HAART has been shown to be effective in children from industrialized countries  and feasible in developing countries [2,3] where 90% of infected children are living. As compliance is essential for individual efficacy , a once-daily administration of HAART could further decrease treatment failure, especially in children from developing countries. The once-a-day combination of didanosine (ddI), lamivudine (3TC) and efavirenz (EFV) has been successfully applied to adults [5,6], improving compliance, antiretroviral efficacy  and long-term tolerance [5,6]. However, in children, the efficacy and tolerance of the combination ddI, 3TC, EFV remained to be investigated. The BURKINAME/ANRS 12103 trial aimed to study the combination ddI–3TC–EFV given once daily in children aged from 30 months to 15 years and evaluate the efficacy of this treatment. Until now, HIV dynamic models have only considered the effect of the most potent drug of the combination [8,9]. Therefore, the relative contribution of each drug in the global efficacy remains to be determined. Generally, drug monitoring is only focused on protease inhibitor or nonnucleoside reverse transcriptase inhibitor (NNRTI) concentration, which may lead to a biased appreciation of efficacy, as the other antiretroviral drugs, that is nucleoside reverse transcriptase inhibitor (NRTI), were not taken into account. Relationships between EFV antiretroviral efficacy/toxicity and plasma concentrations have been previously established in adults . Few pharmacokinetic–pharmacodynamic relationships have been reported in children  and no target exposure value has been reported for ddI or 3TC. Thus, in children, reproducing adult exposure is thought to ensure efficacy.
In this study, we analysed simultaneously the viral load and CD4+ lymphocyte evolutions and estimated the relative contributions of efavirenz, didanosine and lamivudine in the treatment of HIV-1-infected children by using an HIV dynamic model. Pharmacokinetic targets for lamivudine and didanosine were deduced from this model. A composite inhibition score (CIS) has been determined and tested as a predictor of treatment failure in a multidrug therapy.
Materials and methods
The BURKINAME – ANRS 12103 study was an open phase II trial evaluating the pharmacokinetics, efficacy and toxicity of the ddI–3TC–EFV once-daily combination in HIV-infected children. It was conducted in Bobo-Dioulasso, Burkina Faso. The study was approved by the National Ethics Committee Health Research from Burkina Faso and was registered in the ClinicalTrials.gov database (http://clinicaltrials.gov) with the no. NCT00122538.
The patients enrolled in this study included children aged from 30 months to 15 years, weighting at least 10 kg, infected by HIV-1 and naive to all antiretroviral treatments (except a treatment preventing mother-to-child transmission). They were eligible if their HIV disease was classified, according to the Centers for Disease Control and Prevention (CDC) as clinical category:
1. C and/or CD4 cell count 15% or less for children aged 5 years or less or CD4 cell count 200 cells/μl or less for children aged more than 5 years
2. B, A or N and 15 ≤ CD4 cell count ≤ 20% for children aged 5 years or less or 200 ≤ CD4 cell count ≤ 350 cells/μl for children aged more than 5 years and a viral load greater than 100 000 copies/ml.
The following baseline laboratory values were required: haemoglobin concentration of 7 g/dl or greater, a platelet count of at least 50 000 cells/μl, amylase less than 2.5 times the upper limit of normal and aspartate aminotransferase and alanine aminotransferase lower than five times the upper limit of normal. The mother or the legal guardian provided informed consent.
Clinical evaluations were carried out each month during the follow-up period. Children were also seen for any intercurrent diseases if necessary. Consultations, hospitalizations, treatments and tests were free of charge.
Children were administered a once-daily 8 mg/kg dose of 3TC, as tablets (150 mg) or oral solution (10 mg/ml). Children were also given a once-daily 240 mg/m2 of ddI and the recommended bodyweight-dependent dose of efavirenz (200 mg from 13 to <15 kg, 250 mg from 15 to <20 kg, 300 mg from 20 to <25 kg, 350 mg from 25 to <32.5 kg, 400 mg from 32.5 to <40 kg and 600 mg above 40 kg).
All parents were instructed to administer all the treatment every day at 1800 h without food.
The pharmacokinetic study was performed after 15 days of treatment in 38 children and between 2 and 5 months of treatment in 11 children. Time elapsed between administration, and sampling time, age, bodyweight and size were carefully recorded. Blood samples were centrifuged at 3000g for 10 min. Plasma samples were aliquoted and stored at −70°C until assayed for drug concentrations. Virological and biochemical measurements were performed, before treatment and every 3 months up to 1 year after the beginning of the treatment. Adherence to the study treatment was assessed by the trial physician and the pharmacist monthly and a quarterly caregiver questionnaire. The questionnaire characterized the child's primary caregiver, documented the caregivers’ and child's knowledge of the diagnosis, the difficulties in administering the drugs, the disruption of daily life by the treatment, the importance of the treatment, the extent to which the suggested pill administration protocol was followed and the reasons for missed doses.
