Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients

A fully automatic tool for development of population pharmacokinetic models

Population pharmacokinetic (PK) models are widely used to inform drug development by pharmaceutical companies and facilitate drug evaluation by regulatory agencies. Developing a population PK model is a multi-step, challenging, and time-consuming process involving iterative manual model fitting and evaluation. A tool for fully automatic model development (AMD) of common population PK models is presented here. The AMD tool is implemented in Pharmpy, a versatile open-source library for pharmacometrics. It consists of different modules responsible for developing the different components of population PK models, including the structural model, the inter-individual variability (IIV) model, the inter-occasional variability (IOV) model, the residual unexplained variability (RUV) model, the covariate model, and the allometry model. The AMD tool was evaluated using 10 real PK datasets involving the structural, IIV, and RUV modules in three sequences. The different sequences yielded generally consistent structural models; however, there were variations in the results of the IIV and RUV models. The final models of the AMD tool showed lower Bayesian Information Criterion (BIC) values and similar visual predictive check plots compared with the available published models, indicating reasonable quality, in addition to reasonable run time. A similar conclusion was also drawn in a simulation study. The developed AMD tool serves as a promising tool for fast and fully automatic population PK model building with the potential to facilitate the use of modeling and simulation in drug development.

Plan E, Weber B. Bounded integer model-based analysis of psoriasis area and severity index in patients with moderate-to-severe plaque psoriasis receiving BI 730357

BI 730357 is investigated as an oral treatment of plaque psoriasis. We analyzed the impact of three dosage regimens on the Psoriasis Area and Severity Index (PASI) response with modeling based on phase I and II data from 109 healthy subjects and 274 patients with moderate-to-severe plaque psoriasis. The pharmacokinetics (PK) was characterized by a two-compartment model with dual absorption paths and a first-order elimination. Higher baseline C-reactive protein was associated with lower clearance and patients generally had lower clearance compared with healthy subjects. A bounded integer PK/pharmacodynamic model characterized the effect on the observed PASI. The maximum drug effect was largest for patients with no prior biologic use, smaller for patients with prior use of non-interleukin-17 inhibitors, and smallest for patients with prior interleukin-17 inhibitor use. The models allowed robust simulation of large patient populations, predicting a plateau in PASI outcomes for BI 730357 exposure above 2000 nmol/L.

Comparison of Seven Non-Linear Mixed Effect Model-Based Approaches to Test for Treatment Effect

Analyses of longitudinal data with non-linear mixed-effects models (NLMEM) are typically associated with high power, but sometimes at the cost of inflated type I error. Approaches to overcome this problem were published recently, such as model-averaging across drug models (MAD), individual model-averaging (IMA), and combined Likelihood Ratio Test (cLRT). This work aimed to assess seven NLMEM approaches in the same framework: treatment effect assessment in balanced two-armed designs using real natural history data with or without the addition of simulated treatment effect. The approaches are MAD, IMA, cLRT, standard model selection (STDs), structural similarity selection (SSs), randomized cLRT (rcLRT), and model-averaging across placebo and drug models (MAPD). The assessment included type I error, using Alzheimer's Disease Assessment Scale-cognitive (ADAS-cog) scores from 817 untreated patients and power and accuracy in the treatment effect estimates after the addition of simulated treatment effects. The model selection and averaging among a set of pre-selected candidate models were driven by the Akaike information criteria (AIC). The type I error rate was controlled only for IMA and rcLRT; the inflation observed otherwise was explained by the placebo model misspecification and selection bias. Both IMA and rcLRT had reasonable power and accuracy except under a low typical treatment effect.

Investigating the contribution of residual unexplained variability components on bias and imprecision of parameter estimates in population pharmacokinetic mixed-effects modeling

In a nonlinear mixed-effects modeling (NLMEM) approach of pharmacokinetic (PK) and pharmacodynamic (PD) data, two levels of random effects are generally modeled: between-subject variability (BSV) and residual unexplained variability (RUV). The goal of this simulation-estimation study was to investigate the extent to which PK and RUV model misspecification, errors in recording dosing and sampling times, and variability in drug content uniformity contribute to the estimated magnitude of RUV and PK parameter bias. A two-compartment model with first-order absorption and linear elimination was simulated as a true model. PK parameters were clearance 5.0 L/h; central volume of distribution 35 L; inter-compartmental clearance 50 L/h; peripheral volume of distribution 50 L. All parameters were assumed to have a 30% coefficient of variation (CV). One hundred in-silico subjects were administered a labeled dose of 120 mg under 4 sample collection designs. PK and RUV model misspecifications were associated with relatively larger increases in the magnitude of RUV compared to other sources for all levels of sampling design. The contribution of dose and dosing time misspecifications have negligible effects on RUV but result in higher bias in PK parameter estimates. Inaccurate sampling time data results in biased RUV and increases with the magnitude of perturbations. Combined perturbation scenarios in the studied sources will propagate the variability and accumulate in RUV magnitude and bias in PK parameter estimates. This work provides insight into the potential contributions of many factors that comprise RUV and bias in PK parameters.

Population pharmacokinetics and standard uptake value ratio of aducanumab, an amyloid plaque-removing agent, in patients with Alzheimer's disease

Aducanumab is a human immunoglobulin G1 anti-amyloid beta (Aβ) antibody currently being evaluated for potential treatment of patients with early Alzheimer's disease. This paper describes the relationship between the population pharmacokinetics (PopPKs) and pharmacokinetics-pharmacodynamics (PKs-PDs) of aducanumab using data from phase I to III clinical studies, with standard uptake value ratio (SUVR) used as a PD marker. Across clinical studies, aducanumab was administered intravenously either as a single dose ranging from 0.3 to 60 mg/kg or as multiple doses of 1, 3, 6, or 10 mg/kg every 4 weeks. A titration regimen with maintenance doses of 3, 6, or 10 mg/kg was also evaluated. Aducanumab PK was characterized with a two-compartment model with first-order elimination. No nonlinearities in PKs were observed. The PopPK-PD model was developed using a sequential estimation approach. The time course of amyloid plaques, as expressed by composite SUVR measured using positron emission tomography, was described using an indirect response model with drug effect stimulating the elimination of SUVR. None of the identified covariates on PK and the PopPK-PD model were clinically relevant. The PopPK-PD model showed that magnitude, duration, and consistency of dosing are important factors determining the degree of Aβ removal. The intrinsic pharmacology of aducanumab remained consistent across studies.

