Comparison of model-based tests and selection strategies to detect genetic polymorphisms influencing pharmacokinetic parameters

Machine learning-guided covariate selection for time-to-event models developed from a small sample of real-world patients receiving bevacizumab treatment

Therapeutic outcomes in patients with metastatic colorectal cancer (mCRC) receiving bevacizumab treatment are highly variable, and a reliable predictive factor is not available. Progression-free survival (PFS) and overall survival (OS) were recorded from an observational, prospective study after 5 years of follow-up, including 46 patients with mCRC receiving bevacizumab treatment. Three vascular endothelial growth factor (VEGF)-A and two intercellular adhesion molecule-1 genes polymorphisms, age, gender, weight, dosing scheme, and co-treatments were collected. Given the relatively small number of events (37 [80%] for the PFS and 26 [57%] for the OS), to study the effect of these covariates on PFS and OS, a covariate analysis was performed using statistical and supervised machine learning techniques, including Cox regression, penalized Cox regression techniques (least absolute shrinkage and selection operator [LASSO], ridge regression, and elastic net), survival trees, and survival forest. The predictive performance of each method was evaluated in bootstrapped samples, using prediction error curves and the area under the curve of the receiver operating characteristic. The LASSO penalized Cox-regression model showed the best overall performance. Nonlinear mixed effects (NLME) models were developed, and a conventional stepwise covariate search was performed. Then, covariates identified as important by the LASSO model were included in the base NLME models developed for PFS and OS, resulting in improved models as compared to those obtained with the stepwise covariate search. It was shown that having gene polymorphisms in VEGFA (rs699947 and rs1570360) and ICAM1 (rs1799969) are associated with a favorable clinical outcome in patients with mCRC receiving bevacizumab treatment.

Identification of high-dimensional omics-derived predictors for tumor growth dynamics using machine learning and pharmacometric modeling

Pharmacometric modeling can capture tumor growth inhibition (TGI) dynamics and variability. These approaches do not usually consider covariates in high-dimensional settings, whereas high-dimensional molecular profiling technologies ("omics") are being increasingly considered for prediction of anticancer drug treatment response. Machine learning (ML) approaches have been applied to identify high-dimensional omics predictors for treatment outcome. Here, we aimed to combine TGI modeling and ML approaches for two distinct aims: omics-based prediction of tumor growth profiles and identification of pathways associated with treatment response and resistance. We propose a two-step approach combining ML using least absolute shrinkage and selection operator (LASSO) regression with pharmacometric modeling. We demonstrate our workflow using a previously published dataset consisting of 4706 tumor growth profiles of patient-derived xenograft (PDX) models treated with a variety of mono- and combination regimens. Pharmacometric TGI models were fit to the tumor growth profiles. The obtained empirical Bayes estimates-derived TGI parameter values were regressed using the LASSO on high-dimensional genomic copy number variation data, which contained over 20,000 variables. The predictive model was able to decrease median prediction error by 4% as compared with a model without any genomic information. A total of 74 pathways were identified as related to treatment response or resistance development by LASSO, of which part was verified by literature. In conclusion, we demonstrate how the combined use of ML and pharmacometric modeling can be used to gain pharmacological understanding in genomic factors driving variation in treatment response.

In vivo and in silico characterization of apocynin in reducing organ oxidative stress: A pharmacokinetic and pharmacodynamic study

