**DOI:**10.1128/AAC.46.3.746-754.2002

## ABSTRACT

Data from three pharmacokinetic drug interaction studies of amprenavir and ritonavir were used to develop a pharmacokinetic interaction model using NONMEM (nonlinear mixed-effect model). A two-compartment linear model with first-order absorption best fit the amprenavir data, while a one-compartment model was used to describe the ritonavir data. The inhibition of elimination of amprenavir by ritonavir was modeled with a maximum effect (*E*_{max}) inhibition model and the observed ritonavir concentration. Monte Carlo simulation was then used to predict amprenavir concentrations for various combinations of amprenavir and ritonavir in twice-daily and once-daily dosing regimens. Simulated minimum amprenavir concentrations in plasma (*C*_{min}) in twice-daily and once-daily dosing regimens were compared with protein binding-adjusted 50% inhibitory concentrations (IC_{50}s) for clinical human immunodeficiency virus isolates with different susceptibilities to protease inhibitors (central tendency ratios). The model based on the first two studies predicted the results of the third study. Data from all three studies were then combined to refine the final model. The observed and simulated noncompartmental pharmacokinetic parameters agreed well. From this model, several candidate drug regimens were simulated. These simulations suggest that, in patients who have clinically failed a traditional amprenavir regimen, a regimen of 600 mg of amprenavir with 100 mg of ritonavir twice daily would result in *C*_{min}-to-IC_{50} ratios similar to that of 1,200 mg of amprenavir twice daily alone for wild-type viruses. In addition, once-daily regimens that result in *C*_{min}s above the protein binding-corrected IC_{50}s for wild-type virus are clearly feasible.

Human immunodeficiency virus (HIV) protease inhibitors (PIs) in combination with reverse transcriptase inhibitors have prolonged and improved the quality of life for HIV-infected patients (2, 9, 10, 17, 21). Despite these advances, failure of therapeutic regimens to control viral replication is a major concern in the management of patients with HIV infection. Several factors are believed to contribute to this failure, including subtherapeutic drug concentrations resulting from drug interactions (22), adverse events (5), and poor adherence or nonadherence to the prescribed regimen because the regimens are complex and require frequent dosing with a large number of capsules (29).

A strong correlation between antiviral activity and the concentrations of PIs in plasma has been demonstrated in several studies (1, 7, 8, 18, 26, 28). Subtherapeutic concentrations of PIs in plasma can be associated with viral rebound and the development of drug resistance, indicating the importance of maintaining consistent drug concentrations in plasma (1, 7, 8, 18, 26, 28). A regimen that results in increased trough exposures could potentially provide therapy for patients with drug-resistant viruses and make once-daily (q.d.) dosing a feasible therapeutic option.

Amprenavir (Agenerase; formerly 141W94) is a recently introduced HIV PI. Like the other approved PIs, amprenavir is metabolized primarily by the hepatic cytochrome P450 enzyme system, specifically, CYP3A4 (J. Woolley, S. Studenberg, C. Boehlert, G. Bowers, A. Sinhababu, and P. Adams, Abstr. 37th Intersci. Conf. Antimicrob. Agents Chemother., abstr. A-60, 1997). All HIV PIs are substrates and inhibitors of CYP3A4, but the HIV PI ritonavir is the most potent inhibitor of CYP3A4 (Woolley et al., 37th ICAAC). Previous studies have indicated significant increases in drug exposure from coadministration of ritonavir with indinavir, saquinavir, and nelfinavir (12, 13, 18, 19, 22, 23, 30; D. Burger, P. Hugen, H. Hofstede, P. Koopmans, M. Stek, Jr., P. Reiss, and J. Lange, Abstr. 37th Intersci. Conf. Antimicrob. Agents Chemother., abstr. 321, 1999; Woolley et al., 37th ICAAC). The magnitude of pharmacokinetic interaction between ritonavir and amprenavir on coadministration was recently evaluated in a series of three randomized, two-sequence, multiple-dose studies with healthy subjects (25). Those studies demonstrated that ritonavir is a potent inhibitor of amprenavir metabolism and that addition of ritonavir (100 or 300 mg every 12 h) to amprenavir (450 or 900 mg every 12 h) resulted in clinically and statistically significant increases in the amprenavir area under the plasma concentration-versus-time curve (AUC) from time zero to 24 h (AUC_{0-24}) and minimum concentration in plasma (*C*_{min}).

