Race/Ethnicity and Protease Inhibitor Use Influence Plasma Tenofovir Exposure in Adults Living with HIV-1 in AIDS Clinical Trials Group Study A5202

AIDS Clinical Trial Group study A5202 (ClinicalTrials.gov identifier NCT00118898) was a phase 3b, randomized, partially blinded equivalence study of open-label atazanavir/ritonavir or efavirenz, plus either placebo-controlled tenofovir disoproxil fumarate/emtricitabine or abacavir/lamivudine, in treatment-naive adults living with HIV-1, evaluating efficacy, safety, and tolerability. We report an analysis of the contribution of participant characteristics to the disposition of tenofovir plasma concentrations.

ABSTRACT

AIDS Clinical Trial Group study A5202 (ClinicalTrials.gov identifier NCT00118898) was a phase 3b, randomized, partially blinded equivalence study of open-label atazanavir/ritonavir or efavirenz, plus either placebo-controlled tenofovir disoproxil fumarate/emtricitabine or abacavir/lamivudine, in treatment-naive adults living with HIV-1, evaluating efficacy, safety, and tolerability. We report an analysis of the contribution of participant characteristics to the disposition of tenofovir plasma concentrations. Tenofovir concentration data from a total of 817 individuals (88% of the total number of eligible patients randomly assigned to receive treatment in the TDF-containing arms of A5202) were available for analysis. Pharmacokinetic analysis was performed using nonlinear mixed-effects modeling. One- and two-compartment models with first-order absorption and first-order elimination were evaluated. An exponential error model was used for examination of interindividual variability (IIV), and a proportional and mixed-error model was assessed for residual variability. The final structural model contained two compartments with first-order absorption and elimination. IIV was estimated for apparent clearance (CL/F) and the first-order absorption rate constant (k_a), and a proportional residual variability model was selected. The final mean parameter estimates were as follows: k_a = 2.87 h⁻¹, CL/F = 37.2 liters/h, apparent volumes of the central and peripheral compartments = 127 and 646 liters, respectively, and apparent intercompartmental clearance = 107 liters/h. In addition to race/ethnicity, creatinine clearance and assignment to atazanavir/ritonavir or efavirenz were significantly associated with CL/F (P < 0.001). In conclusion, race/ethnicity is associated with tenofovir oral CL in HIV-1 positive, treatment-naive adults. This covariate relationship raises questions about the possibility of differences in efficacy and risk of adverse events in different patient populations and suggests that examining preexposure prophylaxis regimens and tenofovir exposure in different race/ethnicity groups be considered.

INTRODUCTION

Tenofovir disoproxil fumarate (TDF) is an adenosine-analog nucleotide reverse transcriptase inhibitor (NRTI) prodrug that exhibits activity against HIV-1 and hepatitis B virus infections. TDF is converted to its active intracellular form, tenofovir diphosphate, in a stepwise manner: (i) TDF is converted to tenofovir (TFV) in the intestinal lumen and plasma by diester hydrolysis, and (ii) TFV is internalized intracellularly and subsequently phosphorylated into tenofovir monophosphate and then to its active metabolite, tenofovir diphosphate (1, 2). Tenofovir has been examined in those living with HIV and healthy volunteers and has demonstrated that renal function and concomitant use with ritonavir-boosted HIV-1 protease inhibitors affect plasma TFV concentrations (3–6).

The AIDS Clinical Trials Group study A5202 (ClinicalTrials.gov identifier NCT00118898) randomly assigned 1,857 treatment-naive HIV-1-infected adults to one of the following once-daily regimens: open-label atazanavir and ritonavir (ATV/r; 300/100 mg) or efavirenz (EFV; 600 mg), plus either placebo-controlled tenofovir disoproxil fumarate/emtricitabine (TDF/FTC; 300/200 mg) or abacavir/lamivudine (ABC/3TC; 600/300 mg). Plasma concentration data for each of the antiretrovirals were collected from the majority of study participants for further investigation of differences in the pharmacokinetics of subpopulations. Included in the prespecified pharmacology-related secondary objectives was the exploration of the association of ethnicity and other host factors with the disposition of antiretroviral (ARV) agents. It is critical to determine whether clinically relevant differences in ARV drug exposure exist in potential patient subpopulations, since variability in drug exposure may be associated with differences in ARV drug toxicity and virologic response. In this report, we investigated TFV pharmacokinetics using sparse sampling and population pharmacokinetic modeling to conduct a covariate analysis in exploration of significant host factors that may play a role in the time course of TFV exposure.