Plasma HIV-RNA viral load was determined using a real-time reverse transcriptase PCR targeted to the long-terminal repeat of HIV-1 (Generic HIV Viral Load assay; Biocentric, Bandol, France). The detection threshold of this assay was 300 copies/ml using 0.2 ml plasma . Biochemistry analysis were performed by using the Lisa 300 Plus machine (Hycel Diagnostics, Massy, France). CD4 cell counting was performed using Becton Dickinson flow cytometry. Concentration measurements of efavirenz, didanosine and lamivudine in plasma were previously described. [11,13,14]. HIV-1 resistance testing was based on AC11 Resistance Group recommendations (French National Agency for AIDS Research, ANRS). RNA was extracted with the MagNa pure compact apparatus (Roche Applied Science, Indianapolis, Indiana, USA) from samples containing more than 1000 HIV-1 RNA copies per millimetre. Drug susceptibility was deduced from ANRS algorithm (http://www.hivfrenchresistance.org).
HIV dynamic model
A dynamic model with antiviral treatments was considered as follows:
These three differential equations represent three compartments: uninfected target cells (TC), infected cells (IC) and free virions (VL) (Fig. 1). The model assumes that target cells are produced at a constant rate So. These cells die at rate Td and are infected according to infection rate constant β. Infected cells are eliminated at a rate δ. Viral particles (virions) are produced at rate p per infected cell and cleared at rate c. The CIS stands for the resulting effect of the three reverse transcriptase inhibitors and coded as follows:
This mechanistically based equation was established according to pharmacodynamic principles. As didanosine and lamivudine are both within a same class of antiretroviral, same mechanism of action and same target, their effect has been combined according to the first part of the equation as previously described . By contrast, the effect of efavirenz has been added as an independent equation.
CssmEFV, CssmddI and Cssm3TC are the mean steady-state concentrations for the three drugs calculated as dose divided by clearance and administration interval. The individual clearances of each drug were obtained from the three different population pharmacokinetic models previously published [11,13,14]. C503TC, C50ddI and C50EFV were concentrations at which the drug effect reaches 50% of its maximum, when viral resistance had not occurred. In the model, if resistances occurred during follow-up time, the C50 for each drug was estimated before resistance mutation appeared. When a resistance occurred for a drug, the corresponding C50 was set to infinity, that is the inhibition effect was close to zero. Imax3TC, Imaxddi and ImaxEFV were the maximum responses produced by lamivudine, didanosine and efavirenz, respectively.
To have a consistent effect equation, the accumulated maximum response produced by the three drugs association should not exceed 1; thus, the sum of Imax3TC, Imaxddi and ImaxEFV was constrained to the value of 1 as follows:
E3TC and EddI were then two parameters estimated from the model. By this way, the composite score varies from 0 to 1.
If we assume a system at a steady state before initiating antiretroviral treatment, the initial conditions of the system are:
Initial conditions were then reformulated in order to estimate viral load and CD4+ lymphocyte counts as baseline parameters, allowing the determination of the corresponding between-subject variabilities (BSVs). Thus, β and Td were derived from viral load and CD4+ lymphocyte count baselines according to the following equations:
Modelling strategy and population pharmacokinetic model
Data were analysed using the nonlinear mixed effect modelling software program Monolix version 31s (http://wfn.software.monolix.org) . Due to the wide range of viral load values, these were log10 transformed for the analysis. Parameters were estimated by computing the maximum likelihood estimator of the parameters without any approximation of the model (no linearization) using the stochastic approximation expectation maximization (SAEM) algorithm combined to a Markov chain Monte Carlo (MCMC) procedure. BSVs were ascribed to an exponential model. The likelihood ratio test (LRT) including the log-likelihood, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) were used to test different hypotheses regarding the final model, covariate effect(s) on parameter(s), residual variability model (proportional versus proportional along with additive error model) and structure of the variance–covariance matrix for the BSV parameters. Viral load data below the limit of quantification (LOQ) were treated as left-censored data by the program.
Visual predictive check evaluation
Plasma virions concentration profiles and CD4+ lymphocytes kinetics were simulated and compared with the observed data to evaluate the predictive performance of the model. The vector of pharmacokinetic parameters from 400 patients was simulated using the final model. Each vector parameter was drawn in a log-normal distribution with a variance corresponding to the BSV previously estimated. A simulated residual error was added to each simulated concentration. The fifth, 50th and 95th percentiles of the simulated concentrations at each time were then overlaid on the observed concentration data and a visual inspection was performed.
Forty-nine children (19 girls and 30 boys) from 2.5 to 15 years old, 285 plasma virions concentrations and 287 CD4+ lymphocyte counts were available for evaluation. Table 1 summarizes patients’ characteristics.