In this report, we define a model using data from the first two studies (450 mg of amprenavir with 100 or 300 mg of ritonavir) and NONMEM for inhibition of amprenavir elimination by ritonavir. We then validated this model by prospectively estimating the pharmacokinetics of the combination of 900 mg of amprenavir plus 100 mg of ritonavir. Amprenavir data from all three interaction studies were used to develop the final model. This model was then used to assess different dosing regimens based on simulated *C*_{min}s by using Monte Carlo simulation for twice-daily (b.i.d.) and q.d. regimens and to determine regimens for clinical investigation with subject populations whose viruses have different susceptibilities to HIV PIs.

(This work was presented in part at the 7th Conference on Retroviruses and Opportunistic Infections, San Francisco, Calif., 30 January to 2 February 2000 [B. M. Sadler, P. J. Piliero, S. L. Preston, and D. S. Stein, Abstr. 7th Conf. Retrovir. Opportunistic Infect., abstr. G302e, 2000] and the 1st International Workshop on Clinical Pharmacology of HIV Therapy, Noordwijk, The Netherlands, March 2000 [M. Sole, D. S. Stein, and B. Sadler, Abstr. 1st Int. Workshop Clin. Pharmacol. HIV Ther., abstr. 5.2, 2000].)

## MATERIALS AND METHODS

Study population and design.The study design and criteria for study participation have been described in a previous publication (25). Briefly, subjects were eligible for study entry if they were 18 to 55 years of age and were seronegative for HIV (confirmed by standard methodologies). Each of the three multiple-dose, open-label, randomized, two-sequence, crossover drug-drug interaction studies (Glaxo Wellcome protocols PRO10017, PRO10022, and PRO10023) was conducted at a single center in the United States.

In each study, 18 subjects were randomly assigned to receive one of two treatment sequences (nine subjects per sequence) in a two-period, one-way crossover design. In the first study (PRO10017), 450 mg of amprenavir every 12 h (b.i.d.) alone (sequence 1) or 300 mg of ritonavir b.i.d. alone (sequence 2) was administered for 7 days. For the following 7 days, all subjects received both amprenavir and ritonavir at these same doses. In the subsequent two studies, the study design remained the same but a regimen of 450 mg of amprenavir b.i.d. and 100 mg of ritonavir b.i.d. (PRO10022) or a regimen of 900 mg of amprenavir b.i.d. and 100 mg of ritonavir b.i.d. (PRO10023) was investigated. All data from both sequences were used in the analysis.

All subjects provided written informed consent to participate in the trials. All study protocols were reviewed and approved by the institutional review board at each of the study sites.

Blood sampling and amprenavir and ritonavir assays.Blood samples for the determination of plasma amprenavir and ritonavir concentrations were collected on days 1, 7, and 14. Seventeen samples were collected between predosing and 24 h postdosing on day 1, and 15 samples were collected between predosing and 12 h postdosing on days 7 and 14. Details of the sampling and analysis methods have been described previously (25).

Data analysis.Traditional noncompartmental analyses of the data and clinical safety evaluations are reported in a separate publication (25).

Pharmacokinetic modeling.Plasma concentration-time data from each treatment sequence in each study were used to fit a standard linear compartmental model by using the nonlinear mixed-effects model software package NONMEM (version 5) (27). NONMEM was used to describe the interaction between amprenavir and ritonavir and simulate selected amprenavir pharmacokinetic parameters (maximum concentration of drug in plasma [*C*_{max}], AUC_{0-24}, and *C*_{min}) for b.i.d. and q.d. dosing regimens of amprenavir in combination with ritonavir. NONMEM was developed independently for amprenavir and ritonavir. Models were built by forward addition at the *P* < 0.05 significance level and backward elimination at the *P* < 0.01 significance level by a log likelihood test.