Apocynin has been widely used in vivo as a Nox2-contaninig nicotinamide adenine dinucleotide phosphate oxidase inhibitor. However, its time-dependent tissue distribution and inhibition on organ reactive oxygen species (ROS) production remained unclear. In this study, we examined apocynin pharmacokinetics and pharmacodynamics (PKPD) after intravenous (iv) injection (bolus, 5 mg/kg) of mice (CD1, 12-week). Apocynin was detected using a HPLC coupled to a linear ion-trap tandem mass spectrometer. Apocynin peak concentrations were detected in plasma at 1 minute (5494 ± 400 ng/mL) (t1/2  = 0.05 hours, clearance = 7.76 L/h/kg), in urine at 15 minutes (14 942 ± 5977 ng/mL), in liver at 5 minutes (2853 ± 35 ng/g), in heart at 5 minutes (3161 ± 309 ng/g) and in brain at 1 minute (4603 ± 208 ng/g) after iv injection. These were accompanied with reduction of ROS production in the liver, heart and brain homogenates. Diapocynin was not detected in these samples. Therapeutic effect of apocynin was examined using a mouse model (C57BL/6J) of high-fat diet (HFD, 16 weeks)-induced obesity and accelerated aging. Apocynin (5 mmol/L) was supplied in drinking water during the HFD period and was detected at the end of treatment in the brain (5369 ± 1612 ng/g), liver (4818 ± 1340 ng/g) and heart (1795 ± 1487 ng/g) along with significant reductions of ROS production in these organs. In conclusion, apocynin PKPD is characterized by a short half-life, rapid clearance, good distribution and inhibition of ROS production in major organs. Diapocynin is not a metabolite of apocynin in vivo. Apocynin crosses easily the blood-brain barrier and reduces brain oxidative stress associated with metabolic disorders and aging.

Model Averaging in Viral Dynamic Models

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

Modelling of atorvastatin pharmacokinetics and the identification of the effect of a BCRP polymorphism in the Japanese population

AIM

Ethnicity plays a modulating role in atorvastatin pharmacokinetics (PK), with Asian patients reported to have higher exposure compared with Caucasians. Therefore, it is difficult to safely extrapolate atorvastatin PK data and models across ethnic groups. This work aims to develop a population PK model for atorvastatin and its pharmacologically active metabolites specifically for the Japanese population. Subsequently, it aimed to identify genetic polymorphisms affecting atorvastatin PK in this population.

METHODS

Atorvastatin acid (ATA) and ortho-hydroxy-atorvastatin acid (o-OH-ATA) plasma concentrations, clinical/demographic characteristics and genotypes for 18 (3, 3, 1, 1, 7, 2 and 1 in the ABCB1, ABCG2, CYP3A4, CYP3A5, SLCO1B1, SLCO2B1 and PPARA genes, respectively) genetic polymorphisms were collected from 27 Japanese individuals (taking 10 mg atorvastatin once daily) and analysed using a population PK modelling approach.

RESULTS

The population PK model developed (one-compartment for ATA linked through metabolite formation to an additional compartment describing the disposition of o-OH-ATA) accurately described the observed data and the associated population variability. Our analysis suggested that patients carrying one variant allele for the rs2622604 polymorphism (ABCG2) show a 55% (95% confidence interval: 16-131%) increase in atorvastatin oral bioavailability relative to the value in individuals without the variant allele.

CONCLUSION

The current work reports the identification in the Japanese population of a BCRP polymorphism, not previously associated with the PK of any statin, that markedly increases ATA and o-OH-ATA exposure. The model developed may be of clinical importance to guide dosing recommendations tailored specifically for the Japanese.

Pharmacokinetics of oral fludrocortisone in septic shock

AIM

The combination of hydrocortisone and fludrocortisone improved outcomes in septic shock. However, the specific role of fludrocortisone remains controversial and its pharmacokinetics (PK) has never been investigated in septic shock. This study aimed at characterizing the PK of fludrocortisone in septic shock.

METHODS

This was a single-centre ancillary PK study of a large multinational trial of crystalloids versus colloids for acute hypovolemia in intensive care unit (ICU) patients. In 21 adults with septic shock, fludrocortisone plasma concentrations were measured by liquid chromatography-mass spectrometry tandem analysis, before and repeatedly until 18 h after an oral dose of 50 μg. PK parameters were estimated using a nonlinear mixed-effects modelling.

RESULTS

Undetectable plasma concentrations were observed in 7 out of 21 patients. In the remaining 14 patients, plasma fludrocortisone concentrations were best described by a one-compartmental model with first-order absorption, a lag time (T_lag ) before the absorption phase, and first-order elimination. Severity of illness, as quantified by Simplified Acute Physiology Score II, significantly increased T_lag and apparent clearance. There was a large inter-individual variability in PK parameters. The population estimates of PK parameters (inter-individual variability) were: T_lag 0.65 h (98%), apparent clearance 40 l h^-1 (49%) and apparent volume of distribution 78 l (75%). Plasma half-life was estimated at 1.35 h (95% CI, 0.84-2.03) and area under the curve of plasma concentrations was estimated at 1.25 μg h l^-1 (95% CI, 1.09-1.46).