Clinical, immunological and virological data
Clinically, 16 children were at stage A, 28 at stage B and five at stage C of HIV infection, according to the CDC clinical category . Before treatment, the mean percentage of CD4 cell count was 8.62% (median 8%, from 0.4 to >26%) and the average CD4 lymphocytes count was 336 cells/μl (median 257, from 2 to 1513 cells/μl). Median viral load was 5.5 log10 copies/ml (from 4.6 to 6.7 copies/ml). Patients with this high degree of infection severity were included in this trial, because this was the inclusion criteria for HAART in Burkina Faso. Eleven patients developed resistance with a cumulative rate of 22% at 12 months. Resistance to both EFV and 3TC occurred in six patients, to both EFV and ddI in one patient, to 3TC alone in two patients, to EFV alone in one patient and finally one patient developed resistance to the three drugs.
The average yearly adherence for all patients was 97.3% (range: 88.5–99.8%)
The HIV dynamic model adequately described the data with the use of the pharmacokinetic parameters of drugs published previously [11,13,14]. The parameters of the model (see figure, Supplemental Digital Content 1, http://links.lww.com/QAD/A279) were the production rate constant of uninfected target cells (So), elimination rate constant of infected cells (δ), production rate constant of free virions (p), elimination rate constant of free virions (c), free virions at baseline (VL0), CD4 cell count at baseline (CD40) and C503TC, C50ddI, C50EFV. As δ and c were inaccurately estimated from the model, these two parameters were fixed to previously reported values, 15.2 and 91.5 per month, respectively . Residual variabilities were best described by an additive error model. Interindividual variability was retained for p, So, C50EFV, VL0 and CD40 and described by exponential error model.
Table 2 summarizes the final population parameter estimates. All the parameters were well estimated, given their relative standard error (RSE%). The model assumes a maximum effect of 1 (Imax) obtained from the combination of the three drugs; thus, the Imax of each drug has been derived from the model (as described in the Materials and Methods part) and efavirenz was the most potent antiretroviral and responsible for 65% of the maximum total effect, then didanosine for 23% and lamivudine was the less potent with 12% of the total effect.
Our model provided good fits of both viral load and CD4+ lymphocytes as shown on some individual fits for different patients (Fig. 1) and on the visual predictive checks (see figure, Supplemental Digital Content 2, http://links.lww.com/QAD/A279), which shows that the average prediction matches the observations and that the variability is reasonably estimated.
According to the concentration–effect relationship (see figure, Supplemental Digital Content 3, http://links.lww.com/QAD/A279), an EC90 of 3.3 mg/l for efavirenz was determined. The current recommendation for efavirenz is to obtain a Cmin from 1 to 4 mg/l: this range appears to guarantee an optimal efficacy for this drug.
For the two NRTIs, the area under the curve (AUC) effect relationship was performed. AUC50 for lamivudine and didanosine was derived from C503TC and C50ddI (multiplication by administration interval) and AUC90 was then deduced (see figure, Supplemental Digital Content 3, http://links.lww.com/QAD/A279): 8.4 and 1.5 mg h/l, respectively. These values could be taken as pharmacokinetic targets to ensure optimal efficacy for these drugs.
Virologic failure predictor
The three mean drug concentrations and the CIS (calculated for each patient from the equation defined in the Materials and Methods part) were compared between patients with or without virologic failure (>300 copies/ml) during the year of treatment to assess which was the best to discriminate the two groups (Table 3). Virologic failure has been defined as a single free virion more than 300 copies/ml during the year of follow-up; however, the same results regarding the predictivity of the score have been obtained if virologic failure was defined as two successive free virions more than 300 copies/ml. In that case, six children could be considered as blippers. The mean concentrations of the three drugs were not significantly different in the two groups; however, the CIS was significantly lower in patient with virologic failure [mean (SD): 0.45 (0.20) vs. 0.63 (0.10), P < 10−3].
The risk of treatment failure was compared between the patients who reach a CIS lower than 50% and those who reached a score greater than 50% (Fig. 2). The risk of failure was significantly higher in patient with a score less than 50% (log-rank test: P = 0.003). A multivariate Cox analysis was performed in order to obtain the hazard ratio adjusted by viral resistances. Taking into account drug resistances, the risk of failure was significantly lower when the CIS increases with an adjusted hazard ratio (per 10% increase) of 0.6 [95% confidence interval (CI) 0.41–0.88, P = 0.008)]. The adjusted hazard ratio of viral resistances was 5.2 (95% CI 1.7–15.9, P = 0.004).
