Population pharmacokinetic modelling of the changes in atazanavir plasma clearance caused by ritonavir plasma concentrations in HIV‐1 infected patients

Abstract

Aims

The aim of the present study was to develop a simultaneous population pharmacokinetic model for atazanavir (ATV) incorporating the effect of ritonavir (RTV) on clearance to predict ATV concentrations under different dosing regimens in HIV‐1‐infected patients.

Methods

A Cross‐sectional study was carried out in 83 HIV‐1‐infected adults taking ATV 400 mg or ATV 300 mg/RTV 100 mg once daily. Demographic and clinical characteristics were registered and blood samples collected to measure drug concentrations. A population pharmacokinetic model was constructed using nonlinear mixed‐effects modelling and used to simulate six dosing scenarios.

Results

The selected one‐compartmental model described the pharmacokinetics of RTV and ATV simultaneously, showing exponential, direct inhibition of ATV clearance according to the RTV plasma concentration, which explained 17.5% of the variability. A mean RTV plasma concentration of 0.63 mg l^–1 predicted an 18% decrease in ATV clearance. The percentages of patients with an end‐of‐dose‐interval concentration of ATV below or above the minimum and maximum target concentrations of 0.15 mg l^–1 and 0.85 mg l^–1 favoured the selection of the simulated ATV/RTV once‐daily regimens (ATV 400 mg, ATV 300 mg/RTV 100 mg, ATV 300 mg/RTV 50 mg, ATV 200/RTV 100 mg) over the unboosted twice‐daily regimens (ATV 300 mg, ATV 200 mg).

Conclusions

A one‐compartment simultaneous model can describe the pharmacokinetics of RTV and ATV, including the effect of RTV plasma concentrations on ATV clearance. This model is promising for predicting individuals' ATV concentrations in clinical scenarios, and supports further clinical trials of once‐daily doses of ATV 300 mg/RTV 50 mg or ATV 200 mg/RTV 100 mg to confirm efficacy and safety.

What is Already Known about this Subject

• The once‐daily ATV 300 mg/RTV 100 mg regimen is widely used in highly active antiretroviral therapy.

• In some patients, dose adjustments may be necessary to prevent concentrations outside the therapeutic range leading to undesired effects or therapeutic failure.

• Population pharmacokinetic modelling enables us to detect and quantify the effect of different patient characteristics associated with variability.

What this Study Adds

• A simultaneous population pharmacokinetic model described the decrease in atazanavir clearance with an exponential function of ritonavir (RTV) concentrations in HIV‐1‐infected adults.

• RTV plasma concentrations explained 17.5% of interindividual variability in ATV clearance.

• The model supports further clinical trials of once daily doses of atazanavir (ATV) 300 mg/RTV 50 mg or ATV 200 mg/RTV 100 mg to confirm efficacy and safety.

Introduction

Protease inhibitor (PI) antiretrovirals, used since the mid‐1990s, remain a pillar of anti‐HIV therapy. Although regimens based on atazanavir (ATV) are currently proposed by the World |Health Organization guidelines as a second‐line therapy, they have for many years been among the preferred PI options for the initial treatment of HIV‐1‐infected patients because they present a better gastrointestinal profile (including a lower incidence of diarrhoea) and less impact on lipid profiles than the lopinavir/ritonavir (LPV/RTV) regimens 1, 2, 3, 4. Furthermore, ATV‐based regimens have the advantage of being simpler. ATV is able to suppress viral replication in both antiretroviral‐naïve and ‐experienced patients in long‐term treatment 1, 5. Overall, this PI is also generally well tolerated, although it has been associated with reversible asymptomatic elevations of indirect unconjugated bilirubin 6, 7.