CONCLUSIONS

A single oral dose of fludrocortisone yielded undetectable plasma concentrations in one-third of adults with septic shock. Fludrocortisone PK showed a short plasma elimination half-life and a large inter-individual variability.

Safety and pharmacokinetics of multiple dose myo-inositol in preterm infants

BACKGROUND

Preterm infants with respiratory distress syndrome (RDS) given inositol had reduced bronchopulmonary dysplasia (BPD), death and severe retinopathy of prematurity (ROP). We assessed the safety and pharmacokinetics of daily inositol to select a dose providing serum levels previously associated with benefit, and to learn if accumulation occurred when administered throughout the normal period of retinal vascularization.

METHODS

Infants ≤ 29 wk GA (n = 122, 14 centers) were randomized and treated with placebo or inositol at 10, 40, or 80 mg/kg/d. Intravenous administration converted to enteral when feedings were established, and continued to the first of 10 wk, 34 wk postmenstrual age (PMA) or discharge. Serum collection employed a sparse sampling population pharmacokinetics design. Inositol urine losses and feeding intakes were measured. Safety was prospectively monitored.

RESULTS

At 80 mg/kg/d mean serum levels reached 140 mg/l, similar to Hallman's findings. Levels declined after 2 wk, converging in all groups by 6 wk. Analyses showed a mean volume of distribution 0.657 l/kg, clearance 0.058 l/kg/h, and half-life 7.90 h. Adverse events and comorbidities were fewer in the inositol groups, but not significantly so.

CONCLUSION

Multiple dose inositol at 80 mg/kg/d was not associated with increased adverse events, achieves previously effective serum levels, and is appropriate for investigation in a phase III trial.

Approximate testing in two-stage nonlinear mixed models

We investigate here small sample properties of approximate F-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximate F-test is constructed based on large sample approximation to the distribution of nonlinear least squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large sample Fisher information matrix (See [1]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modified F-test under the null hypothesis, especially accuracy of p-values (See [2]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [3, 4]).

Comparison of Nonlinear Mixed Effects Models and Noncompartmental Approaches in Detecting Pharmacogenetic Covariates

Genetic data is now collected in many clinical trials, especially in population pharmacokinetic studies. There is no consensus on methods to test the association between pharmacokinetics and genetic covariates. We performed a simulation study inspired by real clinical trials, using the pharmacokinetics (PK) of a compound under development having a nonlinear bioavailability along with genotypes for 176 single nucleotide polymorphisms (SNPs). Scenarios included 78 subjects extensively sampled (16 observations per subject) to simulate a phase I study, or 384 subjects with the same rich design. Under the alternative hypothesis (H1), six SNPs were drawn randomly to affect the log-clearance under an additive linear model. For each scenario, 200 PK data sets were simulated under the null hypothesis (no gene effect) and H1. We compared 16 combinations of four association tests, a stepwise procedure and three penalised regressions (ridge regression, Lasso, HyperLasso), applied to four pharmacokinetic phenotypes, two observed concentrations, area under the curve estimated by noncompartmental analysis and model-based clearance. The different combinations were compared in terms of true and false positives and probability to detect the genetic effects. In presence of nonlinearity and/or variability in bioavailability, model-based phenotype allowed a higher probability to detect the SNPs than other phenotypes. In a realistic setting with a limited number of subjects, all methods showed a low ability to detect genetic effects. Ridge regression had the best probability to detect SNPs, but also a higher number of false positives. No association test showed a much higher power than the others.