Amprenavir model.A standard two-compartment, first-order absorption model was found to describe the data well. The final pharmacokinetic model for amprenavir included the effects of the observed ritonavir concentration on the elimination rate. The central volume of distribution (*V*/*F*) was found to be a function of weight and α_{1}-acid glycoprotein (AAG) concentration. All parameters included log-normal interindividual error terms. The absorption rate constant (*K _{a}*),

*V*/

*F*, and the transfer rate constants between the central and peripheral compartments (

*K*

_{23}and

*K*

_{32}) were modeled separately for days 1 and 14. It cannot be determined if these effects are dependent on time or on the administration of ritonavir. The effect on

*K*,

_{a}*V*/

*F*

_{,}

*K*

_{23}, and

*K*

_{32}was small. The equations for the parameters for the amprenavir model are given below: $$mathtex$$\[\mathit{K}_{\mathit{a}}{=}{\theta}_{1}\ {\cdot}\ \mathit{e}^{{\eta}_{1}}\]$$mathtex$$$$mathtex$$\[\mathit{K}{=}{\theta}_{2}\left(1{-}\frac{{\theta}_{6}\ {\cdot}\ RTV\ }{{\theta}_{7}{+}RTV}\right)\ {\cdot}\ \mathit{e}^{{\eta}_{2}}\]$$mathtex$$$$mathtex$$\[\mathit{V}/\mathit{F}{=}{\theta}_{3}\ {\cdot}\ \mathit{e}^{{\theta}_{9}\ [(AAG\ {-}70)/70]}\ {\cdot}\ \mathit{e}^{{\theta}_{10}[(WT\ {-}70)/70]}\ {\cdot}\ \mathit{e}^{{\eta}_{3}}\]$$mathtex$$$$mathtex$$\[\mathit{K}_{23}{=}{\theta}_{4}\ {\cdot}\ \mathit{e}^{{\eta}_{5}}\]$$mathtex$$$$mathtex$$\[\mathit{K}_{32}{=}{\theta}_{5}\ {\cdot}\ \mathit{e}^{{\eta}_{6}}\]$$mathtex$$$$mathtex$$\[Lag\ {=}\ {\theta}_{8}\ {\cdot}\ \mathit{e}^{{\eta}_{4}}\]$$mathtex$$ where

*K*is the elimination rate constant; AAG is the AAG concentration (in milligrams per deciliter); Lag is the absorption lag time; RTV is the observed ritonavir concentration (in micrograms per milliliter); and η

_{1}, η

_{2}, and η

_{3}are log-normal interindividual error terms. Weight (WT) was expressed in kilograms. The maximum effect value (

*E*

_{max}; θ

_{6}) was constrained to be less than or equal to 0.99.

Ritonavir model.Because ritonavir concentrations were found to be a significant factor in the final amprenavir model, a population-based model of ritonavir concentrations was also developed and provided input to the amprenavir model during Monte Carlo simulations. Pharmacokinetic data obtained after 14 days of dosing only were used to develop the ritonavir model. This should reflect steady-state dosing. In the initial model developed with data from the first two studies, ritonavir pharmacokinetics were also well described by a two-compartment linear model with first-order absorption and an absorption lag time. In the final model (data from all three studies), a second compartment was not statistically supported by the data. The final pharmacokinetic model for ritonavir included the effects of dose on *K _{a}* and bioavailability (

*F*

_{1}; relative bioavailability of the 300-mg dose compared to that of the 100-mg dose), the effects of age on

*K*, and the effects of sex and weight on the volume of distribution (

*V*).