Similarly to other PIs, ATV undergoes extensive hepatic metabolism, mainly by cytochrome P450 (CYP) 3A4/3 A5 isoenzymes. As ATV is a substrate of P‐glycoprotein, its oral bioavailability is low 8, 9. Nonetheless, it is the only clinically available PI that can be used either alone or boosted with low doses of RTV (100 mg), which improves its pharmacokinetic profile by inhibiting CYP3A and P‐glycoprotein 10, 11 to increase ATV plasma concentrations. The once‐daily ATV 300 mg/RTV 100 mg regimen is widely used in highly active antiretroviral therapy today and its antiviral efficacy has been shown to be non‐inferior to that of LPV/RTV twice daily in antiretroviral‐naïve subjects 1. These patients can also take ATV at doses of 400 mg once a day at the beginning of treatment 12. In addition, once‐daily dosing of this PI can be used as a treatment‐simplification strategy 13. ATV pharmacokinetics have a high intra‐ and interpatient variability 14, 15, however, and in some patients dose adjustments may be necessary to prevent concentrations outside the therapeutic range that could increase their risk of undesired effects (high plasma bilirubin concentrations) or lead to therapeutic failure. In a previous study, our group observed high interindividual variability in the pharmacokinetics of ATV in clinical practice, resulting in ATV concentrations at the end of the dose interval (C_trough) that were lower than the proposed minimum effective concentration in a considerable percentage of HIV‐infected patients on unboosted ATV 16. Further understanding of the sources of ATV pharmacokinetic variability is therefore of interest so that we can anticipate and prevent therapeutic failure.

Population pharmacokinetic modelling enables us to detect and quantify the effect of different patient characteristics associated with variability. To date, five models have been developed to describe the pharmacokinetics of ATV in HIV‐1‐infected adults 17, 18, 19, 20, 21 but only the model of Schipani et al. 21 quantified the effect of RTV plasma concentrations on ATV clearance. However, the number of patients included in that 2013 study was too low to find the sources of the interindividual variability in the pharmacokinetics of either drug. A new model, incorporating more patients, would be likely to provide sufficient data to help us understand the pharmacokinetics of ATV and guide individual therapeutic dosing in clinical settings. If a model were successful, it might be possible to reduce the frequency of therapeutic drug monitoring carried out to identify patients at high risk of therapeutic failure 15, 19, 22.

The aim of the present study was to develop a model for ATV pharmacokinetics incorporating the effect of RTV on ATV clearance that could be used: (i) to explore whether a reduction in the ATV and/or RTV dose might be plausible in a patient; and (ii) to predict the C_trough of a patient when a blood sample cannot be obtained at the end of the dosing interval.

Methods

Study population

This cross‐sectional study enrolled HIV‐1‐infected adult patients taking ATV once daily either alone (400 mg) or in combination with RTV (ATV 300 mg/RTV 100 mg) as part of their stable antiretroviral therapy for at least 4 weeks (steady‐state conditions). Adult male and nonpregnant female patients were recruited and assessed at Hospital Universitari Germans Trias i Pujol (HUGTIP) in Badalona, Catalonia, Spain, between May 2004 and May 2009. Patients were excluded if their self‐reported treatment compliance was lower than 85% within the previous week or they were taking any drugs [other than tenofovir (TDF)] known to interact with ATV or RTV. The study was approved by HUGTIP's ethics committee, and the Spanish Drug Agency (EudraCT 2004–001 516‐32), and all patients provided written informed consent.

Patient characteristics such as gender, age, body weight, hepatitis C virus (HCV) antibody and concomitant medications were recorded, along with clinical variables such as serum levels of aspartate aminotransferase (AST), alanine aminotransferase (ALT), α‐acid glycoprotein (AAG) and albumin.

Blood samples and analytical method

For patients taking their antiretroviral medication in the morning, samples were collected immediately before and up to 12 h after a witnessed dose, at the following times: baseline (appears as 24 h post‐medication in the figures), and 0.5, 1, 2, 4, 6, 8, 10 and 12 h. Samples from patients taking their medication at night (unwitnessed) were collected between 10 h and 24 h later at the following theoretical times: 12, 13, 14, 16, 18, 20 and 22 h postdose. As the dose prior to the sampling was not witnessed in the latter patients, the sampling times were approximate. The actual sampling times were annotated and used for the model development.

Blood samples for ATV and RTV determinations were collected into potassium–ethylenediamine tetra‐acetic acid‐containing tubes. Plasma was isolated by centrifugation (3200 g for 15 min) and stored at −20 °C until analysis. Both drugs were quantified at the HUGTIP retrovirology laboratory by means of high‐performance liquid chromatography (HPLC) with a photodiode array detector (HPLC‐PDA 2996; Waters, Barcelona, Spain) following a validated method. The method involved liquid–liquid extraction of drug from the plasma using tert‐butyl methyl ether after the pH was increased, and a second wash with hexane. The mobile phase consisted of a gradient elution with phosphate buffer : acetonitrile (pH 6.70). The method was linear over the range 0.044–17.5 mg l^–1 for ATV and 0.05–20 mg l^–1 for RTV. The intraday and interday coefficients of variation were lower than 10% for both drugs. The assay was externally validated by the International Interlaboratory Quality Control Program for Therapeutic Drug Monitoring in HIV Infection (KKGT, Nijmegen, Netherlands) 23.

