. 370. IAS International AIDS Society, Stockholm, Sweden.

7 . Egger, M., May, M., Chêne, G. et al. (2002). Prognosis of HIV-1 infected patients starting highly active antiretroviral therapy: a collaborative analysis of prospective studies. Lancet 360, 119–29.[CrossRef][ISI][Medline]

8 . Wilson, J. D. K., Ogg, G. S., Allen, R. L. et al. (2000). Direct visualization of HIV-1-specific cytotoxic T lymphocytes during primary infection. AIDS 14, 225–33.[CrossRef][ISI][Medline]

9 . Giorgi, J. V., Lyles, R. H., Matud, J. L. et al. (2002). Predictive value of immunologic and virologic markers after long or short duration of HIV-1 infection. Journal of Acquired Immune Deficiency Syndromes 29, 346–55.[ISI][Medline]

10 . Macias, J., Leal, M., Delgado, J. et al. (2001). Usefulness of route of transmission, absolute CD8+ T-cell counts, and levels of serum tumor necrosis factor alpha as predictors of survival of HIV-1 infected patients with very low CD4+ T-cell counts. European Journal of Clinical Microbiology and Infectious Diseases 4, 253–9.[CrossRef]

11 . Xu, J., Whitman, L., Lori, F. et al. (2002). Quantification of HIV-specific CD8 T cells by in vitro stimulation with inactivated viral particles. AIDS 16, 1849–57.[CrossRef][ISI][Medline]

12 . DeGruttola, V., Dix, L., D’Aquila, R. et al. (2000). The relation between baseline HIV drug resistance and response to antiretroviral therapy: re-analysis of retrospective and prospective studies using a standardized data analysis plan. Antiviral Therapy 5, 41–8.[ISI][Medline]

13 . Hanna, G. J. & D’Aquila, R. (2001). Clinical use of genotypic and phenotypic drug resistance testing to monitor antiretroviral chemotherapy. Clinical Infectious Diseases 32, 774–82.[CrossRef][ISI][Medline]

14 . Haubrich, R. & Demeter, L. (2001). International perspectives on antiretroviral resistance. Clinical utility of resistance testing: retrospective and prospective data supporting use and current recommendations. Journal of Acquired Immune Deficiency Syndromes 26, S51–9.[ISI][Medline]

15 . Torre, D. & Tambini, R. (2002). Antiretroviral drug resistance testing in patients with HIV-1 infection: a meta-analysis study. HIV Clinical Trials 3, 1–8.[Medline]





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