Ethnobotany of the Himalayas: Safeguarding Medical Practices and Traditional Uses of Kashmir Regions

The present study was carried out to enlist the medicinal plants used by the local inhabitants of developing countries such as India, and the district of Kupwara of the Kashmir Himalaya has been targeted. Our research is one of the first study focusing on the statistical evaluation of the cross-cultural analysis between three different communities i.e., Dard, Kashmiri and Gujjar, of the study area. Sampling was carried out in eight villages in 2017 to 2020, and data were collected from 102 informants based on walking transects, to collect plant specimens, and semi-structured interviews. The medical usages of all collected taxa were grouped into 15 disease categories and 81 biomedical ailments. In this study, we documented around 107 plant taxa belonging to 52 families from the local inhabitants of the Kashmir Himalaya, which regulate the livelihood of the people and support cultural ecosystem services. Asteraceae, Rosaceae, Lamiaceae, Malvaceae, Ranunculaceae, Poaceae, Solanaceae, Polygonaceae, Plantaginaceae and Brassicaceae are the top most dominant families. Herbaceous groups of plants were more common than trees and shrubs, and 71.96% of herb taxa were employed as medicine. Liliaceae, Caprifoliaceae and Portulacaceae (FUV = 0.24 each) have the highest family use value (FUV). The most prominent family was Asteraceae (seven genera, nine taxa), followed by Rosaceae and Lamiaceae (six genera, six taxa each). Persicaria Mill., Rheum L., Aconitum L. and Artemisia L. were prominent genera. Valeriana jatamansi Jones ex Roxb. (47UR), Fritillaria cirrhosa D. Don (45UR), Arisaema jacquemontii Blume (37UR), Asparagus racemosus Willd. (36UR) and Rumex acetosa L. (35UR) were the most important plant taxa with reference to use-reports. The ethnomedicinal applications of Aesculus indica Wall. ex Cambess., Solanum pseudocapsicum L., Ranunculus hirtellus Royle and Cormus domestica (L.) Spach plant taxa are reported here for the first time from the Himalayan Kashmiri people. We recommend further research on ethnopharmacological application of these newly recorded ethnobotanical plants. The medical usage of the plant was limited to different parts of the plant. In terms of the usage percentage, whole plant (26.17%), leaves (24.30%) and roots (19.63%) were found to have the highest utilization. The powder form (40.19%) was the most frequently employed method of drug/medicine preparation, followed by the utilization of extracted juice and/or other extracts (22.43%). The ICF values range from 0.85 to 1.00. Their use to remedy parasitic problems (PAR) and insect bites (IB) (ICF = 1.0 each) had the maximum consensus mentioned by the informants, although the number of taxa employed under this category was very limited. The different plant taxa used for the treatment of the gastrointestinal problems (GAS) was the most prominent disease category (262 URs, 16.19%, 25 taxa, ICF = 0.90). About 65% of the plant taxa studied is indigenous to the Asia or Himalayan regions, and around 35% is found to be exotic in nature. A strong positive correlation was found between age, gender, educational qualification and medicinal plant knowledge. No significant association was between people of different communities interviewed in terms of medical knowledge of the plants, p = 0.347 (>0.05) and χ2 = 2.120. No significant difference was found between the number of species documented concerning gender as p = 0.347 (>0.05) and χ2 =0.885. This study provides the comprehensive status of ethnomedicinal knowledge among three different communities of the study area. This study provided an impetus in discovering the baseline primary data for molecules which would help in drug discovery and management of various diseases, apart from conserving the genepool of plants in the investigated area.

Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models

When data on the degradation of a chemical substance have been collected in a number of environmental media (e.g., in different soils), two strategies can be followed for data evaluation. Currently, each individual dataset is evaluated separately, and representative degradation parameters are obtained by calculating averages of the kinetic parameters. However, such averages often take on unrealistic values if certain degradation parameters are ill-defined in some of the datasets. Moreover, the most appropriate degradation model is selected for each individual dataset, which is time consuming and then requires workarounds for averaging parameters from different models. Therefore, a simultaneous evaluation of all available data is desirable. If the environmental media are viewed as random samples from a population, an advanced strategy based on assumptions about the statistical distribution of the kinetic parameters across the population can be used. Here, we show the advantages of such simultaneous evaluations based on nonlinear mixed-effects models that incorporate such assumptions in the evaluation process. The advantages of this approach are demonstrated using synthetically generated data with known statistical properties and using publicly available experimental degradation data on two pesticidal active substances.

Approaches to handling missing or "problematic" pharmacology data: Pharmacokinetics

Missing or erroneous information is a common problem in the analysis of pharmacokinetic (PK) data. This may present as missing or inaccurate dose level or dose time, drug concentrations below the analytical limit of quantification, missing sample times, or missing or incorrect covariate information. Several methods to handle problematic data have been evaluated, although no single, broad set of recommendations for commonly occurring errors has been published. In this tutorial, we review the existing literature and present the results of our simulation studies that evaluated common methods to handle known data errors to bridge the remaining gaps and expand on the existing knowledge. This tutorial is intended for any scientist analyzing a PK data set with missing or apparently erroneous data. The approaches described herein may also be useful for the analysis of nonclinical PK data.