Pharmacokinetic analysis

The pharmacokinetic model was developed in three stages using nonlinear mixed‐effects modelling (NONMEM, version VI software; ICON Development Solutions, Ellicott City, MD, USA) 24. First, basic population pharmacokinetic models were developed separately for ATV and RTV. Second, intermediate models explored the influence of patient demographic characteristics and clinical variables on the interindividual variability of the parameters of each drug. In the third step, we developed a model simultaneously estimating the pharmacokinetic parameters of ATV and RTV, combining the two previous intermediate models and incorporating the effect of RTV concentrations on ATV clearance.

Less than 1% of our measurements below the limit of quantitation for ATV, and 5% for RTV; therefore, we did not include these observations during model development, in accordance with the guidance of Bergstrand et al. 2009 25.

Basic models for ATV and RTV: describing disposition

One‐ and two‐compartment mammillary models with linear or nonlinear elimination of the drugs were tested. In order to describe the absorption profile, models with and without lag time and those with transit compartments as a more flexible function to describe the delay in the absorption were used 26. Zero‐ or first‐order absorption was evaluated.

Exponential terms following a log‐normal distribution were assumed for the description of interpatient variability in pharmacokinetic parameters as θ _i = θ ⋅ exp(η _i ), where θ _i is the pharmacokinetic parameter of the i ^th individual, θ is the typical population value of the parameter and η _i is the interindividual random effect assumed to have a mean of zero and a variance of ω².

A combined error model was initially incorporated to describe the residual variability and quantify the difference between the observed and model‐predicted concentrations. If one of the components (additive or proportional) of the residual error was negligible, it was deleted from the model.

Intermediate models for ATV and RTV: exploring covariates

In order to elucidate the sources of variability in the estimated pharmacokinetic parameters, the influence of patient demographic characteristics and clinical variables with physiological significance was evaluated using graphical methods and a generalized additive model (GAM) 27 implemented in the software Xpose, version 3.1 (Uppsala University, Uppsala, Sweden) before including a covariate in the selected basic (first‐step) models in NONMEM.

Gender, age, body weight, dose timing (morning/night), HCV coinfection with specification of liver fibrosis 28 and concomitant TDF use, as well as serum levels of AST, ALT, AAG and albumin were the covariates to be tested. RTV was also considered, either as a binary covariate (yes/no) or as the area under the plasma concentration curve (AUC) for RTV, calculated for each patient by means of the log‐linear trapezoidal rule using WinNonlin software (Professional Edition, Version 2.1, Scientific Consulting, Pharsight, Mountain View, CA, USA).

Covariates selected by GAM as significantly related to the parameters, those showing a possible correlation in the eta‐covariate plots and those that might be important from a physiological point of view were further tested for significance in NONMEM.

Final model: describing the interaction between RTV concentrations and ATV clearance

The structure of the intermediate models for both ATV and RTV were considered as the starting points for analysing ATV and RTV pharmacokinetics simultaneously. The inhibition of ATV clearance by RTV was assumed to be dependent on RTV concentration at each time point rather than on the AUC _rtv. A direct relationship between the predicted concentrations of RTV in the plasma (CRTV) and the clearance of oral ATV (CL/F _ATV) was assumed for the models tested as $\mathit{CL}/F_{\mathit{ATV}}={\displaystyle {{\theta }_{\mathit{CL}/F}}_{\mathit{ATV}}}\cdot I\left(t\right)$, where θ _CL/FATV is the value of CL/F _ATV in the absence of RTV and I(t) represents the inhibition of CL/F _ATV by RTV.

The inhibition process was modelled according to a linear function described as I(t) = 1 − (SLP ⋅ C_RTV), where C _RTV is the RTV plasma concentration and SLP is the slope of the linear relationship.A maximum effect model was also tested:

$$I\left(t\right)=1-\frac{I_{max}\cdot C_{\mathit{RTV}}}{I{C}_{50}+C_{\mathit{RTV}}}$$

In this equation, I _max is the maximum theoretical inhibitory effect of RTV on ATV clearance and IC ₅₀ is the RTV plasma concentration that is able to produce 50% of I _max.Finally, an exponential effect model was considered for the pharmacokinetic interaction using the following equation:

$$I\left(t\right)=e^{\left(-\theta \cdot C_{\mathit{RTV}}\right)}$$

Here, θ is the parameter characterizing the exponential effect of RTV concentrations on CL/F _ATV.