RESULTS

Pharmacokinetic data from a total of 817 individuals (88%) were available for analysis. The majority of participants had 3 samples drawn (range, 1 to 5), with a total of 2,166 evaluable plasma concentrations within approximately 6 months of beginning antiretroviral treatment. Information on the previous 3 days of TDF dosing prior to pharmacokinetic sampling was available for 98% of the 2,166 evaluable plasma concentrations, in which 42 and 18 sample collections reported a 2-day difference between the dose prior to sampling and the second dose prior to sampling and between the second and third dose prior to sampling, respectively. One participant reported a 3-day window between the dose prior to sampling and the second dose prior to sampling.

Population pharmacokinetic model.

A two-compartment model with first-order absorption and elimination was ultimately the most appropriate choice to describe the data. A mixture model identified a subpopulation with large residual variability (n = 30), and a total of 78 observations were removed from the data set for model building. The demographics of the remaining participants (n = 787) used in the pharmacokinetic analysis are given in Table 1. The final model included interindividual variability (IIV) terms on apparent clearance (CL/F) and the first-order absorption rate constant (k_a), and a proportional model was selected for residual variability. The base model was able to accommodate IIV on k_a in addition to CL/F, but the only covariate that was biologically plausible to affect the absorption rate constant (i.e., age) was not significant. Whereas IIV on k_a and CL/F during forward selection would not allow estimation of race/ethnicity as a covariate on CL/F with 1 or 2 degrees of freedom, forward selection was continued with IIV on CL/F only, and IIV on k_a was added during the multivariable evaluation. This allowed for greater precision of parameter estimates, clinically valuable covariate information to be included in the model, and retention of IIV on k_a. In the final model, the IIV variability on CL/F and k_a were 18% and 85% (% coefficient of variation [% CV]), with information on covariate model development summarized in Table 2. The eta distribution associated with the absorption rate constant had moderate asymmetrical shrinkage (57%) due to missing data in the absorption phase.

TABLE 1.

Demographics of study participants

Demographic	Value (n = 787)a
Treatment arm (3rd drug), no. (%) of participants
ATV/r	387 (49)
EFV	400d (51)
Sex, no. (%) of participants
Female	127 (16)
Male	660d (84)
Race/ethnicity, no. (%) of participants
White (non-Hispanic)	339d (43)
Black (non-Hispanic)	236 (30)
Hispanic	190 (24)
Asian	14 (2)
American Indian/Alaskan	3 (0.4)
Multiracial	5 (1)
Age (yr), median (Q1, Q3)b	39 (31, 45)
Wt (kg), median (Q1, Q3)c	77.3 (68.2, 88.8)
CLCR (ml/min), median (Q1, Q3)c	113.7 (97.4, 133.6)

^aPercentages are rounded to the nearest whole number; Q₁ and Q₃ represent the 1st and 3rd quartiles, respectively.

^bThree subjects had no age reported, so the mean was used (38.9 years).

^cOne subject had no CL_CR or weight data, so the means were used (117.9 ml/min and 79.5 kg, respectively).

^dFour subjects had no race/ethnicity reported and three subjects had no sex or third drug reported, so the mode was used for all three categorical covariates.

TABLE 2.