*K*,

_{a}*K*, and

*V*included log-normal interindividual error terms (η

_{1}, η

_{2}, and η

_{3}, respectively). It should be noted that the effect of dose on

*F*could as well have been applied to

*V*/

*F*. However, it was believed to be biologically more reasonable to have a dose effect on

*F*

_{1}than on

*V*/

*F*. The results of the subsequent simulation would have been identical in either case. The equations for the ritonavir model are given below: $$mathtex$$\[\mathit{K}_{\mathit{a}}{=}({\theta}_{1}\ {\cdot}\ \mathit{e}^{{\theta}_{6}\ {\cdot}\ Dose_{300}})\ {\cdot}\ \mathit{e}^{{\eta}_{1}}\]$$mathtex$$$$mathtex$$\[\mathit{K}{=}({\theta}_{2}\ {\cdot}\ \mathit{e}^{\frac{{\theta}_{7}\ {\cdot}\ (Age\ {-}40)}{40}})\ {\cdot}\ \mathit{e}^{{\eta}_{2}}\]$$mathtex$$$$mathtex$$\[\mathit{V}{=}{\theta}_{3}\ {\cdot}\ WT\ {\cdot}\ e^{\mathrm{{\theta}}_{8}\ {\cdot}\ GEN\ }\mathit{e}^{{\eta}_{3}}\]$$mathtex$$$$mathtex$$\[Lag_{1}\ {=}\ {\theta}_{4}\]$$mathtex$$$$mathtex$$\[\mathit{F}_{1}{=}<\mathit{mdit}>\mathit{e}^{{\theta}_{5}\ {\cdot}\ Dose_{300}}\]$$mathtex$$ Weight (WT) and age (Age) were expressed in kilograms and years, respectively. Sex was coded as a dichotomous variable (1 = female; 0 = male). The variable Dose

_{300}was also coded as a dichotomous variable (1 = 300 mg; 0 = 100 mg) and was used to estimate the dose-dependence in

*K*and

_{a}*F*

_{1}between the 100- and 300-mg doses. The residual error (σ) was best expressed in terms of a constant coefficient of variation (ε

_{1}) of the predicted concentration () plus a simple additive error term (ε

_{2}).

Monte Carlo simulation.Simulations were performed by using a composition of the amprenavir and ritonavir models. The ritonavir model was used to simulate ritonavir concentrations, which where then used to calculate the amprenavir *K*. Weight and AAG concentration were simulated from distributions derived from the study data. Sex was equally distributed between men and women. The value of Dose_{300} was 0 for 100 mg, 0.5 for 200 mg, and 1 for 300 mg. Pharmacokinetic parameters from day 14 were used for the amprenavir model.

Sensitivity analyses.The concentration of ritonavir that results in 50% of the maximum inhibition (*K _{m}*) predicted by the model was 0.0122 μg/ml. This is below the smallest observed concentration of ritonavir (0.028 μg/ml) in any of the three studies, suggesting that the inhibition of elimination of amprenavir was essentially saturated in all subjects for the duration of the b.i.d. dosing interval. Because of the lack of data near the

*K*, this value was in question. Log likelihood plots were constructed to test the range of values for

_{m}*K*that were consistent with the observed data.

_{m}Model validation.The initial model was developed with data from studies PRO10017 and PRO10022. These studies included doses of 450 mg of amprenavir plus 100 mg of ritonavir b.i.d. and 450 mg of amprenavir plus 300 mg of ritonavir b.i.d.. The results from this analysis were then used to predict the outcome of study PRO10023 (900 mg of amprenavir plus 100 mg of ritonavir b.i.d.). When the simulations and prediction for PRO10023 were done, the study had not yet been completed and no data were available. The two endpoints of interest were AUC_{0-24} and *C*_{min}. The AUC_{0-24} predicted by the simulations was within 3.9% of the observed value (48.95 ng · h/ml predicted versus 47.71 ng · h/ml observed), and the *C*_{min} was within 19.4% (2.95 ng/ml predicted versus 2.47 ng/ml observed). The final simulations were based on the analysis of data from all three studies.

*C*
_{min}-to-protein binding-adjusted IC_{50} ratio central tendency estimates.Amprenavir *C*_{min}s obtained from simulated pharmacokinetic parameters for the b.i.d. and q.d. dosing regimens of amprenavir in combination with ritonavir were compared with protein binding-adjusted 50% inhibitory concentrations (IC_{50}s) for clinical viral isolates from PI-naïve and -experienced patients to determine if the amprenavir *C*_{min} would exceed the IC_{50}s for the viral isolates.