Bounded Integer Modeling of Symptom Scales Specific to Lower Urinary Tract Symptoms Secondary to Benign Prostatic Hyperplasia

The International Prostate Symptom Score (IPSS), the quality of life (QoL) score, and the benign prostatic hyperplasia impact index (BII) are three different scales commonly used to assess the severity of lower urinary tract symptoms associated with benign prostatic hyperplasia (BPH-LUTS). Based on a phase II clinical trial including 403 patients with moderate to severe BPH-LUTS, the objectives of this study were to (i) develop traditional pharmacometric and bounded integer (BI) models for the IPSS, QoL score, and BII endpoints, respectively; (ii) compare the power and type I error in detecting drug effects of BI modeling with traditional methods through simulation; and (iii) obtain quantitative translation between scores on the three abovementioned scales using a BI modeling framework. All developed models described the data adequately. Pharmacometric modeling using a continuous variable (CV) approach was overall found to be the most robust in terms of type I error and power to detect a drug effect. In most cases, BI modeling showed similar performance to the CV approach, yet severely inflated type I error was generally observed when inter-individual variability (IIV) was incorporated in the BI variance function (g()). BI modeling without IIV in g() showed greater type I error control compared to the ordered categorical approach. Lastly, a multiple-scale BI model was developed and estimated the relationship between scores on the three BPH-LUTS scales with overall low uncertainty. The current study yields greater understanding of the operating characteristics of the novel BI modeling approach and highlights areas potentially requiring further improvement.

Population pharmacokinetics and pharmacodynamics of a novel vascular adhesion protein-1 inhibitor using a multiple-target mediated drug disposition model

ASP8232 is a novel inhibitor of vascular adhesion protein-1 that was under evaluation for reducing residual albuminuria in patients with diabetic kidney disease. To characterize the pharmacokinetics (PK) of ASP8232 and its effect on vascular adhesion protein 1 (VAP-1) plasma activity and VAP-1 concentrations (pharmacodynamics, PD) in an integrated and quantitative manner, a target mediated drug disposition model was developed based on pooled data from four completed clinical trials with ASP8232 in healthy volunteers, and in patients with diabetic kidney disease and diabetic macular edema, respectively. In this model, the binding of ASP8232 to its soluble and membrane-bound target in the central and peripheral compartments were included. The model was able to adequately describe the non-linear PK and PD of ASP8232. The observed difference in PK between healthy volunteers and renally impaired patients could be explained by an effect of baseline estimated glomerular filtration rate on ASP8232 clearance and relative bioavailability. The relationship between ASP8232 concentration and VAP-1 inhibition was successfully established and can be applied to simulate drug exposure and degree of VAP-1 inhibition for any given dose of ASP8232 across the spectrum of renal function.

The Effect of Size, Maturation, Global Asphyxia, Cerebral Ischemia, and Therapeutic Hypothermia on the Pharmacokinetics of High-Dose Recombinant Erythropoietin in Fetal Sheep

High-dose human recombinant erythropoietin (rEPO) is a promising potential neuroprotective treatment in preterm and full-term neonates with hypoxic-ischemic encephalopathy (HIE). There are limited data on the pharmacokinetics of high-dose rEPO in neonates. We examined the effects of body weight, gestation age, global asphyxia, cerebral ischemia, hypothermia and exogenous rEPO on the pharmacokinetics of high-dose rEPO in fetal sheep. Near-term fetal sheep on gestation day 129 (0.87 gestation) (full term 147 days) received sham-ischemia (n = 5) or cerebral ischemia for 30 min followed by treatment with vehicle (n = 4), rEPO (n = 8) or combined treatment with rEPO and hypothermia (n = 8). Preterm fetal sheep on gestation day 104 (0.7 gestation) received sham-asphyxia (n = 1) or complete umbilical cord occlusion for 25 min followed by i.v. infusion of vehicle (n = 8) or rEPO (n = 27) treatment. rEPO was given as a loading bolus, followed by a prolonged continuous infusion for 66 to 71.5 h in preterm and near-term fetuses. A further group of preterm fetal sheep received repeated bolus injections of rEPO (n = 8). The plasma concentrations of rEPO were best described by a pharmacokinetic model that included first-order and mixed-order elimination with linear maturation of elimination with gestation age. There were no detectable effects of therapeutic hypothermia, cerebral ischemia, global asphyxia or exogenous treatment on rEPO pharmacokinetics. The increase in rEPO elimination with gestation age suggests that to maintain target exposure levels during prolonged treatment, the dose of rEPO may have to be adjusted to match the increase in size and growth. These results are important for designing and understanding future studies of neuroprotection with high-dose rEPO.

Mechanistic Pharmacokinetic/Pharmacodynamic Model of Sunitinib and Dopamine in MCF-7/Adr Xenografts: Linking Cellular Heterogeneity to Tumour Burden

The self-renewal and differentiation of cancer stem-like cells (CSCs) leads to cellular heterogeneity, causing one of the greatest challenges in cancer therapy. Growing evidence suggests that CSC-targeting therapy enhances the effect of concomitant antitumour therapy. To gain an in-depth understanding of this enhanced effect, the kinetic profile of estimated CSC frequency (the fraction of CSCs in tumour) was evaluated for in vivo characterization of cellular heterogeneity using sunitinib and dopamine as a paradigm combination therapy. Female MCF-7/Adr xenografted Balb/c nude mice were treated with sunitinib (p.o., 20 mg/kg) and dopamine (i.p., 50 mg/kg), alone or in combination. Estimated CSC frequency and tumour size were measured over time. Mechanistic PK/PD modelling was performed to quantitatively describe the relationship between drug concentration, estimated CSC frequency and tumour size. Sunitinib reduced tumour size by inducing apoptosis of differentiated tumour cells (DTCs) and enriched CSCs by stimulating its proliferation. Dopamine exhibited anti-CSC effects by suppressing the capacity of CSCs and inducing its differentiation. Simulation and animal studies indicated that concurrent administration was superior to sequential administration under current experimental conditions. Alongside tumour size, the current study provides mechanistic insights into the estimation of CSC frequency as an indicator for cellular heterogeneity. This forms the conceptual basis for in vivo characterization of other combination therapies in preclinical cancer studies.