Pharmacokinetic model development^a

Phase of development	MVOF	IIV CL (% CV)	IIV ka (% CV)	CCV RV
Base	17,173	23.9		0.0697
R1 FS—CLCR	17,021	20.8		0.0703
R2 FS—CLCR/3rd drug	16,887	18.5		0.0701
R3 FS—CLCR/3rd drug/race or ethnicity	16,860	18.1		0.07
Multivariable—IIV ka	16,839	17.7	84.5	0.0645
R1 BE	All covariates significant on CL, with addition of IIV on ka

^aMVOF, minimum value of the objective function; IIV, interindividual variability; CL, apparent tenofovir plasma clearance; k_a, absorption rate constant; % CV, % coefficient of variation; CCV RV, constant coefficient of variation, residual variability; R1, R2, and R3, round of covariate analysis; FS, forward selection; CL_CR, creatinine clearance; 3rd drug, treatment arm (ATV/r versus EFV); BE, backwards elimination.

The final significant covariates that were identified were creatinine clearance (power model), treatment arm (additive shift; ATV/r as the reference), and race/ethnicity (additive shift; 2 degrees of freedom; white non-Hispanic race as the reference) on apparent clearance (Table 3). The final covariate relationship with apparent clearance was described as follows:

$$\text{CL}={\theta }_{\text{TVCL}}·{\left({\text{CL}}_{\text{CR}}/113.5\right)}^{\theta {\text{CL}}_{\text{CR}}}+{\theta }_{3\text{rd\hspace{0.17em}drug}}·3\text{rd\hspace{0.17em}drug}+{\theta }_{\text{RACB}}·\text{RACB}+{\theta }_{\text{RACO}}{·}_{}\text{RACO}$$

with CL as the apparent total drug clearance, θ_TVCL as the estimated typical value of clearance, CL_CR/113.5 as the creatinine clearance centered to a value of 113.5 ml/min, θCL_CR as an estimated factor for CL_CR, θ_{3rd drug} as the estimated shift in clearance for those in the efavirenz arm compared to those in the atazanavir/r arm, RACB as an indicator variable for black non-Hispanic race/ethnicity compared to white non-Hispanic race/ethnicity, and RACO as the indicator variable for the combination of Hispanic, Asian, American Indian, Alaskan, and multiracial compared to white non-Hispanic.

TABLE 3.

Final model parameter estimates for tenofovir pharmacokinetics

Parametere	Model estimate (95% CI)	% RSEf (% shrinkage)	Bootstrap estimateg (95% CI)
ka (h−1)	2.87 (1.83, 3.91)	18.5	2.87 (2.27, 4.16)
CL/F (liters/h)	37.2 (34.10, 40.29)	4.2	37.40 (33.57, 40.26)
Vc/F (liters)	127 (83.10, 170.90)	17.6	128.73 (86.26, 188.48)
Vp/F (liters)	646 (555.45, 736.55)	7.2	649.55 (547.62, 737.81
Q/F (liters/h)	107 (70.94, 143.06)	17.2	108.60 (73.26, 144.98)
IIV in ka	0.714 (0.389, 1.039)	23 (57)d	0.817 (0.350, 1.497)
IIV in CL	0.0312 (0.025, 0.037)	10 (17)	0.0309 (0.025, 0.038)
CLCRa,b	0.442 (0.375, 0.509)	8	0.445 (0.372, 0.511)
Treatment arma,c	8 (6.47, 9.53)	10	7.93 (6.51, 9.55)
Black non-Hispanica,c	3.17 (1.54, 4.80)	26	3.29 (1.65, 4.90)
“Other” race/ethnicitya,c	4.09 (2.40, 5.78)	21	4.11 (2.53, 5.84)
CCV RV	0.0645 (0.0576, 0.0714)	5 (16)	0.0641 (0.0575, 0.0712)

^aOn CL/F.

^bPower model.

^cAdditive shift.

^dSignificant ETABAR.

^ek_a, absorption rate constant; CL/F, apparent plasma clearance; V_c/F, apparent volume of distribution in the central compartment. V_p/F, apparent volume of distribution in the peripheral compartment; Q/F, apparent intercompartmental clearance; IIV, interindividual variability; CL_CR, creatinine clearance; CCV RV, constant coefficient of variation, residual variability.

^fRSE, relative standard error.