The distribution of the ratios of *C*_{min} to IC_{50} in the population was calculated by resampling from the observed IC_{50}s for the viral isolates and the observed *C*_{min}s (for 1,200 mg b.i.d.) or the simulated *C*_{min}s (for 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. and 1,200 mg of amprenavir plus 200 mg of ritonavir q.d.). The ratios were adjusted for the ∼90% protein binding of amprenavir. Phenotypic assays for IC_{50} were performed by Virco NV (Mechelen, Belgium) by the method of Hertogs et al. (11) to determine the amprenavir IC_{50} for the viral isolates. The three populations used were wild-type isolates (*n* = 334; IC_{50} = 14.6 ± 12.5 ng/ml), isolates from patients clinically described as first-time amprenavir failures (*n* = 36; IC_{50} = 61.4 ± 83.9 ng/ml), and isolates from patients described clinically as multiple PI failures (*n* = 328; IC_{50} = 90.3 ± 84.6 ng/ml).

## RESULTS

Study population.The demographic and baseline characteristics for the subjects enrolled in each study were comparable between the studies and have been described previously (25).

Pharmacokinetic modeling.The initial model, based on data from the first two studies, was revised with the data from the third study. In the full data set, a two-compartment model for ritonavir was not statistically supported by a log likelihood test, and so a one-compartment model was used. A two-compartment model was once again supported for amprenavir. The pharmacokinetic parameter estimates of the models for amprenavir and ritonavir are presented in Table 1.
In the amprenavir model, weight and AAG were found to have an effect on *V*. *K* was found to be dependent on the (observed) ritonavir concentration by the (*E*_{max}) relationship:
$$mathtex$$\[\mathit{K}{=}0.50\ h^{{-}1}\ {\cdot}\ \left(1{-}\ \frac{0.663\ {\cdot}\ RTV\ }{0.0122{+}RTV\ }\right)\]$$mathtex$$
where RTV is the (observed) ritonavir concentration (in micrograms per milliliter).

In the ritonavir model, *K _{a}* and

*F*

_{1}were both found to be dose dependent. The estimates of

*K*for the 100- and 300-mg doses were 1.31 and 2.81 h

_{a}^{−1}, respectively. The relative

*F*

_{1}of the 300-mg dose of ritonavir was 108% greater than that of the 100-mg dose. The value of

*K*increased with age. The values of

*K*for typical subjects 20 and 40 years of age were 0.160 and 0.198 h

^{−1}, respectively. Despite their covariance, both sex and body weight had a significant effect on

*V*.

*V*was 32% lower in women than in men at any given body weight. The average weights of the men and women in the present study were 76.6 and 67.2 kg, respectively. If these body weights are used as typical values for men and women, respectively, the typical

*V*in women is lower than that in men by 40%. This effect was not confounded with the effect of ritonavir. The interindividual variability terms (OMEGAs) are provided in Table 2.

Sensitivity analysis.A likelihood plot for the value of *K _{m}* was constructed and showed that the upper limit of the 95% confidence interval is approximately 0.035 μg/ml (Fig. 1).
This confidence interval is wider than that suggested by the standard error of the estimate from NONMEM. A second analysis examined the impact of misestimation of the

*K*on the simulation outcomes. In this analysis the (fixed) value of

_{m}*K*was varied and the other parameters of the model were then estimated in NONMEM. The resulting parameter values were then used for simulation and the effect on

_{m}*C*

_{min}was assessed. Figures 2A and B show the sensitivity of

*C*

_{min}to

*K*for 100, 200, or 300 mg of ritonavir q.d. plus 900 mg or 1,200 mg of amprenavir q.d. These plots suggest that there is a dose-response relationship for the effect of ritonavir on the amprenavir

_{m}*C*

_{min}. However, the additional effect of increasing the dose from 200 to 300 mg is less than the effect of increasing the dose from 100 to 200 mg. This is consistent with the

*K*value of 0.0122 ng/ml for ritonavir inhibition of amprenavir elimination.