Identification of the effect of multiple polymorphisms on the pharmacokinetics of simvastatin and simvastatin acid using a population-modeling approach

The aim of this work was to develop a joint population pharmacokinetic model for simvastatin (SV) and its active metabolite, simvastatin acid (SVA), that incorporates the effects of multiple genetic polymorphisms and clinical/demographic characteristics. SV/SVA plasma concentrations, demographic/clinical data, and genotypes for 18 genetic variants were collected from 74 individuals (three clinical trials) and analyzed using a nonlinear mixed-effects modeling approach. The structural model that best described the data included a two- and a one-compartment disposition model for SV and SVA, respectively. Age, weight, Japanese ethnicity, and seven genetic polymorphisms-rs4149056 (SLCO1B1), rs776746 (CYP3A5), rs12422149 (SLCO2B1), rs2231142 (ABCG2), rs4148162 (ABCG2), rs4253728 (PPARA), and rs35599367 (CYP3A4)-were identified as significantly affecting model parameters. The developed model was used to assess combinations of these covariates, highlighting specific risk factors associated with altered SV/SVA pharmacokinetics, and consequently myopathy cases that cannot be solely attributed to the rs4149056 CC genotype.

Pharmacokinetics and safety of a single intravenous dose of myo-inositol in preterm infants of 23-29 wk

BACKGROUND

Myo-inositol given to preterm infants with respiratory distress has reduced death, increased survival without bronchopulmonary dysplasia, and reduced severe retinopathy of prematurity in two randomized trials. Pharmacokinetic (PK) studies in extremely preterm infants are needed before efficacy trials.

METHODS

Infants born in 23-29 wk of gestation were randomized to a single intravenous (i.v.) dose of inositol at 60 or 120 mg/kg or placebo. Over 96 h, serum levels (sparse sampling population PK) and urine inositol excretion were determined. Population PK models were fit using a nonlinear mixed-effects approach. Safety outcomes were recorded.

RESULTS

A single-compartment model that included factors for endogenous inositol production, allometric size based on weight, gestational age strata, and creatinine clearance fit the data best. The central volume of distribution was 0.5115 l/kg, the clearance was 0.0679 l/kg/h, endogenous production was 2.67 mg/kg/h, and the half-life was 5.22 h when modeled without the covariates. During the first 12 h, renal inositol excretion quadrupled in the 120 mg/kg group, returning to near-baseline value after 48 h. There was no diuretic side effect. No significant differences in adverse events occurred among the three groups (P > 0.05).

CONCLUSION

A single-compartment model accounting for endogenous production satisfactorily described the PK of i.v. inositol.

Optimal sampling times for a drug and its metabolite using SIMCYP(®) simulations as prior information

BACKGROUND

Since 2007, it is mandatory for the pharmaceutical companies to submit a Paediatric Investigation Plan to the Paediatric Committee at the European Medicines Agency for any drug in development in adults, and it often leads to the need to conduct a pharmacokinetic study in children. Pharmacokinetic studies in children raise ethical and methodological issues. Because of limitation of sampling times, appropriate methods, such as the population approach, are necessary for analysis of the pharmacokinetic data. The choice of the pharmacokinetic sampling design has an important impact on the precision of population parameter estimates. Approaches for design evaluation and optimization based on the evaluation of the Fisher information matrix (M(F)) have been proposed and are now implemented in several software packages, such as PFIM in R.

OBJECTIVES

The objectives of this work were to (1) develop a joint population pharmacokinetic model to describe the pharmacokinetic characteristics of a drug S and its active metabolite in children after intravenous drug administration from simulated plasma concentration-time data produced using physiologically based pharmacokinetic (PBPK) predictions; (2) optimize the pharmacokinetic sampling times for an upcoming clinical study using a multi-response design approach, considering clinical constraints; and (3) evaluate the resulting design taking data below the lower limit of quantification (BLQ) into account.

METHODS

Plasma concentration-time profiles were simulated in children using a PBPK model previously developed with the software SIMCYP(®) for the parent drug and its active metabolite. Data were analysed using non-linear mixed-effect models with the software NONMEM(®), using a joint model for the parent drug and its metabolite. The population pharmacokinetic design, for the future study in 82 children from 2 to 18 years old, each receiving a single dose of the drug, was then optimized using PFIM, assuming identical times for parent and metabolite concentration measurements and considering clinical constraints. Design evaluation was based on the relative standard errors (RSEs) of the parameters of interest. In the final evaluation of the proposed design, an approach was used to assess the possible effect of BLQ concentrations on the design efficiency. This approach consists of rescaling the M(F), using, at each sampling time, the probability of observing a concentration BLQ computed from Monte-Carlo simulations.