^g960/1,000 = 96% runs contributed; 36 runs with minimization terminated were skipped when calculating the bootstrap results, and 4 runs with estimates near a boundary were skipped when calculating the bootstrap results.

The final estimated covariate effects showed that there was an average 0.442 change in the natural log of tenofovir plasma CL/F (liters/h) per ml/min in the ln CL_CR compared to the centered value (113.5 ml/min) [e.g., for an individual, ln(CL/F) = ln(37.2 liters/h) + 0.442 · ln(CrCl/113.5 ml/min)]. For the median (113.7 ml/min), first quartile (Q₁) (97.4 ml/min), third quartile (Q₃) (133.6 ml/min), and lowest CL_CR (44.4 ml/min) values in the data set, the resultant oral CL values for these individuals would be 37.2, 34.8, 40.0, and 24.6 liters/h, respectively. Those in the efavirenz treatment arm were found to have an average apparent tenofovir clearance that was 8 liters/h greater than that of participants in the atazanavir/ritonavir arm. In comparison to white non-Hispanic individuals, black non-Hispanic participants and those combined into the “other” group (Hispanic, Asian, American Indian/Alaskan, and multiracial) had average apparent tenofovir clearances that were 3.17 liters/h and 4.09 liters/h greater, respectively. A simulation of population predicted values in male participants with median values for weight, CL_CR, and age (with no variability) shows the difference in plasma tenofovir exposure between different race/ethnicity groups assigned to either the ATV/r or EFV arms of study A5202 (Fig. 1). Among both treatment arms, those of the “other” and black non-Hispanic race/ethnicity groups were associated with a faster TFV plasma clearance (and therefore reduced plasma exposure) than that of white non-Hispanic participants. A comparison of plasma exposures between racial/ethnic groups per third drug treatment arm is provided in Fig. 2.

FIG 1.

Comparison of predicted TFV concentrations based on race/ethnicity and treatment arm. Simulations are population predictions for males with median values for creatinine clearance, weight, and age. The AUCs (ng · h/ml) were as follows: 2,752 (“other,” EFV), 2,804 (black/non-Hispanic, EFV), 3,001 (white/non-Hispanic, EFV), 3,647 (white/non-Hispanic, ATV/r), 3,361 (black/non-Hispanic, ATV/r), and 3,286 (“other,” ATV/r).

FIG 2.

Comparison of TFV plasma exposures in racial/ethnic groups per third drug. AUC, area under the plasma concentration-time curve; EFV, efavirenz; ATV/r, ritonavir-boosted atazanavir; NG, nanogram; ML, milliliter.

The estimated mean population pharmacokinetic parameters for the final model, with 95% confidence intervals compared to the bootstrap analysis (96% of runs successfully contributed to the bootstrap analysis and met the predefined convergence criteria), are given in Table 3. The prediction-corrected visual predictive check (pcVPC) was generated with model predictions from 2,000 simulations and shows that the observed median (red line) and 5th and 95th percentiles of the data (blue lines) were included within the model-predicted 95% confidence intervals (shaded areas) (Fig. 3). These internal validation techniques show appropriate model specification.

FIG 3.

Prediction-corrected visual predictive check comparing observed and model predicted drug concentrations. Observed concentrations and their 5th, 50th, and 95th percentiles are overlaid on the simulated 95% confidence intervals of the corresponding percentiles.

DISCUSSION

This study has identified CL_CR, treatment arm, and race/ethnicity as significant covariates associated with apparent clearance following the recommended TDF dose in treatment-naive adults living with HIV. Tenofovir disoproxil fumarate is recommended as a first-line nucleotide reverse transcriptase inhibitor in national HIV treatment guidelines (7), and its use has increased among non-HIV-infected individuals for preexposure prophylaxis, when used with emtricitabine (8, 9). These findings may provide additional considerations for individualizing TDF-based regimens.