_{m}Simulations.The mean concentration-versus-time curves for amprenavir at steady state derived from pharmacokinetic parameters of amprenavir plus ritonavir given b.i.d. and q.d. in simulated subjects is presented in Fig. 3 and 4, respectively. The simulations for amprenavir were compared with pooled estimates of observed pharmacokinetic parameters for the 1,200-mg dose of amprenavir b.i.d. from three Glaxo Wellcome-sponsored steady-state studies (PROA1002, PROA1012, and PROA1013; total *n* = 43). The observed and simulated pharmacokinetic parameters agreed well, but the simulated *C*_{max} was lower than the observed values (Table 3). The pharmacokinetic simulations indicated that 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. results in a *C*_{min} that is approximately threefold greater and an AUC that is approximately 40% higher than those for amprenavir (b.i.d.) alone. Regimens of 900 and 1,200 mg of amprenavir plus 200 mg of ritonavir q.d. resulted in *C*_{min}s that were approximately 50% higher and twofold greater and AUCs that were equal to and 15% higher, respectively, than those for amprenavir at 1,200 mg b.i.d. alone.

Figure 5
shows the variability in *C*_{min}-to-amprenavir IC_{50} central tendency ratios for wild-type and PI-resistant clinical isolates following adjustment of the IC_{50} for the observed 90% protein binding of amprenavir. Figure 5 suggests that a regimen of 1,200 mg of amprenavir plus 200 mg of ritonavir q.d. will typically result in a higher ratio of *C*_{min} to IC_{50} for wild-type virus than a regimen of 1,200 mg of amprenavir b.i.d. alone will. A comparison of the *C*_{min} for the combination of 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. with the IC_{50}s for different virus populations demonstrated central tendency ratios (ranges) for wild-type viral isolates, viral isolates from patients with first-time amprenavir failures, and viral isolates from patients with multiple PI failures of 11.3 (1.63 to 67.9), 3.52 (0.322 to 51.3), and 0.98 (0.143 to 10.3), respectively. A regimen of 1,200-mg amprenavir b.i.d. alone for wild-type virus gave a ratio of 3.05 (range, 0.687 to 14.6). A regimen of 1,200 mg of amprenavir plus 200 mg of ritonavir q.d. gave a ratio for wild-type virus of 6.66 (range, 0.68 to 50.2).

## DISCUSSION

The *C*_{min}-to-protein binding-adjusted IC_{50} ratio has been hypothesized as a useful metric for describing the likely efficacy of a given antiviral regimen for a given virus (3; D. S. Stein, Y. Lou, M. Johnson, and S. Randall, Abstr. 2nd Int. Workshop Clin. Pharmacol. HIV Ther., abstr. 5.6, 2001). In this study, pharmacokinetic modeling demonstrated that a simulated regimen of 600 mg of amprenavir plus 100 mg of ritonavir administered b.i.d. provides amprenavir *C*_{min}-to-protein binding-adjusted IC_{50} ratios substantially above those for the 1,200-mg dose of amprenavir b.i.d. alone for wild-type viruses. Furthermore, the simulations suggest that the regimen of 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. results in a *C*_{min}-to-protein binding-adjusted *C*_{min}-to-protein binding-adjusted IC_{50} ratio for viral isolates from patients who have clinically failed traditional amprenavir therapy that is similar to that of amprenavir alone for wild-type virus. A simulated q.d. regimen of 1,200 mg of amprenavir plus 200 mg of ritonavir also gave rise to *C*_{min}s that were higher than those observed with regimens known to be effective against wild-type virus. The AUCs of these simulated regimens were between equivalent to and 40% above those obtained with 1,200 mg of amprenavir b.i.d. alone.