Modelling of viral dynamics in HIV-1-infected patients has played an important role to describe and understand the effect of antiretroviral drugs on HIV-1 RNA production. However, all of these models were performed either on a monotherapy or on a multidrug therapy but only by taking into account the effect of the most potent drug that was assumed to be 100% effective. In this study, we established the virologic and CD4+ cells responses as a function of the three drug exposures (efavirenz, didanosine and lamivudine) and characterized the relative weight of each drug on the total effect in 49 children aged from 2.5 to 15 years. This model has been successfully developed, thanks to the variability of the viral and CD4 cell responses. This dataset including responders and nonresponders was allowed to perform this modelling and relate these different responses to the drug exposures. The HIV dynamic model used has been previously described  and usually used for the characterization of one drug effect [8,9]. The physiological mechanism of the three drugs has been taken into account, as the effect of the two NRTIs (3TC + ddI) has been combined contrary to the NRTI (EFV) effect that has been characterized as an independent equation. The sum of these three effects was equal to 1. The estimation of all HIV dynamic parameters has been performed using SAEM algorithm, which is computationally efficient on dynamic models and is able to handle correctly the censored data from viral load, which are the main source of biased estimates of the parameters . A comparison with classic methods of handling censored data shows that the extended SAEM algorithm was the less biased method .
Efavirenz and didanosine concentrations were modelled by a one-compartment model with first-order elimination. Lamivudine concentrations were described by a two-compartment model with first-order elimination where the fast distribution rate constant is assumed to be equal to the absorption rate constant. These models have been established in the same paediatric patients and detailed in previous published studies [11,13,14]. These models were used to obtain the individual exposure to each drug for each patient.
The pharmacological active form for lamivudine and didanosine is the triphosphate anabolite, and no link between plasma concentrations and effect has been already shown. Exposures defined as AUC to these drugs appear to be more effective than concentrations to reflect the link to efficacy; thus, 24-h exposures were chosen as targets in stade of mean concentrations as made for efavirenz, which does not need to be converted to an active form.
According to our modelling, the order of potency of the three drugs was as follows: efavirenz (65% of the total effect), then didanosine (23%) and finally lamivudine was the less potent with 12% of the total effect. Regarding the estimated potency of each drug, it was expected that the NNRTI drug (EFV) would be responsible of the most part of the effect compared with the NRTI backbone. If we focus on the monotherapy efficacy studies of the two NRTIs, we notice that after 48 weeks of treatment, the mean change from baseline for viral load was −0.62 and −0.42 for ddI  and 3TC , respectively. These results suggest a higher potency of ddI than 3TC as shown in our findings. However, at this time, there are no published data on how these three drugs contribute to the resulting response.
The model allowed us to determine pharmacokinetic targets (AUC90) for the two NRTIs: didanosine and lamivudine (1.5 and 8.4 mg h/l, respectively). AUC90 found for lamivudine and didanosine was closed to adult exposure reported with the standard dose [23–26]. EC90 found for efavirenz was between 1 and 4 mg/l, which is the reported range of efficacy for efavirenz . The CIS determined in this study was the best predictor of virologic failure compared with the concentrations of each drug taken independently. In the multivariate Cox analysis, viral resistance was the major determinant of virologic failure (hazard ratio 5.2, 95% CI 1.7–15.9). However, taking into account viral resistances, the time to virologic failure analysis has shown that the increase of CIS in patients leads to decrease in the risk of failure with an adjusted hazard ratio of 0.6 (95% CI 0.41–0.88).
The average yearly level of adherence in the first year of this once-daily dose of antiretroviral therapy combination was very high for all patients (97.5%) probably due to the fact that caregivers were regularly reminded to provide the medication during all the trials.
In conclusion, this study reports, for the first time, the relative contributions of three combined drugs, thanks to a population modelling of their effects on plasma virions and CD4+ lymphocyte counts kinetics in HIV-1-infected children. A CIS based upon pharmacodynamic principles was determined from the concentrations of the three drugs and measured the total effect of the multidrug therapy. This score was the best predictor of virologic failure compared with the concentrations of each drug taken independently. New pharmacokinetic targets have been derived and proposed for lamivudine and didanosine. The EC90 for efavirenz derived from the model was well in the range of previously recommended concentrations values.
We acknowledge the French ‘Agence Nationale de Recherche contre le VIH/SIDA et les hepatitis virales’ (ANRS) for sponsoring the trial and the children of the study and their parents. We acknowledge Pediatric European Network Treatment AIDS Laboratory Network (PENTA-LABNET) for financial support.
N.B., J.M.T., P.M., P.V.P. and S.U. designed research; P.M., P.V.P., S.D., B.N., H.H., E.Z., F.R., A.O. and S.B. conducted research; N.B., S.U., D.H. and J.M.T. analysed data; N.B. and S.U. wrote the article; N.B., J.M.T. and S.U. had primary responsibility for the final content.
Conflicts of interest
There are no conflicts of interest.
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