Evaluation of Assumptions Underpinning Pharmacometric Models

Assumptions inherent to pharmacometric model development and use are not routinely acknowledged, described, or evaluated. The aim of this work is to present a framework for systematic evaluation of assumptions. To aid identification of assumptions, we categorise assumptions into two types: implicit and explicit assumptions. Implicit assumptions are inherent in a method or model and underpin its derivation and use. Explicit assumptions arise from heuristic principles and are typically defined by the user to enable the application of a method or model. A flowchart was developed for systematic evaluation of assumptions. For each assumption, the impact of assumption violation ('significant', 'insignificant', 'unknown') and the probability of assumption violation ('likely', 'unlikely', 'unknown') will be evaluated based on prior knowledge or the result of an additional bespoke study to arrive at a decision ('go', 'no-go') for both model building and model use. A table of assumptions with standardised headings has been proposed to facilitate the documentation of assumptions and evaluation of results. The utility of the proposed framework was illustrated using four assumptions underpinning a top-down model describing the warfarin-coagulation proteins' relationship. The next step of this work is to apply the framework to a series of other settings to fully assess its practicality and its value in identifying and making inferences from assumptions.

Model-free and kinetic modelling approaches for characterising non-equilibrium pharmacological pathway activity: Internalisation of cannabinoid CB1 receptors

BACKGROUND AND PURPOSE

Receptor internalisation is by nature kinetic. Application of a standard equilibrium dose response model to describe the properties of a ligand inducing internalisation, while commonly used, are therefore problematic. Here, we propose two quantitative approaches to address this issue-(a) a model-free method and (b) a kinetic modelling approach-and systematically evaluate the performance of these methods against traditional equilibrium methods to characterise the internalisation profiles of cannabinoid CB1 receptor agonists.

EXPERIMENTAL APPROACH

Kinetic internalisation assays were conducted using a concentration series of six CB1 receptor ligands. Internalisation rate analysis and snapshot equilibrium analysis were performed. A model-free method was developed based on the mean residence time of internalisation. A kinetic internalisation model was developed under the quasi-steady state assumption.

KEY RESULTS

Rates of receptor internalisation depended on both agonist and concentration. Agonist potencies from snapshot equilibrium analysis increased with stimulation time, and there was no single time point at which internalisation profiles could infer agonist properties in a comparative manner. The model-free method yielded a time-invariant measure of potency/efficacy for internalisation. The kinetic model adequately described the internalisation of CB1 receptors over time and provided robust estimates of both potency and efficacy.

CONCLUSION AND IMPLICATIONS

Applying equilibrium analysis to a non-equilibrium pathway cannot provide a reliable estimate of agonist potency. Both the model-free and kinetic modelling approaches characterised the internalisation profiles of CB1 receptor agonists. The kinetic model provides additional advantages as a method to capture changes in receptor number during other functional assays.

A Bounded Integer Model for Rating and Composite Scale Data

Rating and composite scales are commonly used to assess treatment efficacy. The two main strategies for modelling such endpoints are to treat them as a continuous or an ordered categorical variable (CV or OC). Both strategies have disadvantages, including making assumptions that violate the integer nature of the data (CV) and requiring many parameters for scales with many response categories (OC). We present a method, called the bounded integer (BI) model, which utilises the probit function with fixed cut-offs to estimate the probability of a certain score through a latent variable. This method was successfully implemented to describe six data sets from four different therapeutic areas: Parkinson's disease, Alzheimer's disease, schizophrenia, and neuropathic pain. Five scales were investigated, ranging from 11 to 181 categories. The fit (likelihood) was better for the BI model than for corresponding OC or CV models (ΔAIC range 11-1555) in all cases but one (∆AIC - 63), while the number of parameters was the same or lower. Markovian elements were successfully implemented within the method. The performance in external validation, assessed through cross-validation, was also in favour of the new model (ΔOFV range 22-1694) except in one case (∆OFV - 70). A residual for diagnostic purposes is discussed. This study shows that the BI model respects the integer nature of data and is parsimonious in terms of number of estimated parameters.

Population Pharmacokinetic Modeling in the Presence of Missing Time-Dependent Covariates: Impact of Body Weight on Pharmacokinetics of Paracetamol in Neonates

Body weight is the primary covariate in pharmacokinetics of many drugs and dramatically changes during the first weeks of life of neonates. The objective of this study is to determine if missing body weights in preterm and term neonates affect estimates of model parameters and which methods can be used to improve performance of a population pharmacokinetic model of paracetamol. Data for our analysis were obtained from previously published studies on the pharmacokinetics of intravenous paracetamol in neonates. We adopted a population model of body weight change in neonates to implement three previously introduced methods of handling missing covariates based on data imputation, likelihood function modification, and full random effects modeling. All models were implemented in NONMEM 7.4, and population parameters were estimated using the FOCE method. Our major finding was that missing body weights minimally affect population estimates of pharmacokinetic parameters but do affect the covariate relationship parameters, particularly the one describing dependence of clearance on body weight. None of the tested methods changed estimates of between-subject variability nor impacted the predictive performance of the model. Our analysis shows that a modeling approach towards handling missing covariates allows borrowing information gathered in various studies as long as they target the same population. This approach is particularly useful for handling time-dependent missing covariates.

Translation Between Two Models; Application with Integrated Glucose Homeostasis Models

PURPOSE

For some biological systems, there exist several models with somewhat different features and perspectives. We propose an evaluation method for NLME models by analyzing real and simulated data from the model of main interest using a structurally different, but similar, NLME model. We showcase this method using the Integrated Glucose Insulin (IGI) model and the Integrated Minimal Model (IMM). Additionally, we try to map parameters carrying similar information between the two models.

METHODS

A bootstrap of real data and simulated datasets from both the IMM and IGI models were analyzed with the two models. Important parameters of the IMM were mapped to IGI parameters using a large IMM simulated dataset analyzed under the IGI model.