We also tested a hepatic first‐pass model to evaluate if we could capture the enzyme inhibitory effect of RTV on bioavailability.

During the three steps of the analysis, we used the first‐order conditional estimation method, with the INTERACTION option in NONMEM, and the model fit was assessed statistically and graphically. To decide between hierarchical models, the minimal objective function value (OFV) provided by NONMEM was used as a part of the goodness‐of‐fit diagnostic, and a statistically significant decrease of 3.84 points (P = 0.05, χ² distribution, one degree of freedom) was considered. We performed graphical diagnostics and constructed goodness‐of‐fit plots using S‐PLUS (Statistical Sciences, version 6.2, Insightful Corporation, 2003, Seatle, Washington, USA), and the standard errors of the parameter estimated were calculated as the ratio between the standard error provided by NONMEM and the parameter value, and expressed as a percentage using the COVARIANCE option.

The mean prediction error of the concentrations measured between 23 h and 25 h postdose was calculated from the final model to evaluate whether the model could be used to predict the C_trough for patients when a blood sample could not be taken at the end of the dosing interval.

Model validation

The predictive capability of the final model was evaluated using a visual predictive check with PsN (Uppsala, Sweden) 29, 30. One thousand data sets were simulated using the typical population parameter estimates and the values of interindividual variability and residual error of the final model. The proportion of patients taking ATV 300 mg/RTV 100 mg and ATV 400 mg was the same in the simulations and the real data set. The observed concentrations were then plotted and superimposed on the median profile, with the 5th and 95th percentiles of the simulated concentrations. The 90% confidence intervals around the simulated median and percentiles were also included. Agreement between simulations and observations was judged visually.

Simulations

One thousand individual pharmacokinetic profiles were simulated to evaluate the percentage of patients predicted to have plasma concentrations below or above the established cutoffs (0.15 mg l^–1 and 0.85 mg l^–1, respectively). The percentages of individuals below and above these values were calculated for each of the following simulated scenarios: ATV 400 mg once daily, ATV 300 mg/RTV 100 mg once daily, ATV 300 mg/RTV 50 mg once daily, ATV 200 mg/RTV 100 mg once daily, ATV 300 mg twice daily and ATV 200 mg twice daily.

Results

Study population

A total of 83 Caucasian HIV‐positive patients were included in the study. The mean adherence to treatment was 98.95%. A total of 53 and 30 patients were using boosted and unboosted ATV, respectively; 38 patients (of whom two were on unboosted ATV) were also taking TDF. Sixteen patients were taking the medication at night. The patient characteristics are summarized in Table 1. The observed concentration vs. time profiles for ATV and RTV are depicted in Figures 1 and 2, respectively.

Table 1.

Patients' demographic and clinical characteristics (n = 83)

Characteristic
Age, years	42 [26–75]
Gender, male, n (%)	57 (68.67)
Weight, kg	70 [40–91]
AST, U l –1	27 [11–185]
ALT, U l –1	30 [7–279]
Proteins in plasma, g dl –1	7.4 [6.3–8.7]
Albumin, g dl –1	4.3 [2.8–5.25]
α 1 ‐acid glycoprotein, mg dl –1	79 [36–156]
Boosted with RTV, n (%)	53 (63.85)
Treatment with TDF, n (%)	38 (45.78)
HCV coinfection, n (%)	30 (36.14)
Advanced liver fibrosis, n (%)	5 (6.02)

Values are expressed as median [range] unless specified otherwise. ALT, alanine aminotransferase; AST, aspartate aminotransferase; HCV, hepatitis C virus; RTV, ritonavir; TDF, tenofovir

Figure 1.

The red lines represent the 5th (lower dashed line), 50th (solid line) and 95th (upper dashed line) of the observed data (blue circles). The shaded areas represent the 90% confidence intervals of the 10th, 50th and 90th percentiles of the simulated data. TPD, time postdose (h)

Figure 2.

