Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear mixed effects models

Pharmacokinetics of eperisone following oral administration in healthy Korean volunteers

Eperisone is an oral muscle relaxant used to treat musculoskeletal diseases, which exhibits high pharmacokinetic (PK) variability in bioequivalence studies. The aim of this study was to characterize the PKs of eperisone following its oral administration to Korean volunteers through the conduct of a noncompartmental and population analysis. A total of 360 concentration-time measurements collected on two separate occasions from 15 healthy volunteers during a bioequivalent study of eperisone 50 mg (Murex^® ) were used in the PK analysis. Noncompartmental analysis was performed using WinNonLin^TM and population analysis was performed using NONMEM^® . The possible influence of thirty demographic and pathophysiological characteristics on the PKs of eperisone were explored. Based on noncompartmental analysis mean eperisone elimination half-life, apparent clearance (CL/F), and apparent volume of distribution were estimated to be 3.81 h, 39.24 × 10³  l/h × 10³  L, respectively. During population PK modeling a two-compartment model with first-order absorption rate constant (typical population K _a  = 1.5 h^-1 ) and first-order elimination (typical population CL/F and apparent volume of distribution in the central compartment [V _c /F] = 30.8 × 10³  l/h and 86.2 × 10³  l, respectively) best described the PKs of eperisone. Interindividual variability in CL/F and V _c /F were estimated to be 87.9% and 130.3%, respectively and interoccasion variability in CL/F and V _c /F were estimated to be 23.8% and 30.8%, respectively. Aspartate aminotransferase level and smoking status were identified as potential covariates that may influence the CL/F of eperisone. This is the first study to develop a disposition model for eperisone and investigate the potential influence of covariate factors on it PK variability.

Prospective Cohort Study of Population Pharmacokinetics and Pharmacodynamic Target Attainment of Vancomycin in Adults on Extracorporeal Membrane Oxygenation

The aim of this study was to develop a population pharmacokinetics (PK) model for vancomycin and to evaluate its pharmacodynamic target attainment in adults on extracorporeal membrane oxygenation (ECMO). After a single 1,000-mg dose of vancomycin, samples were collected 9 times per patient prospectively. A population PK model was developed using a nonlinear mixed-effect model. The probability of target attainment (PTA) of vancomycin was evaluated for various dosing strategies using Monte Carlo simulation. The ratio of the area under the vancomycin concentration-time curve at steady state over 24 h to the MIC (AUC/MIC ratio) was investigated by applying the vancomycin breakpoint distribution of MICs for methicillin-resistant Staphylococcus aureus A total of 22 adult patients with 194 concentration measurements were included. The population PK was best described by a three-compartment model with a proportional residual error model. Vancomycin clearance and steady-state volume of distribution were 4.01 liters/h (0.0542 liters/h/kg) and 29.6 liters (0.400 liters/kg), respectively. If the treatment target AUC/MIC value was only ≥400, a total daily dose of 3 to 4 g would be optimal (PTA of ≥90%) for patients with normal renal function (estimated glomerular filtration rate [eGFR] = 60 to 120 ml/min/1.73 m²) when the MIC was presumed to be 1 mg/liter. However, AUC/MIC values of 400 to 600 were difficult to attain with any dosing strategy regardless of MIC and eGFR. Thus, it is hard to achieve efficacy and safety targets in patients on ECMO using the population dosing approach with Monte Carlo simulations, and therapeutic drug monitoring should be implemented in these patients.