RESULTS

A joint pharmacokinetic model with three compartments for the parent drug and one for its active metabolite, with random effects on four parameters, was used to fit the simulated PBPK concentration-time data. A combined error model best described the residual variability. Parameters and dose were expressed per kilogram of bodyweight. Reaching a compromise between PFIM results and clinical constraints, the optimal design was composed of four samples at 0.1, 1.8, 5 and 10 h after drug injection. This design predicted RSE lower than 30 % for the four parameters of interest. For this design, rescaling M(F) for BLQ data had very little influence on predicted RSE.

CONCLUSION

PFIM was a useful tool to find an optimal sampling design in children, considering clinical constraints. Even if it was not forecasted initially by the investigators, this approach showed that it was really necessary to include a late sampling time for all children. Moreover, we described an approach to evaluate designs assuming expected proportions of BLQ data are omitted.

A simultaneous d-optimal designed study for population pharmacokinetic analyses of mycophenolic Acid and tacrolimus early after renal transplantation

Mycophenolic acid (MPA) and tacrolimus (TAC) are immunosuppressive agents used in combination with corticosteroids for the prevention of acute rejection after solid organ transplantation. Their pharmacokinetics (PK) show considerable unexplained intraindividual and interindividual variability, particularly in the early period after transplantation. The main objective of the present work was to design a study based on D-optimality to describe the PK of the 2 drugs with good precision and accuracy and to explain their variability by means of patients' demographics, biochemical test results, and physiological characteristics. Pharmacokinetic profiles of MPA and TAC were obtained from 65 stable adult renal allograft recipients on a single occasion (ie, day 15 after transplantation). A sampling schedule was estimated based on the D-optimality criterion with the POPED software, using parameter values from previously published studies on MPA and TAC modeling early after transplantation. Subsequently, a population PK model describing MPA and TAC concentrations was developed using nonlinear mixed-effects modeling. Optimal blood-sampling times for determination of MPA and TAC concentrations were estimated to be at 0 (predose) and at 0.24, 0.64, 0.98, 1.37, 2.38, and 11 hours after oral intake of mycophenolate and TAC. The PK of MPA and TAC were best described by a 2-compartment model with first-order elimination. For MPA, the absorption was best described by a transit compartment model, whereas first-order absorption with a lag time best described TAC transfer from the gastrointestinal tract. Parameters were estimated with good precision and accuracy. While hematocrit levels and CYP3A5 genetic polymorphism significantly influenced TAC clearance, the pharmaceutical formulation and MRP2 genetic polymorphism were retained as significant covariates on MPA absorption and elimination, respectively. The prospective use of the simultaneous D-optimal design approach for MPA and TAC has allowed good estimation of MPA and TAC PK parameters in the early period after transplantation characterized by a very high unexplained variability. The influence of some relevant covariates could be shown.

Pharmacokinetic similarity of biologics: analysis using nonlinear mixed-effects modeling

Our objective was to show, using two examples, that a pharmacokinetic (PK) similarity analysis can be performed using nonlinear mixed-effects models (NLMEM). We used two studies that compared different biosimilars: a three-way crossover trial with somatropin and a parallel-group trial with epoetin-α. For both data sets, the results of NLMEM-based analysis were compared with those of noncompartmental analysis (NCA). For the latter analysis, we performed an NLMEM-based equivalence Wald test on secondary parameters of the model: the area under the curve and the maximal concentration. Somatropin PK was described by a one-compartment model and epoetin-α PK by a two-compartment model with linear and Michaelis-Menten elimination. For both studies, similarity of PK was demonstrated by means of both NCA and NLMEM, and both methods led to similar results. Therefore, for establishing similarity, PK data can be analyzed by either of the methods. NCA is an easier approach because it does not require data modeling; however, NLMEM leads to a better understanding of the underlying biological system.