Multiple structural population pharmacokinetic models for plasma tenofovir have been reported as two-compartment models with first-order absorption and elimination (4, 5, 10, 11). Previous population analyses (3–5, 10, 11) have identified plasma tenofovir pharmacokinetic parameters in the following ranges: CL/F, 42 to 66.6 liters/h, apparent volume of distribution in the central compartment (V_c/F), 268 to 1,040 liters; apparent intercompartmental clearance (Q/F), 13.2 to 197 liters/h; apparent volume of distribution in the peripheral compartment (V_p/F), 398 to 1,630 liters; and k_a, 0.82 to 1.35 h⁻¹. These values were similar to those estimated in the current analysis: CL/F, 37.2 liters/h; V_c/F, 127 liters; Q/F, 107 liters/h; V_p/F, 646 liters; and k_a, 2.87 h⁻¹. The difference noted in the absorption rate constant may be due to differences in population administration of tenofovir in relation to food, as food delays the time to tenofovir maximum concentration in serum (C_max) (1). Previous pharmacokinetic studies of TFV have also identified renal function and ritonavir-enhanced protease inhibitors as significant covariates in the plasma exposure of TFV (3–5, 10, 11). Our analysis confirms that ATV/r in combination with TDF results in increased TFV plasma concentrations compared to coadministration with EFV. In a study of 12 participants listed in the prescribing information for atazanavir, there was a 37% (90% confidence interval [CI], 1.30 to 1.45) increase in the TFV area under the concentration-time curve (AUC) when coadministered with ATV/r (12).

Study 5202 was a multicenter clinical trial across the United States, including Puerto Rico, which enrolled a large number of participants, including well-represented minority populations. Approximately 23% (n = 429) of the study population were Hispanic, and 33% (n = 615) were black non-Hispanic, allowing for the evaluation of the pharmacokinetics of TFV in these patient populations. Among the three race/ethnicity groups evaluated (white non-Hispanic versus black non-Hispanic and versus “other”), there was a significant difference in TFV oral CL when the white non-Hispanic group was compared to the other two groups. To our knowledge, this is the first report to identify race/ethnicity as a significant covariate for TFV oral CL. The “other” race/ethnicity group in this study consisted predominantly of participants who were Hispanic (190 Hispanic participants out of 212 in this group). Individuals in this race/ethnicity group were associated with a faster TFV oral clearance, compared to white non-Hispanic participants, and therefore reduced plasma exposure (Fig. 1). The question arises if a difference in clearance could affect adverse effects over time. ACTG study A5224s was a substudy of A5202 (n = 269) focused on assessing longer-term changes in metabolic outcomes in participants treated with FTC/TDF or ABC/3TC with either EFV or ATV/r. A5224s compared changes in areas such as limb fat, renal function, glucose, insulin and insulin sensitivity, urine albumin, and urine protein/creatinine ratios between different race/ethnicity groups. However, information comparing these groups within the TDF/FTC arms to the ABC/3TC arms (13–16) was not reported. In the univariate analysis, there was no significant association between race/ethnicity (compared to white non-Hispanic participants) with changes in body mass and bone mineral density adjusted for treatment arm (17).

In the iPrEx trial evaluating oral daily doses of TDF/FTC or placebo as preexposure prophylaxis in HIV-seronegative men or transgender women who have sex with men, a relative risk reduction from contracting HIV of 92% was found in those with detectable drug concentrations (quantification range, 10 to 1,500 ng/ml) in the treatment arm (8). The majority of the iPrEx study population was Hispanic (approximately 72%), with the largest number of participants from Peru; however, a separate analysis of ARV exposures by race/ethnicity has not been reported.

Limitations of the current analysis include unknown reasons for variability of drug concentrations, such as other potential drug-drug interactions, effects of comorbid conditions, or other unmeasured confounding factors. In addition, the observations identified by the residual variability mixture model represent apparent nonadherence, since only 2 of the 78 observations identified by the mixture model reported slight deviations from daily dosing (2 days between the second and third dose prior to pharmacokinetic sampling). Unreported noncompliance may be one possible source of the large residual variability seen within the data.