RESULTS

Comparison of the parameters estimated from real data and data simulated with the IMM and analyzed with the IGI model demonstrated differences between real and IMM-simulated data. Comparison of the parameters estimated from real data and data simulated with the IGI model and analyzed with the IMM also demonstrated differences but to a lower extent. The strongest parameter correlations were found for: insulin-dependent glucose clearance (IGI) ~ insulin sensitivity (IMM); insulin-independent glucose clearance (IGI) ~ glucose effectiveness (IMM); and insulin effect parameter (IGI) ~ insulin action (IMM).

CONCLUSIONS

We demonstrated a new approach to investigate models' ability to simulate real-life-like data, and the information captured in each model in comparison to real data, and the IMM clinically used parameters were successfully mapped to their corresponding IGI parameters.

Variability Attribution for Automated Model Building

We investigated the possible advantages of using linearization to evaluate models of residual unexplained variability (RUV) for automated model building in a similar fashion to the recently developed method “residual modeling.” Residual modeling, although fast and easy to automate, cannot identify the impact of implementing the needed RUV model on the imprecision of the rest of model parameters. We used six RUV models to be tested with 12 real data examples. Each example was first linearized; then, we assessed the agreement in improvement of fit between the base model and its extended models for linearization and conventional analysis, in comparison to residual modeling performance. Afterward, we compared the estimates of parameters’ variabilities and their uncertainties obtained by linearization to conventional analysis. Linearization accurately identified and quantified the nature and magnitude of RUV model misspecification similar to residual modeling. In addition, linearization identified the direction of change and quantified the magnitude of this change in variability parameters and their uncertainties. This method is implemented in the software package PsN for automated model building/evaluation with continuous data.

Model-Based Conditional Weighted Residuals Analysis for Structural Model Assessment

Nonlinear mixed effects models are widely used to describe longitudinal data to improve the efficiency of drug development process or increase the understanding of the studied disease. In such settings, the appropriateness of the modeling assumptions is critical in order to draw correct conclusions and must be carefully assessed for any substantial violations. Here, we propose a new method for structure model assessment, based on assessment of bias in conditional weighted residuals (CWRES). We illustrate this method by assessing prediction bias in two integrated models for glucose homeostasis, the integrated glucose-insulin (IGI) model, and the integrated minimal model (IMM). One dataset was simulated from each model then analyzed with the two models. CWRES outputted from each model fitting were modeled to capture systematic trends in CWRES as well as the magnitude of structural model misspecifications in terms of difference in objective function values (ΔOFV_Bias). The estimates of CWRES bias were used to calculate the corresponding bias in conditional predictions by the inversion of first-order conditional estimation method’s covariance equation. Time, glucose, and insulin concentration predictions were the investigated independent variables. The new method identified correctly the bias in glucose sub-model of the integrated minimal model (IMM), when this bias occurred, and calculated the absolute and proportional magnitude of the resulting bias. CWRES bias versus the independent variables agreed well with the true trends of misspecification. This method is fast easily automated diagnostic tool for model development/evaluation process, and it is already implemented as part of the Perl-speaks-NONMEM software.

Full-Profile Pharmacokinetic Study of High Dose Baclofen in Subjects With Alcohol Use Disorder

Baclofen a gamma amino-butyric acid type B (GABA-B) receptor agonist, which has raised some interest for the treatment of alcohol use disorder (AUD), occasionally at dose up to 300 mg/d. We conducted the first full-profile pharmacokinetic study on baclofen in AUD subjects, up to the oral daily dose of 300 mg. Sixty subjects treated for AUD with marketed baclofen were enrolled in a prospective phase-1 study. Participants were divided into four dose groups (1: <60 mg/d; 2: 60-120 mg/d; 3: >120 mg/d-180 mg/d; and 4: >180 mg/d), and they underwent a full-profile pharmacokinetic analysis of baclofen, using a nonlinear mixed effects modeling. The influence of different clinical and biological covariates was assessed in an upward modeling. Fifty-seven participants completed the study (522 observed concentrations collected). Racemic baclofen showed a linear pharmacokinetic profile, corresponding to a one-compartment model, with no influencing clinical or biological factor. The pharmacokinetic parameters of baclofen were (bootstrap 95% confidence intervals): absorption constant (Ka) 1.64 1/h (1.34-2), clearance (Cl/F) 11.6 L/h (10.8-12.3) and volume of distribution (Vd/F) 72.8 L (66.5-80.4) leading to a half-life of 4.4 h. The interindividual variability (IIV) was 44% (19-65), 21% (16-27), and 22% (11-36) for Ka, Cl/F, and Vd/F, respectively. The residual variability was 24% (21-26). No serious adverse event was reported. Registration: EudraCT #2013-003412-46.

Model-Based Residual Post-Processing for Residual Model Identification

The purpose of this study was to investigate if model-based post-processing of common diagnostics can be used as a diagnostic tool to quantitatively identify model misspecifications and rectifying actions. The main investigated diagnostic is conditional weighted residuals (CWRES). We have selected to showcase this principle with residual unexplained variability (RUV) models, where the new diagnostic tool is used to scan extended RUV models and assess in a fast and robust way whether, and what, extensions are expected to provide a superior description of data. The extended RUV models evaluated were autocorrelated errors, dynamic transform both sides, inter-individual variability on RUV, power error model, t-distributed errors, and time-varying error magnitude. The agreement in improvement in goodness-of-fit between implementing these extended RUV models on the original model and implementing these extended RUV models on CWRES was evaluated in real and simulated data examples. Real data exercise was applied to three other diagnostics: conditional weighted residuals with interaction (CWRESI), individual weighted residuals (IWRES), and normalized prediction distribution errors (NPDE). CWRES modeling typically predicted (i) the nature of model misspecifications, (ii) the magnitude of the expected improvement in fit in terms of difference in objective function value (ΔOFV), and (iii) the parameter estimates associated with the model extension. Alternative metrics (CWRESI, IWRES, and NPDE) also provided valuable information, but with a lower predictive performance of ΔOFV compared to CWRES. This method is a fast and easily automated diagnostic tool for RUV model development/evaluation process; it is already implemented in the software package PsN.