Design of pharmacokinetic studies for latent covariates

Latent covariates are covariates that are known to exist but are either observable but unavailable or unobservable at the time of the clinical study. Designs to account for latent covariates must incorporate both uncertainty in the prevalence of the covariate and the data-type of the covariate. The informativeness of the covariate will then depend on whether the covariate data is continuous, ordinal or nominal. In this work we consider designs for latent covariates that may either directly influence the parameter of interest, or indirectly via actions on an observable covariate which then influences the parameter of interest. We consider a motivating example based on the effect of a genetic polymorphism on the influence of a continuous covariate (age) on drug clearance (CL). The polymorphism could take the case of a haplotype with many variant alleles, or a copy number variation in genes with different phenotypic expressions which could be treated as continuous data, or as a bi- or tri-allelic single nucleotide polymorphism that could form either an ordinal or nominal covariate on drug CL. The aim of this study was to investigate designs for clinical studies for latent covariates that accommodate both unknown prevalence and unknown data-type. Initially, the informativeness of a covariate was explored using linear regression assuming the three data-types continuous, ordinal and nominal. The linear covariate model was then considered within a nonlinear mixed effects modelling framework. Two simulation scenarios were considered: (1) the influence of the latent covariate directly on the parameter of interest and (2) the influence of the latent covariate on an observable non-latent continuous covariate, which was assumed to follow a normal or stratified distribution, and the effect of this covariate on the parameter of interest. A power analysis for population PK modelling (1) where the latent covariate had direct influence on the parameter also showed similar behaviour to the linear regression solution. When the influence of the latent covariate was mediated via another observable non-latent continuous covariate, the power for the continuous model was highest but the power of the ordinal model was indistinguishable from that of the nominal model. Stratification of the observable non-latent continuous covariate did not appreciably change the power to identify the latent covariate from that when we assumed the observable covariate conformed to a normal distribution. It was found that parameter estimation is generally at least 1.5 to 7 fold more precise for continuous models than for categorical models.

A mechanism-based model for the population pharmacokinetics of free and bound aflibercept in healthy subjects

AIM

Aflibercept (VEGF-Trap), a novel anti-angiogenic agent that binds to VEGF, has been investigated for the treatment of cancer. The aim of this study was to develop a mechanism-based pharmacokinetic (PK) model for aflibercept to characterize its binding to VEGF and its PK properties in healthy subjects.

METHODS

Data from two phase I clinical studies with aflibercept administered as a single intravenous infusion were included in the analysis. Free and bound aflibercept concentration-time data were analysed using a nonlinear mixed-effects modelling approach with MONOLIX 3.1.

RESULTS

The best structural model involved two compartments for free aflibercept and one for bound aflibercept, with a Michaelis-Menten type binding of free aflibercept to VEGF from the peripheral compartment. The typical estimated clearances for free and bound aflibercept were 0.88 l day(-1) and 0.14 l day(-1), respectively. The central volume of distribution of free aflibercept was 4.94 l. The maximum binding capacity was 0.99 mg day(-1) and the concentration of aflibercept corresponding to half of maximum binding capacity was 2.91 µg ml(-1). Interindividual variability of model parameters was moderate, ranging from 13.6% (V(max) ) to 49.8% (Q).

CONCLUSION

The present PK model for aflibercept adequately characterizes the underlying mechanism of disposition of aflibercept and its nonlinear binding to VEGF.

Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses

Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic χ(2) distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications.

Maximum likelihood estimation of long-term HIV dynamic models and antiviral response

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

Development of a complex parent-metabolite joint population pharmacokinetic model

This study aimed to develop a joint population pharmacokinetic model for an antipsychotic agent in development (S33138) and its active metabolite (S35424) produced by reversible metabolism. Because such a model leads to identifiability problems and numerical difficulties, the model building was performed using the FOCE-I and the Stochastic Approximation Expectation Maximization (SAEM) estimation algorithms in NONMEM and MONOLIX, respectively. Four different structural models were compared based on Bayesian information criteria. Models were first written as ordinary differential equations systems and then in closed form (CF) to facilitate further analyses. The impact of polymorphisms on genes coding for the CYP2C19 and CYP2D6 enzymes, respectively involved in the parent drug and the metabolite elimination were investigated using permutation Wald test. The parent drug and metabolite plasma concentrations of 101 patients were analyzed on two occasions after 4 and 8 weeks of treatment at 1, 3, 6, and 24 h following daily oral administration. All configurations led to a two compartment model with back-transformation of the metabolite into the parent drug and a first-pass effect. The elimination clearance of the metabolite through other processes than back-transformation was decreased by 35% [9-53%] in CYP2D6 poor metabolizer. Permutation tests were performed to ensure the robustness of the analysis, using SAEM and CF. In conclusion, we developed a complex joint pharmacokinetic model adequately predicting the impact of CYP2D6 polymorphisms on the parent drug and its metabolite concentrations through the back-transformation mechanism.