Observed plasma concentrations of patients receiving ritonavir. The red lines represent the 10th, 50th and 90th percentiles of the observed data (blue circles). The shaded areas represent the 95% confidence intervals of the 10th, 50th and 90th percentiles of the simulated data. TPD, time postdose (h)

Pharmacokinetic analysis

Basic and intermediate models for ATV

ATV plasma concentrations were best described by a one‐compartment model with first‐order absorption and elimination, with a transit absorption model. Interindividual variability in the absorption rate constant (k_a), the CL/F and the apparent volume of distribution (V/F) was described by an exponential model. The parameter estimates are listed in Table 2. Limited shrinkage was observed for the parameters: 2.6% for CL/F, 25% for V/F and 24% for k _a. The inclusion of interindividual or interoccasion variability in the bioavailability did not improve the model. No reduction in the OFV was achieved by using models with zero‐order absorption, nonlinear elimination, the incorporation of circadian variation of bioavailability or a relative bioavailability depending on whether ATV was boosted with RTV or not, and these models did not improve the goodness‐of‐fit plots. The assignment of a combined error model (additive and proportional) to describe the residual variability was adequate and none of the components (proportional or additive) had to be removed. We tested only weight (allometric function), concomitant medication with TDF as a binary covariate, concomitant medication with RTV as a binary or continuous (AUC _RTV) covariate, HCV coinfection (binary) and dose timing (morning or night) during the development of the intermediate model in NONMEM. Only AUC _RTV on CL/F _ATV remained in the model after this step. The decrease in CL/F _ATV was modelled as an exponential function of AUC _RTV.

Table 2.

Population pharmacokinetic parameter estimates for the basic and final models for atazanavir and ritonavir

Parameter	Basic model		Final model
	Parameter	RSE, %	Parameter	RSE, %
Atazanavir
k a , h −1	1.94	23.2	2.05	19.5
MTT, h	0.81	6.9	0.8	6.2
N transit	7	–	7	–
CL/F, l h −1	10.4	7.1	11.7	6.8
θ C(RTV),CL/F			0.296	3.5
V/F, l	91.0	6.0	95.7	6.5
IIV k a , %	202.5	26.1	200.2	22.4
IIV CL/F, %	63.2	17.5	57.4	18.1
IIV V/F, %	37.4	14.2	37.4	21.4
Residual error, %	27.8	10.7	27.0	7.4
Residual error, mg l −1	0.07	20.0	0.07	14.2
Ritonavir
k a , h −1	1.25	35.2	1.21	24.7
MTT, h	0.525	5.5	0.522	3.8
N transit	11	–	11	–
CL/F, l h −1	9.68	10.6	9.68	3.0
V/F, l	69.9	9.5	70.5	8.8
IIV k a , %	211.9	26.0	207.8	26.1
IIV CL/F, %	60.0	25.0	60.0	27.7
IIV V/F, %	47.0	31.8	49	29.1
Residual error, %	28.0	10.0	28.0	3.5

CL/F, apparent oral clearance; IIV, interindividual variability; k _a, first‐order absorption rate constant; MTT, mean transit time; N, number of transit compartments; RSE, relative standard error of estimation (estimation error divided by parameter estimate), expressed as a percentage; θ _C(RTV),CL/F, influence of ritonavir concentration on the atazanavir CL/F; V/F, apparent volume of distribution.

Basic and intermediate models for RTV

A one compartment model with first‐order absorption and elimination, and an exponential model for interindividual variability in k_a, CL/F and V/F best described RTV plasma concentrations (Table 2). A transit absorption model was used to describe the delay in the start of the absorption process. We saw no improvements in the OFV or goodness‐of‐fit plots when we constructed models with zero‐order absorption, nonlinear elimination or interindividual/interoccasion variability in the bioavailability. In addition, neither the use of two‐compartment models nor the inclusion of lag time led to improvements. The additive component of the initial combined error model used to describe the residual variability was negligible, and was deleted from the model. The shrinkage was limited, with values of 4.25 for CL/F, 21.3% for V/F and 22.1% for k _a. The inclusion of weight as an allometric function did not improve the OFV or the predictions, so this was not kept in the model. Although the exploratory plots and the GAM suggested that HCV coinfection may influence the V/F _RTV, its inclusion in the basic model did not significantly reduce the OFV, so it was not maintained in the model. The evaluation of dose timing (morning or night) in NONMEM did not reveal differences in CL/F, V/F or k _a.

Final model

Among the tested models to describe ATV and RTV plasma concentrations simultaneously, the one incorporating the the inhibition of CL/F_ATV by RTV according to an exponential model (Table 2) best described the data, with a decrease in the objective function value of 28 points with respect to the base model. The unrealistic parameter estimates of the I _max model, together with the bias observed with the linear interaction model, were the reasons for selecting the exponential model. The incorporation of a hepatic first‐pass model did not show any advantage over the exponential model.