A tutorial on model informed approaches to cardiovascular safety with focus on cardiac repolarisation

Drugs can affect the cardiovascular (CV) system either as an intended treatment or as an unwanted side effect. In both cases, drug-induced cardiotoxicities such as arrhythmia and unfavourable hemodynamic effects can occur, and be described using mathematical models; such a model informed approach can provide valuable information during drug development and can aid decision-making. However, in order to develop informative models, it is vital to understand CV physiology. The aims of this tutorial are to present (1) key background biological and medical aspects of the CV system, (2) CV electrophysiology, (3) CV safety concepts, (4) practical aspects of development of CV models and (5) regulatory expectations with a focus on using model informed and quantitative approaches to support nonclinical and clinical drug development. In addition, we share several case studies to provide practical information on project strategy (planning, key questions, assumptions setting, and experimental design) and mathematical models development that support decision-making during drug discovery and development.

Population Pharmacokinetics of Lopinavir in Severely Malnourished HIV-infected Children and the Effect on Treatment Outcomes

BACKGROUND

In developing countries, malnutrition remains a common clinical syndrome at antiretroviral treatment (ART) initiation. Physiologic changes because of malnutrition and during nutritional recovery could affect the pharmacokinetics of antiretroviral drugs.

METHODS

HIV-infected children admitted with severe acute malnutrition were randomized to early or delayed initiation of lopinavir (LPV)/ritonavir, abacavir and lamivudine using World Health Organization weight band dosage charts. LPV concentrations were measured on day 1 and day 14. Thereafter, patients were followed-up to week 48. The population pharmacokinetics of LPV was described using NONMEM v7.3. Covariates were screened to assess their influence on the pharmacokinetics of LPV, and the relationship between pharmacokinetic variability and treatment outcomes were assessed.

RESULTS

Five hundred and two LPV concentrations were collected from 62 pediatric patients 0.1-3.9 years of age (median: 0.9 years). Rifampin-based antituberculosis treatment and "super-boosted" LPV/ritonavir were prescribed in 20 patients. LPV disposition was well described by a one-compartment model with first-order elimination. Neither randomization to early or delayed ART, tuberculosis comedications nor anthropometrical measurements explained the pharmcokinetic variability. Allometrically scaled fat-free mass influenced apparent clearance (CL/F) and volume of distribution (Vd/F). Pharmacokinetic exposure did not correlate with virologic outcomes or death at 12 or 48 weeks.

CONCLUSIONS

LPV pharmacokinetics was influenced by fat-free mass and not by timing of ART initiation or tuberculosis comedication in severely malnourished HIV-infected children. LPV pharmacokinetics was found to be highly variable and bioavailability greatly reduced, resulting in a high CL estimate in this population. The role of LPV dose adjustment should be further evaluated in severely malnourished children initiating ART.

An automated sampling importance resampling procedure for estimating parameter uncertainty

Quantifying the uncertainty around endpoints used for decision-making in drug development is essential. In nonlinear mixed-effects models (NLMEM) analysis, this uncertainty is derived from the uncertainty around model parameters. Different methods to assess parameter uncertainty exist, but scrutiny towards their adequacy is low. In a previous publication, sampling importance resampling (SIR) was proposed as a fast and assumption-light method for the estimation of parameter uncertainty. A non-iterative implementation of SIR proved adequate for a set of simple NLMEM, but the choice of SIR settings remained an issue. This issue was alleviated in the present work through the development of an automated, iterative SIR procedure. The new procedure was tested on 25 real data examples covering a wide range of pharmacokinetic and pharmacodynamic NLMEM featuring continuous and categorical endpoints, with up to 39 estimated parameters and varying data richness. SIR led to appropriate results after 3 iterations on average. SIR was also compared with the covariance matrix, bootstrap and stochastic simulations and estimations (SSE). SIR was about 10 times faster than the bootstrap. SIR led to relative standard errors similar to the covariance matrix and SSE. SIR parameter 95% confidence intervals also displayed similar asymmetry to SSE. In conclusion, the automated SIR procedure was successfully applied over a large variety of cases, and its user-friendly implementation in the PsN program enables an efficient estimation of parameter uncertainty in NLMEM.

Pharmacokinetics of S-ketamine during prolonged sedation at the pediatric intensive care unit

BACKGROUND

S-ketamine is the S(+)-enantiomer of the racemic mixture ketamine, an anesthetic drug providing both sedation and analgesia. In clinical practice, significant interpatient variability in drug effect of S-ketamine is observed during long-term sedation.

AIMS

The aim of this study was to evaluate the pharmacokinetic variability of S-ketamine in children aged 0-18 years during long-term sedation. Twenty-five children (median age: 0.42 years, range: 0.02-12.5) received continuous intravenous administrations of 0.3-3.6 mg/kg/h S-ketamine for sedation during mechanical ventilation. Infusion rates were adjusted to the desired level of sedation and analgesia based on the COMFORT-B score and Visual Analog Scale. Blood samples were drawn once daily at random time-points, and at 1 and 4 hours after discontinuation of S-ketamine infusion. Time profiles of plasma concentrations of S-ketamine and active metabolite S-norketamine were analyzed using nonlinear mixed-effects modeling software. Clearance and volume of distribution were allometrically scaled using the ¾ power model.

RESULTS

A total of 86 blood samples were collected. A 2-compartment and 1-compartment model adequately described the PK of S-ketamine and S-norketamine, respectively. The typical parameter estimates for clearance and central and peripheral volumes of distribution were: CL_S-KETAMINE =112 L/h/70 kg, V1_S-KETAMINE =7.7 L/70 kg, V2_S-KETAMINE =545L/70 kg, Q_S-kETAMINE =196 L/h/70 kg, and CL_{S-NORKETAMINE} =53 L/h/70 kg. Interpatient variability of CL_S-KETAMINE and CL_{S-NORKETAMINE} was considerable with values of 40% and 104%, respectively, leading to marked variability in steady-state plasma concentrations.

CONCLUSION

Substantial interpatient variability in pharmacokinetics in children complicates the development of adequate dosage regimen for continuous sedation.