Pharmacokinetic analysis of two different doses of simvastatin following oral administration in dogs

Simvastatin, used orally to treat hyperlipidemia, exhibits highly variable pharmacokinetics (PKs) in humans. The aim of this study was to investigate simvastatin PKs using noncompartmental analysis and population PK models following a single oral administration of two doses (20 and 80 mg) in dogs. Forty beagle dogs were randomly divided into two groups corresponding to the two doses. Blood samples were collected from each group according to the assigned schedule after oral administration. The plasma concentration of simvastatin was determined using liquid chromatography-tandem mass spectrometry. The area under the curve and maximum concentration of simvastatin increased in a dose-dependent manner with high variability. A two-compartment model with first-order absorption (K_a  = 1.83 hr^-1 ) and first-order elimination (clearance [CL/F] = 292 L/h; volume of distribution in the central compartment [V_c /F] = 1506 L) well described the PKs of simvastatin in dogs. Large variability in the PKs of simvastatin was quantitated via modeling approaches, allowing the differentiation of between-subject variability (144.8 CV% for K_a ; 94.7 CV% for CL/F; 97.5 CV% for V_c /F) and residual variability (62.7%). These findings will help facilitate the development of an optimal dose regimen of simvastatin in canines with hypercholesterolemia and may be useful in developing novel formulations.

Nonparametric Methods in Population Pharmacokinetics

Population pharmacokinetic (PK) modeling is a widely used approach to analyze PK data obtained from groups of individuals, in both industry and academic research. The approach can also be used to analyze pharmacodynamic (PD) data and pooled PK/PD data. There are 2 main families of population PK methods: parametric and nonparametric. The objectives of this article are to present an overview of nonparametric methods used in population pharmacokinetic modeling and to explain their specific characteristics to inform scientists and clinicians about their potential value for data analysis, simulation, dosage design, and therapeutic drug monitoring (TDM). Nonparametric methods have several interesting characteristics for population PK analysis, including computation of exact likelihoods, the ability to accommodate parameter probability distributions of any shape (eg, non-Gaussian), and to detect subpopulations and outliers. Nonparametric population methods are also highly relevant for model-based TDM and design of individualized drug dosage regimens. Several algorithms have been developed to estimate model parameter values within an individual and compute that individual's dosage to achieve target drug exposure with maximum precision and accuracy. Nonparametric modeling methods for both population and individual PK analysis are available under user-friendly packages.

Population Pharmacokinetics of Imipenem in Critically Ill Patients: A Parametric and Nonparametric Model Converge on CKD-EPI Estimated Glomerular Filtration Rate as an Impactful Covariate

BACKGROUND

Population pharmacokinetic (popPK) models for antibiotics are used to improve dosing strategies and individualize dosing by therapeutic drug monitoring. Little is known about the differences in results of parametric versus nonparametric popPK models and their potential consequences in clinical practice. We developed both parametric and nonparametric models of imipenem using data from critically ill patients and compared their results.

METHODS

Twenty-six critically ill patients treated with intravenous imipenem/cilastatin were included in this study. Median estimated glomerular filtration rate (eGFR) measured by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was 116 mL/min/1.73 m2 (interquartile range 104-124) at inclusion. The usual dosing regimen was 500 mg/500 mg four times daily. On average, five imipenem levels per patient (138 levels in total) were drawn as peak, intermediate, and trough levels. Imipenem concentration-time profiles were analyzed using parametric (NONMEM 7.2) and nonparametric (Pmetrics 1.5.2) popPK software.

RESULTS

For both methods, data were best described by a model with two distribution compartments and the CKD-EPI eGFR equation unadjusted for body surface area as a covariate on the elimination rate constant (Ke). The parametric population parameter estimates were Ke 0.637 h-1 (between-subject variability [BSV]: 19.0% coefficient of variation [CV]) and central distribution volume (Vc) 29.6 L (without BSV). The nonparametric values were Ke 0.681 h-1 (34.0% CV) and Vc 31.1 L (42.6% CV).

CONCLUSIONS

Both models described imipenem popPK well; the parameter estimates were comparable and the included covariate was identical. However, estimated BSV was higher in the nonparametric model. This may have consequences for estimated exposure during dosing simulations and should be further investigated in simulation studies.

The Population Pharmacokinetics of High-Dose Methotrexate in Infants with Acute Lymphoblastic Leukemia Highlight the Need for Bedside Individualized Dose Adjustment: A Report from the Children's Oncology Group

BACKGROUND

Infants with acute lymphoblastic leukemia (ALL) treated with high-dose methotrexate may have reduced methotrexate clearance (CL) due to renal immaturity, which may predispose them to toxicity.