The *K _{m}* estimated in our model for ritonavir was 0.0122 μg/ml (total concentration). This is in reasonable agreement with the range of

*K*or

_{m}*K*values reported for ritonavir in in vitro investigations under various experimental conditions (14). Koudriakova et al. (14) calculated a ritonavir

_{i}*K*of 0.068 μM (total concentration, 0.034 ng/ml) for expressed CYP3A4 and a value of 0.063 ± 0.045 μM in microsomes. They noted that ritonavir's inhibitory effect lasted well after its removal, indicating that ritonavir inactivated CYP3A4. Kumar et al. (16) calculated a

_{m}*K*of 0.08 μM (0.040 ng/ml) for the formation of ritonavir's primary CYP3A4 metabolite, M1. Ritonavir has a

_{m}*K*of 0.013 μM (0.0066 ng/ml) for inhibition of metabolism of ABT-378, another HIV PI (15), and has

_{i}*K*values of 0.017 μM (0.008 ng/ml) for terfenadine (16) and 0.019 μM (0.009 ng/ml) for testosterone (6), which are classic CYP3A4 substrates. All concentrations are given as total concentrations. The level of protein binding of ritonavir in plasma is high (∼98%). The protein binding in the medium used for these in vitro estimates of

_{i}*K*and

_{m}*K*is not known. However, differences in free drug concentration could bias these comparisons.

_{i}As the calculated *K _{m}* affects the model predictions of different regimens, we conducted a sensitivity analysis to further explore this source of variability. This sensitivity analysis indicated that for a wide range of

*K*values the greatest effect (sensitivity to

_{m}*K*) occurred in the simulated q.d. regimens. It is for this reason that we would not currently recommend the use of q.d. regimens with less than 200 mg of ritonavir.

_{m}The pharmacokinetic profiles of PIs show variability among different patients, leading to low *C*_{min}s in some patients (4, 7, 20). Multiple studies have found a relationship between *C*_{min} or average exposure (i.e., AUC) and antiviral activity or time to the development of resistance for PIs. Prior studies of indinavir, saquinavir, and amprenavir have all demonstrated that the relationships of AUC or *C*_{min} to antiviral activity are well described by a sigmoid *E*_{max} curve. For both indinavir and amprenavir the plateau of the relationship occurs at average exposures at or above the protein binding-adjusted average IC_{50} for the viral population. This suggests that maintenance of a concentration above the IC_{50} could lead to a better overall antiviral effect and possibly better long-term suppression of virus. The lower limit of the 95% confidence interval for the amprenavir concentration in the regimen of 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. was 0.264 μg/ml. This value is above the mean (protein binding-adjusted) IC_{50} for wild-type virus examined in this study (0.146 μg/ml).

In the traditional analysis of the three pharmacokinetic drug interaction studies (25), the addition of 100 or 300 mg of ritonavir b.i.d. to 450 mg of amprenavir b.i.d. resulted in statistically significant increases in the amprenavir *C*_{min} and AUC compared with those achieved when amprenavir was administered alone. The modeling clearly showed that this is due to a decrease in elimination of amprenavir. In the present study, sensitivity analyses with simulations of the effect of the predicted amprenavir *C*_{min} on variable ritonavir *K _{m}* values calculated that the maximum reduction in amprenavir clearance was 66%. A 66% magnitude of inhibition was predicted to be maintained throughout a 24-h dosing interval if the

*K*value is <0.001, but no inhibition would occur throughout this interval if

_{m}*K*was >0.1. Between these values of

_{m}*K*(which includes the point estimate for

_{m}*K*), the 200-mg dose of ritonavir would be expected to sustain a greater and longer duration of inhibition of amprenavir clearance than the 100-mg dose of ritonavir, but it would be less than that seen with the 300-mg dose. This expectation is highly dependent on the estimate of the concentration at the site of effect that causes 50% of the maximal effect.

_{m}Several sources of potential bias exist in this analysis. First, the assumption of the model was an *E*_{max} inhibition of the elimination of amprenavir by ritonavir. This model fit the data best. However, in vitro work has suggested a persistent or even irreversible inhibition of cytochrome P450 CYP3A4 activity. Attempts to construct a model based on this assumption were unsuccessful. These models were unsuccessful either because they were not numerically stable or the model did not fit the data as well as a traditional *E*_{max} model did. It should be noted that if the effect of ritonavir were persistent rather than instantaneous, as assumed in this model, the results presented here would underestimate the magnitude of the effect for the q.d. dosing. The actual *C*_{min} would be expected to be even higher than the concentration suggested by this model, presumably with more antiviral activity. Preliminary clinical data obtained with a regimen of 1,200 mg of amprenavir and 200 mg of ritonavir q.d. in HIV-infected subjects indicate that *C*_{min}s are higher than those predicted by the conservative assumptions of our model, suggesting some degree of persistence of the effect of ritonavir on amprenavir clearance in vivo (R. Wood, C. Trepo, J. M. Livrozet, K. Arasteh, J. Eron, P. Kaur, O. Naderer, and M. B. Wire, 8th Conf. Retrovir. Opportunistic Infect., poster 332, 2001).