Although the exponential model slightly underestimated the high ATV concentrations when boosted with RTV (Figure 3), it described the data for RTV adequately (Figure 4). The model predicted an 18% decrease in CL/F _ATV when the RTV plasma concentration is 0.63 mg l^–1 (the mean RTV concentration in this group of patients). The model also indicated that approximately 17.5% of the variability in CL/F _ATV could be explained by the effect of RTV concentrations.

Figure 3.

Goodness‐of‐fit plots of the final simultaneous model for atazanavir. (A) Observed concentrations vs. population‐predicted concentrations. (B) Observed concentrations vs. individual‐predicted concentrations. The thin lines in both panels represent the line of unity

Figure 4.

Goodness‐of‐fit plots of the simultaneous final model for ritonavir. (A) Observed concentrations vs. population‐predicted concentrations. (B) Observed concentrations vs. individual‐predicted concentrations. The thin lines represent the line of unity

The mean prediction error (expressed as a percentage) of the model at the end of the dosing interval (time postdose = 23–25 h), expressed as a percentage, was 11.40%.

Model validation

The visual predictive check of ATV concentrations when boosted or unboosted with RTV, shown in Figure 1, indicates that the final model provided an adequate fit for unboosted ATV and slightly underpredicted the maximum concentrations when ATV was boosted with RTV.

Figure 2 shows the visual predictive check for RTV concentrations. The plot indicated that the final model provided an adequate fit.

Simulations

The percentages of simulated patients whose ATV C_trough fell below 0.15 mg l^–1 or rose above 0.85 mg l^–1 are listed in Table 3. The simulations showed similar percentages of patients with ATV C_trough values below 0.15 mg l^–1 for all the once‐daily regimens. The twice‐daily regimens were associated with the lowest percentages of patients with C_trough values below 0.15 mg l^–1 but these regimens also had higher percentages of patients with C_trough values above 0.85 mg l^–1: more than 40% of patients had concentrations above the high cutoff, vs. fewer than 25% for the once‐daily regimens.

Table 3.

Percentages of patients predicted by the selected model to have an ATV C_trough below 0.15 mg l⁻¹ or above 0.85 mg l⁻¹ in the simulation of a thousand patients for each dosage scenario

Scenario	C trough <0.15 mg l −1 (%)	C trough >0.85 mg l −1 (%)
ATV 400 mg once daily	25.7	27.4
ATV 300 mg/RTV 100 mg once daily	24.5	26.2
ATV 300 mg/RTV 50 mg once daily	26.7	22.6
ATV 200 mg/RTV 100 mg once daily	30.3	16.6
ATV 200 mg twice daily	31.9	31.3
ATV 300 mg twice daily	24.5	29.8

ATV, atazanavir; C_trough, concentration at the end of the dose interval; RTV, ritonavir

Discussion

We have reported a one‐compartment simultaneous population pharmacokinetic model that describes the disposition of ATV and RTV in HIV‐1‐infected patients receiving boosted or unboosted ATV. This model incorporated the influence of RTV concentrations at each time point on CL/F _ATV and was used to simulate different dosing scenarios that have been, or could be, used in the clinical setting.

Our finding that this model best fitted ATV plasma concentrations is consistent with previously published results 17, 18, 20, 21, 31. The apparent CL/F _ATV estimated by our model when RTV is not present was 11.71 l h^–1, in line with the values reported in the cited papers. An added value of the present study was the inclusion of patients taking ATV with and without RTV, which enabled the pharmacokinetic parameters of ATV to be calculated appropriately, in the absence and presence of the booster, for the first time. We developed a direct exponential model that incorporated the inhibitory effect of plasma concentrations of RTV on CL/F _ATV, better to reflect the physiological understanding of this interaction. In fact, the incorporation of RTV plasma concentrations into this model explained 17.5% of the interindividual variability associated with CL/F _ATV. Up until now, only Schipani et al. 21 had tried a similar strategy but they described the relationship between the RTV plasma concentrations and ATV clearance using an E _max model. Although their model is similar to ours regarding ATV pharmacokinetics, RTV pharmacokinetics are modelled differently, probably related to the fact that Schipani et al. needed to incorporate a lag time in the absorption phase and fix k _a. We did not incorporate lag time in the absorption phase into our model, but rather used a more flexible function (transit compartments) and also allowed the value of k _a to be estimated. Some differences in the predictions made by the two models may have been related to our inclusion of patients taking their medication at night, which can be an advantage, whereas the model used by Schipani did not include such patients, and 16 of our patients took their medication on the night before the pharmacokinetic samples were obtained. Although we found no differences in the pharmacokinetics of RTV when taken in the morning or at night, we cannot rule out the possibility that our design, which reflects clinical conditions, might explain differences in the predictions of the two models. In any case, it is important to note that our model predicted an average reduction of 18% in ATV clearance when boosted with 100 mg of RTV. The same value that would be obtained if applying the model described by Schipanni et al., demonstrating that the differences found in the pharmacokinetics of RTV are not likely to have a clinical impact on the pharmacokinetics of ATV. The effect of RTV on ATV pharmacokinetics that we observed, however, was different from that reported by Foissac et al. 31 in children and adolescents. These authors found only a 45% reduction in ATV clearance when boosted with RTV compared with the value obtained in their patients who were not treated with RTV. However, as these authors did not measure RTV concentrations in that study, we cannot say whether the discrepancy between the two studies was due to real differences in the inhibition of RTV in adults in comparison with children and adolescents, or to differences in RTV exposure between these two populations.