OBJECTIVE

The aim of this study was to develop a population pharmacokinetic (PK) model of methotrexate in infants with ALL.

METHODS

A total of 672 methotrexate plasma concentrations were obtained from 71 infants enrolled in the Children's Oncology Group (COG) Clinical Trial P9407. Infants received methotrexate 4 g/m2 intravenously for four cycles during weeks 4-12 of intensification. A population PK analysis was performed using NONMEM® version 7.4. The final model was evaluated using a non-parametric bootstrap and a visual predictive check. Simulations were performed to evaluate methotrexate dose and the utility of a bedside algorithm for dose individualization.

RESULTS

Methotrexate was best characterized by a two-compartment model with allometric scaling. Weight was the only covariate included in the final model. The coefficient of variation for interoccasion variability (IOV) on CL was relatively high at 25.4%, compared with the interindividual variability for CL and central volume of distribution (10.7% and 13.2%, respectively). Simulations identified that 21.1% of simulated infants benefitted from bedside dose adjustment, and adjustment of methotrexate doses during infusions can avoid supratherapeutic concentrations.

CONCLUSION

Infants treated with high-dose methotrexate demonstrated a relatively high degree of IOV in methotrexate CL. The magnitude of IOV in the CL of methotrexate suggests that use of a bedside algorithm may avoid supratherapeutic methotrexate concentrations resulting from high IOV in methotrexate CL.

Benefit versus Severe Side Effects of Opioid Analgesia

Background

Previous studies integrated opioid benefit and harm into one single function—the utility function—to determine the drug toxicity (respiratory depression) in light of its wanted effect (analgesia). This study further refined the concept of the utility function using the respiratory and analgesic effects of the opioid analgesic alfentanil as example.

Methods

Data from three previous studies in 48 healthy volunteers were combined and reanalyzed using a population pharmacokinetic–pharmacodynamic analysis to create utility probability functions. Four specific conditions were defined: probability of adequate analgesia without severe respiratory depression, probability of adequate analgesia with severe respiratory depression, probability of inadequate analgesia without severe respiratory depression, and probability of inadequate analgesia with severe respiratory depression.

Results

The four conditions were successfully identified with probabilities varying depending on the opioid effect-site concentration. The optimum analgesia probability without serious respiratory depression is reached at an alfentanil effect-site concentration of 68 ng/ml, and exceeds the probability of the most unwanted effect, inadequate analgesia with severe respiratory depression (odds ratio, 4.0). At higher effect-site concentrations the probability of analgesia is reduced and exceeded by the probability of serious respiratory depression.

Conclusions

The utility function was successfully further developed, allowing assessment of specific conditions in terms of wanted and unwanted effects. This approach can be used to compare the toxic effects of drugs relative to their intended effect and may be a useful tool in the development of new compounds to assess their advantage over existing drugs.

A Population Pharmacokinetic Model for Vancomycin in Adult Patients Receiving Extracorporeal Membrane Oxygenation Therapy

The literature on the pharmacokinetics of vancomycin in patients undergoing extracorporeal membrane oxygenation (ECMO) therapy is sparse. A population pharmacokinetic (PK) model for vancomycin in ECMO patients was developed using a nonlinear mixed effects modeling on the concentration–time profiles of 14 ECMO patients who received intravenous vancomycin. Model selection was based on log‐likelihood criterion, goodness of fit plots, and scientific plausibility. Identification of covariates was done using a full covariate model approach. The pharmacokinetics of vancomycin was adequately described with a two‐compartment model. Parameters included clearance of 2.83 L/hr, limited central volume of distribution 24.2 L, and low residual variability 0.67%. Findings from the analysis suggest that standard dosing recommendations for vancomycin in non‐ECMO patients are adequate to achieve therapeutic trough concentrations in ECMO patients. This further shows that ECMO minimally affects the PK of vancomycin in adults including in higher‐weight patients.

Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org.