A population pharmacokinetic meta-analysis of custirsen, an antisense oligonucleotide, in oncology patients and healthy subjects

AIMS

Custirsen (OGX-011/TV-1011), a second-generation antisense oligonucleotide that reduces clusterin production, is under investigation with chemotherapy in prostate and lung cancer. This meta-analysis evaluated the population pharmacokinetics (PK) of custirsen in cancer patients and healthy subjects.

METHODS

The population PK analysis used custirsen plasma concentrations from five Phase 1 studies, one Phase 1/2 study, and one Phase 3 study in two stages. Cancer patients received multiple doses of custirsen (40-640 mg intravenously over 120 min) with chemotherapy; healthy subjects received single or multiple doses (320-640 mg). An interim population PK model was developed using a nonlinear mixed-effect approach incorporating data from four Phase 1 or 1/2 studies, followed by model refinement and inclusion of two Phase 1 and one Phase 3 studies.

RESULTS

The final model was developed with 5588 concentrations from 631 subjects with doses of 160-640 mg. Custirsen PK was adequately described by a three-compartment model with first-order elimination. For a representative 66-year-old individual with body weight 82 kg and serum creatinine level 0.933 mg dl^-1 , the estimated typical (95% CI) parameter values were clearance (CL) = 2.36 (2.30-2.42) l h^-1 , central volume of distribution (V₁ ) = 6.08 (5.93-6.23) l, peripheral volume of distribution (V₂ ) = 1.13 (1.01-1.25) l, volume of the second peripheral compartment (V₃ ) = 15.8 (14.6-17.0) l, inter-compartmental clearance Q₂ = 0.0755 (0.0689-0.0821) l h^-1 , and Q₃ = 0.0573 (0.0532-0.0614) l h^-1 . Age, weight and serum creatinine were predictors of CL; age was a predictor of Q₃ .

CONCLUSION

A population PK model for custirsen was successfully developed in cancer patients and healthy subjects, including covariates contributing to variability in custirsen PK.

Phxnlme: An R package that facilitates pharmacometric workflow of Phoenix NLME analyses

BACKGROUND AND OBJECTIVE

Pharmacometric analyses are integral components of the drug development process, and Phoenix NLME is one of the popular software used to conduct such analyses. To address current limitations with model diagnostic graphics and efficiency of the workflow for this software, we developed an R package, Phxnlme, to facilitate its workflow and provide improved graphical diagnostics.

METHODS

Phxnlme was designed to provide functionality for the major tasks that are usually performed in pharmacometric analyses (i.e. nonlinear mixed effects modeling, basic model diagnostics, visual predictive checks and bootstrap). Various estimation methods for modeling using the R package are made available through the Phoenix NLME engine. The Phxnlme R package utilizes other packages such as ggplot2 and lattice to produce the graphical output, and various features were included to allow customizability of the output. Interactive features for some plots were also added using the manipulate R package.

RESULTS

Phxnlme provides enhanced capabilities for nonlinear mixed effects modeling that can be accessed using the phxnlme() command. Output from the model can be graphed to assess the adequacy of model fits and further explore relationships in the data using various functions included in this R package, such as phxplot() and phxvpc.plot(). Bootstraps, stratified up to three variables, can also be performed to obtain confidence intervals around the model estimates. With the use of an R interface, different R projects can be created to allow multi-tasking, which addresses the current limitation of the Phoenix NLME desktop software. In addition, there is a wide selection of diagnostic and exploratory plots in the Phxnlme package, with improvements in the customizability of plots, compared to Phoenix NLME.

CONCLUSIONS

The Phxnlme package is a flexible tool that allows implementation of the analytical workflow of Phoenix NLME with R, with features for greater overall efficiency and improved customizable graphics. Phxnlme is freely available for download on the CRAN repository (https://cran.r-project.org/web/packages/Phxnlme/).

Improving the estimation of parameter uncertainty distributions in nonlinear mixed effects models using sampling importance resampling

Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.

Prediction of Intravenous Busulfan Clearance by Endogenous Plasma Biomarkers Using Global Pharmacometabolomics

INTRODUCTION

High-dose busulfan (busulfan) is an integral part of the majority of hematopoietic cell transplantation conditioning regimens. Intravenous (IV) busulfan doses are personalized using pharmacokinetics (PK)-based dosing where the patient's IV busulfan clearance is calculated after the first dose and is used to personalize subsequent doses to a target plasma exposure. PK-guided dosing has improved patient outcomes and is clinically accepted but highly resource intensive.

OBJECTIVE

We sought to discover endogenous plasma biomarkers predictive of IV busulfan clearance using a global pharmacometabolomics-based approach.

METHODS

Using LC-QTOF, we analyzed 59 (discovery) and 88 (validation) plasma samples obtained before IV busulfan administration.

RESULTS

In the discovery dataset, we evaluated the association of the relative abundance of 1885 ions with IV busulfan clearance and found 21 ions that were associated with IV busulfan clearance tertiles (r² ≥ 0.3). Identified compounds were deoxycholic acid and/or chenodeoxycholic acid, and linoleic acid. We used these 21 ions to develop a parsimonious seven-ion linear predictive model that accurately predicted IV busulfan clearance in 93% (discovery) and 78% (validation) of samples.

CONCLUSION

IV busulfan clearance was significantly correlated with the relative abundance of 21 ions, seven of which were included in a predictive model that accurately predicted IV busulfan clearance in the majority of the validation samples. These results reinforce the potential of pharmacometabolomics as a critical tool in personalized medicine, with the potential to improve the personalized dosing of drugs with a narrow therapeutic index such as busulfan.