The highest interindividual variability estimated in our model was associated with the ATV k _a, which confirms the findings of previous studies 17, 18, 20. The reasons for high variability include the lack of the intensive determinations of ATV plasma concentrations in the absorption phase, and the possible effect of food on the absorption process because food intake was only controlled on the day of extraction in patients taking their medication in the morning. Food intake around previous dosing times were not controlled for in these patients; food intake was also not controlled in patients taking their medication at night. Further studies, in which food intake is controlled for, should be performed to determine the causes of high interindividual variability in ATV absorption. Reducing unexplained interindividual variability in predictive models could be of great help in clinical settings, especially considering the recent results reported by Goutelle et al. 32, indicating that patients treated with ATV showing virological failure had lower k _a values than those without failure.

Some authors have described an increase in CL/F _ATV due to TDF coadministration in adults 19, 33 and in children or adolescents 31, although others have not found such a relationship 17, 18, 21. In our study, 36 out of the 38 patients taking TDF were using RTV‐boosted ATV, which might have offset the impact of TDF on ATV pharmacokinetics, a proportion that precluded exploring such an interaction in our model.

RTV disposition was also best described by our one‐compartmental model with first‐order absorption and elimination, consistent with previous studies 21, 34, 35, 36, 37, 38, 39, 40, 41. Considering the values of k _a reported for RTV when coadministered with LPV or darunavir (DRV) 34, 35, 41 and our results, the RTV k _a is not likely to be affected by the coadministered PI. However, in the RTV‐boosted ATV regimens in the present study, CL/F _RTV was almost half of the value reported for this parameter in RTV‐boosted LPV or DRV regimens, and therefore, plasma concentrations were higher 34, 35, 38, 41. The difference can probably be attributed to the effect of LPV and DRV as inducers of several CYP isoforms 42; ATV, on the other hand, acts only as an inhibitor. Although other studies have included liver fibrosis as a covariate responsible for part of the variability in CL/F _RTV 34, liver function was not found to be relevant in our study, probably because we included no patients with advanced liver fibrosis.