In conclusion, a population pharmacokinetic model with covariate analysis was developed for ACTG study A5202 to analyze the TFV plasma concentration data available from the diverse participant population. The significant covariates associated with apparent TFV clearance included creatinine clearance, treatment arm, and race/ethnicity. As the number of low- and middle-income countries are moving toward antiretroviral regimens containing dolutegravir (DTG) as the preferred first-line treatment, including the fixed-dose combination of TDF/3TC/DTG (18), the findings of this analysis are timely and relevant. These data suggest that additional research examining preexposure prophylaxis regimens and use for treatment may consider possible TFV exposure differences between race/ethnicity groups.

MATERIALS AND METHODS

Participants and study design.

Study A5202 was a phase 3b, randomized, partially blinded equivalence study of four once-daily ARV regimens in treatment-naive adults (≥16 years of age). Participants were randomized 1:1:1:1 and balanced by study site. At screening, study participants were stratified by HIV-1 RNA level (<100,000 or ≥100,000 copies/ml). Participants in the high-screening viral load stratum (based on data safety monitoring board recommendations) and those with toxicity associated with the NRTI backbone who had virologic failure or hepatitis B were unblinded. The primary efficacy, safety, and tolerability results have been reported (19–21).

A sparse sampling strategy for the measurement of plasma drug concentrations was designed to collect three steady-state samples per participant during the first 24 weeks of therapy, including dosing information on the previous 4 doses prior to sampling. Pharmacokinetic drug concentration sampling occurred at week 4, 8, 16, or 24. Three samples were to be collected over two visits, visits A and B. Visit A could occur before or after visit B, or the visits could be combined if medications were regularly scheduled for the morning. At visit A, two plasma samples were obtained, one before a dose and one 3 to 4 h after an observed dose; at visit B, one sample was to be obtained 5 to 15 h (5 to 12 h if all medications were taken in the morning) after a dose (22–24).

Assurances.

The human subject committees of all sites approved the A5202 protocol, and written informed consent was obtained from all participants in compliance with human experimentation guidelines of the U.S. Department of Health and Human Services.

Tenofovir sample processing.

Plasma concentrations of tenofovir were measured at the ACTG Pharmacology Laboratory at the University of Alabama at Birmingham using a high-performance liquid chromatography with tandem mass spectrometry (HPLC-MS) assay (25). After the addition of stably labeled isotope internal standards (IS), samples were processed using a solid-phase extraction method on 30-mg (1-cm³) Oasis MCX cartridges. The eluate was then evaporated under a nitrogen stream and reconstituted in 175 μl of 0.01% trifluoroacetic acid (TFA) for injection. Using a Shimadzu XR HPLC system, reversed phase chromatographic separation of the drug and the internal standard was performed on an Atlantis dC₁₈ analytical column (2.1 by 100 mm, 3.0 μm) under isocratic conditions. A Supelco C₁₈ in-line guard cartridge was used to protect the column from contaminants. A column temperature of 30°C, a rate of 0.2 ml/min, and an injection volume of 10 μl were used. The binary mobile phase consisted of 0.1% formic acid (A)and 0.1% formic acid (B) in acetonitrile with a composition of 90% A to 10% B. Under these conditions, the retention time for tenofovir and its respective internal standard was approximately 2.12 min. A total run time of 5 min was used to ensure complete elution of all peaks of interest. Detection and quantification were accomplished on an API 5500 mass spectrometer by multireaction monitoring. Tenofovir and the IS were detected using the following transitions for protonated products [M + H]⁺: m/z 288.2 > 176.1 for tenofovir; m/z 293.2 > 181.0 for tenofovir-IS. Mass spectrometer settings were as follows: an API 5500 instrument was used in positive TubolonSpray mode with a source temperature of 500°C. Nitrogen was used as the nebulizer, auxiliary, collision, and curtain gas. The calibration curve was linear over the range of 5 to 1,000 ng/ml for tenofovir using a 50-μl aliquot of human plasma. Validation of the plasma assay showed precision with less than 8% coefficient of variation between calibration standards on different assay runs and accuracy with less than 6% deviation from known concentrations. Plasma quality controls showed overall precision [(SD/mean) × 100%)] with less than 7% and accuracy [(mean − target)/target × 100%] within 10% CV.