Another potential source of bias is the possibility that amprenavir affects the metabolism of ritonavir. Given the study design, this effect could not be distinguished from a time effect on ritonavir clearance, which is known to occur. However, if the *K _{m}* of the interaction is as small as is suggested by these analyses, this effect should be small since the effect of ritonavir on amprenavir is already nearly saturated. Finally, the clinical studies suggested that the 100- and 300-mg b.i.d doses of ritonavir had very similar effects on amprenavir clearance. In fact, study PRO10017 suggested that the concentrations of amprenavir when given with 100 mg of ritonavir b.i.d. would be higher than those seen when amprenavir was given with 300 mg of ritonavir. The model used here (

*E*

_{max}inhibition of clearance) would not permit a lower dose (100 mg) to have a larger effect than the higher dose (300 mg). Instead, the model suggests that the concentrations achieved with either dose nearly saturate the inhibition. Hence, in the final simulations, the concentrations simulated with the 300-mg dose of ritonavir are slightly higher than those seen with the 100-mg dose.

It should be noted that healthy volunteers have a fairly constant AAG concentration, and that concentration is significantly lower than those in HIV-positive patients. The model suggested that AAG influences *V*. This is likely related to the binding of amprenavir to AAG, reducing the free fraction available for diffusion into tissues outside the plasma. No effect of AAG is seen on elimination, which is where the effect of ritonavir is seen. Therefore, we believe that differences in AAG concentrations should not preclude extrapolation of these results to HIV-positive patients. Other studies have shown that the AAG concentration does not affect the free drug concentration (but does affect the total drug concentration and free fraction [24]).

In summary, NONMEM analysis and Monte Carlo simulation were used to predict the pharmacokinetic parameters of amprenavir in the presence of ritonavir. A combination of 600 mg of amprenavir plus 100 mg of ritonavir b.i.d. is predicted to result in clinically and statistically significant increases in amprenavir *C*_{min}s. This combination has the potential to reduce the pill count from 16 to 10 capsules per day, which may reduce the adherence problems observed with some patients. In addition, the potential exists to enhance efficacy in salvage regimens, particularly against PI-resistant virus, as a result of the increase in *C*_{min} above that obtained with the 1,200-mg dose of amprenavir b.i.d. alone. In the case of patients who have failed a traditional amprenavir regimen, these simulations suggest that a regimen of 600 mg of amprenavir with 100 mg of ritonavir b.i.d. would restore the *C*_{min}-to-IC_{50} ratio to a value similar to that achieved with 1,200 mg of amprenavir b.i.d. alone for wild-type viruses. Regimens of 900 or 1,200 mg of amprenavir q.d. in combination with 200 mg of ritonavir q.d. were also predicted to give trough concentrations comparable to those achieved with the approved 1,200-mg dose of amprenavir b.i.d. alone. These regimens could offer the potential of a further reduction in pill burden and the advantage of less frequent dosing. Clinical studies are in progress to evaluate the pharmacokinetics, efficacies, and safety profiles of different doses of amprenavir in combination with ritonavir for b.i.d. and q.d. regimens. Clinicians should exercise appropriate caution if they are basing their dosing regimens for HIV-positive subjects on a model derived from studies conducted with healthy volunteers.

## ACKNOWLEDGMENTS

We thank Michael Maguire and Sharon Randall for assistance with the virology and Terry R. Paul for writing and editorial assistance with the manuscript.

## FOOTNOTES

- Received 12 January 2001.
- Returned for modification 1 August 2001.
- Accepted 26 November 2001.

- Copyright © 2002 American Society for Microbiology