Joint population pharmacokinetic analysis of zidovudine, lamivudine, and their active intracellular metabolites in HIV patients

The population pharmacokinetic parameters of zidovudine (AZT), lamivudine (3TC), and their active intracellular metabolites in 75 naïve HIV-infected patients receiving an oral combination of AZT and 3TC twice daily as part of their multitherapy treatment in the COPHAR2-ANRS 111 trial are described. Four blood samples per patient were taken after 2 weeks of treatment to measure drug concentrations at steady state. Plasma AZT and 3TC concentrations were measured in 73 patients, and among those, 62 patients had measurable intracellular AZT-TP and 3TC-TP concentrations. For each drug, a joint population pharmacokinetic model was developed and we investigated the influence of different covariates. We then studied correlations between the mean plasma and intracellular concentrations of each drug. A one-compartment model with first-order absorption and elimination best described the plasma AZT concentration, with an additional compartment for intracellular AZT-TP. A similar model but with zero-order absorption was found to adequately described concentrations of 3TC and its metabolite 3TC-TP. The half-lives of AZT and 3TC were 0.81 h (94.8%) and 2.97 h (39.2%), respectively, whereas the intracellular half-lives of AZT-TP and 3TC-TP were 10.73 h (69%) and 21.16 h (44%), respectively. We found particularly a gender effect on the apparent bioavailability of AZT, as well as on the mean plasma and intracellular concentrations of AZT, which were significantly higher in females than in males. Relationships between mean plasma drug and intracellular metabolite concentrations were also highlighted both for AZT and for 3TC. Simulation with the model of plasma and intracellular concentrations for once- versus twice-daily regimens suggested that a daily dosing regimen with double doses could be appropriate.

Population pharmacokinetic-pharmacogenetic study of nevirapine in HIV-infected Cambodian patients

The aims of this ANRS12154 open-label, single-center, multiple-dose pharmacokinetic study were to characterize nevirapine pharmacokinetics in a Cambodian population of HIV-infected patients and to identify environmental and genetic factors of variability, focusing on the CYP2B6, CYP3A5, and ABCB1 (MDR1) genes. A total of 170 Cambodian HIV-infected patients were included. Nevirapine trough concentrations were measured after 18 and 36 months of starting antiretroviral treatment and in samples drawn during a dosing interval in a subset of 10 patients. All data were analyzed by nonlinear mixed-effects modeling. The effect of covariates was investigated using the population pharmacokinetic model. Patients carrying homozygous loss-of-function alleles CYP3A5 6986A>G, CYP2B6 516G>T, CYP2B6 1459C>T, and ABCB1 3435C>T represent 42.4%, 9.2%, 0%, and 18% of the population, respectively. The median nevirapine trough concentrations did not differ after 18 and 36 months of treatment (5,705 ng/ml [range, ≤50 to 13,871] and 5,709 ng/ml [range, ≤50 to 15,422], respectively). Interpatient and intrapatient variabilities of nevirapine apparent clearance were 28% and 17%, respectively. CYP2B6 516G>T and creatinine clearance were found to significantly affect nevirapine apparent clearance. The estimated nevirapine apparent clearances were 2.95 liters/h, 2.62 liters/h, and 1.86 liters/h for CYP2B6 516GG, CYP2B6 516GT, and CYP2B6 516TT genotypes, respectively. The impact of creatinine clearance was small. This study demonstrates that 95% of the patients had sustained nevirapine exposure well above the 3,000-ng/ml threshold. Nevirapine clearance was shown to be affected by CYP2B6 516G>T genetic polymorphism and creatinine clearance, although this explained only part of the interpatient variability, which remains low compared to that for other antiretroviral drugs.