The main contribution of the present study was to describe ATV and RTV pharmacokinetics simultaneously, using a model that was able to simulate different scenarios to predict the best possible combination of these agents. This model is likely to be valid in clinical settings to help to predict ATV plasma concentrations for patients taking doses at night, or others for whom it is not convenient to give blood samples when concentrations need to be monitored (23–25 h after drug intake). In addition, given the increasing interest in lowering antiretroviral doses to attenuate adverse events, we used our model to predict ATV plasma concentrations when using different dose combinations of ATV and RTV. The model predicted that 32.7% of the patients treated with unboosted ATV (400 mg once daily) would have C_trough values below the recommended minimum effective concentration 43. Although this prediction was lower than the percentages observed in clinical settings 14, 16, 44, it should be noted that the concentrations we used to develop the model in the present study did not come from routine therapeutic drug monitoring but from a clinical trial; it is therefore likely that our patients' adherence was better. Based on our simulations, we can conclude that all the studied once‐daily regimens of ATV boosted with RTV would lead to fewer than 40% of patients with C_trough values under the minimum effective concentration. The main advantage of unlicensed once‐daily combinations of ATV and RTV regimens (ATV 300 mg/RTV 50 mg and ATV 200 mg/RTV 100 mg) is the expectation that the percentage of patients with C_trough values above 0.85 mg l^–1 (linked to ATV toxicity) would be lower than with the currently recommended ATV 300 mg/RTV 100 mg regimen. The second option (ATV 200 mg/RTV 100 mg) would be favoured by our model as the predicted percentage of patients with potentially toxic concentrations would be only 16.6%. These results are in line with previous suggestions to use these regimens in the clinical setting 21, 45, 46, 47 in the interest of decreasing bilirubin concentrations and improving lipid profiles. However, clinical trials should be performed to confirm the efficacy and safety of these regimens. Lower percentages of patients with C_trough values below 0.15 mg l^–1 were obtained with twice‐daily regimens of uboosted atazanavir than with once daily dosin; moreover, the twice daily regimens were associated with higher rates of patients with C_{trou gh} values above 0.85 mg l^–1. This strategy might therefore be associated with a greater risk of higher unconjugated bilirubin levels in the plasma. In fact, one trial in which ATV 300 mg was administered twice daily was stopped when safety was questioned owing to associated high rates of grade 3–4 bilirubin disorders 48. In a recent study, Bonora et al. 49 found no differences in total and unconjugated bilirubin concentrations or in lipid profile when a total daily dose of 400 mg ATV was administered as a single dose or as a twice‐daily dose of 200 mg. We would not recommend further clinical testing of either the ATV 300 mg or the ATV 200 mg twice‐daily regimens.

It is known that self‐reported adherence may be inflated, and that it does not make any reference to the exact time of drug intake. The measured concentrations in our study were higher than those reported in clinical drug monitoring programmes, so we were confident that the drugs were taken as prescribed. However, we cannot rule out that part of the large residual error of the model may be due to the lack of this information. The large residual error may have affected the predictions of the model, and clinical trials should be directed to determining the best dose regimen of ATV in patients (ATV 200 mg/RTV 100 mg one daily or ATV 300 mg/RTV 50 mg once daily).

In conclusion, a simultaneous population model describing the pharmacokinetics of ATV and RTV administered once daily to HIV‐1‐infected patients was developed and validated. The incorporation of the effect of RTV plasma concentrations on ATV disposition into the model allowed us to examine different hypothetical dosing regimens. The simulations suggested that ATV 300 mg/RTV 50 mg or ATV 200 mg/RTV 100 mg once daily could be tested in clinical trials. Bayesian estimates of individual ATV and RTV parameters, as provided by the model we developed, could be useful for individual predictions of the pharmacokinetic behaviour of boosted or unboosted ATV, including C_trough when needed as part of a therapeutic drug monitoring programme.

Competing Interest

All authors have completed the Unified Competing Interest form at www.icmje.org/coi_disclosure.pdf(available on request from the corresponding author) and declare: no support from any organization for the submitted work; no financial relationships with any organizations that might have an interest in the submitted work in the previous 3 years; no other relationships or activities that could appear to have influenced the submitted work.

The authors would like to thank all the patients who participated in the study, and the staff of the hospital in which the patients were treated. We would also like to thank Mary Ellen Kerans for reviewing the English in the last version of the manuscript. The study received funding from FIPSE, from ISCIII‐RETIC RD06/006 and from the ‘Lluita contra la SIDA’ Foundation – Gala contra la SIDA, Barcelona 2011. Javier Estévez was supported by a grant from the Spanish Ministry of Health, Project TRA‐076; he was also partially supported by the Alβan Program, the European Union Program of High Level Scholarships for Latin America (scholarship No.E06D101499CU). Marta Valle was supported by FIS trough grant CP04/00 121 from the Spanish Health Ministry in collaboration with Institut de Recerca de l'Hospital de la Santa Creu i Sant Pau, Barcelona; she is a member of CIBERSAM (funded by the Spanish Health Ministry, Instituto de Salud Carlos III).

Contributors

All authors had roles in the design and conduct of the study, collection and management of the data, and review and approval of the article. J.M., J.A.E. and M.V. also performed the analysis and interpretation of the data, and preparation of the paper.

Moltó, J. , Estévez, J. A. , Miranda, C. , Cedeño, S. , Clotet, B. , and Valle, M. (2016) Population pharmacokinetic modelling of the changes in atazanavir plasma clearance caused by ritonavir plasma concentrations in HIV‐1 infected patients. Br J Clin Pharmacol, 82: 1528–1538. doi: 10.1111/bcp.13072.