Population pharmacokinetic modeling.

An exploratory pharmacokinetic analysis identified significant differences in TFV oral CL when participant characteristics for A5202 were compared (22). With this previously identified structure as a starting base model, the goal of the current analysis was to identify and quantify sources of variability in TFV exposure, while confirming and refining the exploratory base structural model. Pharmacokinetic analysis of TFV (136-mg dose) was performed using nonlinear mixed-effects modeling with NONMEM (version 7.1.0; ICON Development Solutions, Ellicott City, MD, USA) interfaced with Perl-speaks-NONMEM (PsN; https://uupharmacometrics.github.io/PsN/) through Pirana (version 2.9.4; http://www.pirana-software.com/) as the modeling environment (26, 27). The first-order conditional estimation method with interaction was used with a steady-state assumption. One- and two-compartment models with first-order absorption and first-order elimination were evaluated. An exponential error model with log-normal distribution was used for examination of intersubject variability of all pharmacokinetic parameters, adding to the intersubject variability on CL/F which was already contained in the exploratory model. A proportional and mixed (additive and proportional) error model was assessed for residual variability on one- and two-compartment models. In addition, a mixture model of residual variability was used to detect apparent nonadherence during the model building process (28). Goodness-of-fit plots were used to evaluate the base structural model: observations versus individual and population predictions (IPRED and PRED), conditional weighted residuals versus PRED and time, and absolute individual weighted residuals versus IPRED.

Covariate selection.

A covariate analysis was performed to explore the association of several factors with plasma TFV pharmacokinetic parameters. Race/ethnicity, sex, and third drug treatment arm (ATV/r or EFV) were evaluated as categorical covariates using an additive functional form. Race/ethnicity groups available for model building included white non-Hispanic, black non-Hispanic, Hispanic, Asian, American Indian/Alaskan, and multiracial (although the sample size was small for the last three groups). Each group was evaluated individually and combined in stepwise increments starting with those groups with the smallest number of participants. Continuous covariates, which included age at study entry, creatinine clearance (CL_CR; calculated by the Cockcroft-Gault equation) (29), and weight in kilograms, were centered and evaluated using power and linear functional forms. Weight and CL_CR measurements were obtained at the same time or in close proximity to the time points for tenofovir sampling. Significant covariates were selected using the classical stepwise approach (30). Forward selection was conducted in a univariate manner, with covariate inclusion into the model being determined by a reduction in minimum value of the objective function (MVOF) by >3.84 (P < 0.05; 1 degree of freedom, in a χ² distribution) and by a reduction in the interindividual variability (IIV) of the pharmacokinetic parameter of interest. For the backward elimination step, covariates were removed separately and considered significant if their removal resulted in an increase in the MVOF of at least 10.83 (α < 0.001; 1 degree of freedom, in a χ² distribution). Time-varying covariates (CL_CR and weight) were included in the data set if CL_CR changed to a different stage of renal function (table can be found in the Food and Drug Administration’s “Guidance for Industry on Pharmacokinetics in Patients with Impaired Renal Function” [31]) and weight if it changed by >20 lb. Between forward selection and backward elimination, multivariable model evaluation occurred by exploring the addition of interindividual variability on additional parameters and examination of the residual variability model by precision.

Model evaluation.

The final model was evaluated using 2,000 simulations in a prediction-corrected visual predictive check (pcVPC). Observed concentrations and their 5th, 50th, and 95th percentiles were overlaid on the 95% confidence interval of the corresponding percentiles of the simulations for visual assessment. Prediction correction was used to take into account the differences within a bin coming from the included covariates (32). All the observations and predictions were then normalized using the typical population prediction in relation to the median of typical population predictions per bin across the covariates (32). Nonparametric bootstrap resampling was also performed to evaluate the model (33). One thousand bootstrap data sets were generated to obtain a median and 95% confidence interval for each model parameter for comparison with the original final parameter estimates, with an a priori convergence criterion set at 90% when modeling the bootstrap data sets for evaluation of the convergence rate.