Pharmacogenetics and population pharmacokinetics: impact of the design on three tests using the SAEM algorithm

Pharmacogenetics is now widely investigated and health institutions acknowledge its place in clinical pharmacokinetics. Our objective is to assess through a simulation study, the impact of design on the statistical performances of three different tests used for analysis of pharmacogenetic information with nonlinear mixed effects models: (i) an ANOVA to test the relationship between the empirical Bayes estimates of the model parameter of interest and the genetic covariate, (ii) a global Wald test to assess whether estimates for the gene effect are significant, and (iii) a likelihood ratio test (LRT) between the model with and without the genetic covariate. We use the stochastic EM algorithm (SAEM) implemented in MONOLIX 2.1 software. The simulation setting is inspired from a real pharmacokinetic study. We investigate four designs with N the number of subjects and n the number of samples per subject: (i) N = 40/n = 4, similar to the original study, (ii) N = 80/n = 2 sorted in 4 groups, a design optimized using the PFIM software, (iii) a combined design, N = 20/n = 4 plus N = 80 with only a trough concentration and (iv) N = 200/n = 4, to approach asymptotic conditions. We find that the ANOVA has a correct type I error estimate regardless of design, however the sparser design was optimized. The type I error of the Wald test and LRT are moderatly inflated in the designs far from the asymptotic (<10%). For each design, the corrected power is analogous for the three tests. Among the three designs with a total of 160 observations, the design N = 80/n = 2 optimized with PFIM provides both the lowest standard error on the effect coefficients and the best power for the Wald test and the LRT while a high shrinkage decreases the power of the ANOVA. In conclusion, a correction method should be used for model-based tests in pharmacogenetic studies with reduced sample size and/or sparse sampling and, for the same amount of samples, some designs have better power than others.

Influence of pharmacogenetics on indinavir disposition and short-term response in HIV patients initiating HAART

AIMS

To assess the relationship between genetic polymorphisms and indinavir pharmacokinetic variability and to study the link between concentrations and short-term response or metabolic safety.

METHODS

Forty protease inhibitor-naive patients initiating highly active antiretroviral therapy (HAART) including indinavir/ritonavir and enrolled in the COPHAR 2-ANRS 111 trial were studied. At week 2, four blood samples were taken before and up to 6 h following drug intake. A population pharmacokinetic analysis was performed using the stochastic approximation expectation maximization (SAEM) algorithm implemented in MONOLIX software. The area under the concentration-time curve (AUC) and maximum (C(max)) and trough concentrations (C(trough)) of indinavir were derived from the population model and tested for their correlation with short-term viral response and safety measurements, while for ritonavir, these same three parameters were tested for their correlation with short-term biochemical safety

RESULTS

A one-compartment model with first-order absorption and elimination best described both indinavir and ritonavir concentrations. For indinavir, the estimated clearance and volume of distribution were 22.2 L/h and 97.3 L, respectively. The eight patients with the *1B/*1B genotype for the CYP3A4 gene showed a 70% decrease in absorption compared to those with the *1A/*1B or *1A/*1A genotypes (0.5 vs. 2.1, P = 0.04, likelihood ratio test by permutation). The indinavir AUC and C(trough) were positively correlated with the decrease in human immunodeficiency virus RNA between week 0 and week 2 (r = 0.4, P = 0.03 and r = -0.4, P = 0.03, respectively). Patients with the *1B/*1B genotype also had a significantly lower indinavir C(max) (median 3.6, range 2.1-5.2 ng/mL) than those with the *1A/*1B or *1A/*1A genotypes (median 4.4, range 2.2-8.3 ng/mL) (P = 0.04) and a lower increase in triglycerides during the first 4 weeks of treatment (median 0.1, range -0.7 to 1.4 vs. median 0.6, range -0.5 to 1.7 mmol/L, respectively; P = 0.02). For ritonavir, the estimated clearance and volume of distribution were 8.3 L/h and 60.7 L, respectively, and concentrations were not found to be correlated to biochemical safety. Indinavir and ritonavir absorption rate constants were found to be correlated, as well as their apparent volumes of distribution and clearances, indicating correlated bioavailability of the two drugs.

CONCLUSION

The CYP3A4*1B polymorphism was found to influence the pharmacokinetics of indinavir and, to some extent, the biochemical safety of indinavir.