Population Pharmacokinetics of Tenofovir in HIV-1-Uninfected Members of Serodiscordant Couples and Effect of Dose Reporting Methods

Antiretroviral preexposure prophylaxis (PrEP) with once-daily dosing of tenofovir and tenofovir-emtricitabine was shown to be effective for preventing HIV-1 infection in individuals who had HIV-1-seropositive partners (the Partners PrEP Study). We developed a population pharmacokinetic model for tenofovir and investigated the impacts of different dose reporting methods. Dosing information was collected as patient-reported dosing information (PRDI) from 404 subjects (corresponding to 1,280 drug concentration records) from the main trial and electronic monitoring-based adherence data collected from 211 subjects (corresponding to 327 drug concentration records) in an ancillary adherence study. Model development was conducted with NONMEM (7.2), using PRDI with a steady-state assumption or using PRDI replaced with electronic monitoring records where available. A two-compartment model with first-order absorption was the best model in both modeling approaches, with the need for an absorption lag time when electronic monitoring-based dosing records were included in the analysis. Age, body weight, and creatinine clearance were significant covariates on clearance, but only creatinine clearance was retained in the final models per stepwise selection. Sex was not a significant covariate on clearance. Tenofovir population pharmacokinetic parameter estimates and the precisions of the parameters from the two final models were comparable with the point estimates of the parameters, differing from 0% to 35%, and bootstrap confidence intervals widely overlapped. These findings indicate that PRDI was sufficient for population pharmacokinetic model development in this study, with a high level of adherence per multiple measures.

Therapeutic drug monitoring of cancer chemotherapy

Therapeutic drug monitoring is not routinely used for chemotherapy agents. There are Several reasons, but one major drawback is the lack of established therapeutic Concentration ranges. Combination chemotherapy makes the establishment of Therapeutic ranges for individual drugs difficult, the concentration-effect relationship for a single drug may not be the same as when that drug is used in a drug combination. Pharmacokinetic optimization protocols for many classes of cytotoxic compounds exist in specialized centers, and some of these protocols are now part of large multicentre trials. Nonetheless, TDM clearly has the potential to improve the clinical use of chemotherapy gents, most of which have very narrow therapeutic indices and highly variable pharmacokinetics. A substantial body of literature accumulating during the past 15 years demonstrates relationships between systemic exposure to various chemotherapy agents and their toxic or therapeutic effects. This article reviews TDM concepts in addition to tools based on pharmacokinetic modeling of chemotherapy agents. The administered dose of chemotherapy agents is sometimes adjusted individually using either a priori or a posteriori methods. These models can only be applied by using the same dose and schedule as the original study. Bayesian estimation offers more flexibility in blood sampling times and, owing to its precision and to the amount of information provided is the method of choice for ensuring that a given patient benefits from the desired systemic exposure. Moreover, the role and application of Pharmacogenetics as a tool for individualizing chemotherapy is discussed highlighting the agents and mechanisms that have been well studied and defined and their relevance to clinical practice. Finally, this paper address issues critical to the optimal use of TDM in a clinical setting, and the role of clinical pharmacist in this regard. In addition, it discusses future developments in this field that can contribute to improving cancer chemotherapy In terms of patient outcome and survival. J Oncol Pharm Practice (2007) 13: 207—221.

A diagnostic tool for population models using non-compartmental analysis: The ncappc package for R

BACKGROUND AND OBJECTIVE

Non-compartmental analysis (NCA) calculates pharmacokinetic (PK) metrics related to the systemic exposure to a drug following administration, e.g. area under the concentration-time curve and peak concentration. We developed a new package in R, called ncappc, to perform (i) a NCA and (ii) simulation-based posterior predictive checks (ppc) for a population PK (PopPK) model using NCA metrics.

METHODS

The nca feature of ncappc package estimates the NCA metrics by NCA. The ppc feature of ncappc estimates the NCA metrics from multiple sets of simulated concentration-time data and compares them with those estimated from the observed data. The diagnostic analysis is performed at the population as well as the individual level. The distribution of the simulated population means of each NCA metric is compared with the corresponding observed population mean. The individual level comparison is performed based on the deviation of the mean of any NCA metric based on simulations for an individual from the corresponding NCA metric obtained from the observed data. The ncappc package also reports the normalized prediction distribution error (NPDE) of the simulated NCA metrics for each individual and their distribution within a population.

RESULTS

The ncappc produces two default outputs depending on the type of analysis performed, i.e., NCA and PopPK diagnosis. The PopPK diagnosis feature of ncappc produces 8 sets of graphical outputs to assess the ability of a population model to simulate the concentration-time profile of a drug and thereby evaluate model adequacy. In addition, tabular outputs are generated showing the values of the NCA metrics estimated from the observed and the simulated data, along with the deviation, NPDE, regression parameters used to estimate the elimination rate constant and the related population statistics.

CONCLUSIONS

The ncappc package is a versatile and flexible tool-set written in R that successfully estimates NCA metrics from concentration-time data and produces a comprehensive set of graphical and tabular output to summarize the diagnostic results including the model specific outliers. The output is easy to interpret and to use in evaluation of a population PK model. ncappc is freely available on CRAN (http://cran.r-project.org/web/packages/ncappc/index.html/) and GitHub (https://github.com/cacha0227/ncappc/).

Reporting Guidelines for Clinical Pharmacokinetic Studies: The ClinPK Statement

BACKGROUND AND OBJECTIVE

Transparent reporting of all research is essential for assessing the validity of any study. Reporting guidelines are available and endorsed for many types of research but are lacking for clinical pharmacokinetic studies. Such tools promote the consistent reporting of a minimal set of information for end users, and facilitate knowledge translation of research. The objective of this study was to create a guideline to assist in the transparent and complete reporting of clinical pharmacokinetic studies.

METHODS

Preliminary content to be considered was identified from a systematic search of the literature and regulatory documents. Stakeholders were identified to participate in a modified Delphi exercise and a virtual meeting to generate consensus for items considered essential in the reporting of clinical pharmacokinetic studies. The proposed checklist was pilot tested on 100 recently published clinical pharmacokinetic studies. Overall and itemized compliance with the proposed guidance was determined for each study.

RESULTS

Sixty-eight stakeholders from nine countries consented to participate. Four rounds of a modified Delphi survey and a series of small virtual meetings were required to generate consensus for a 24-item checklist considered to be essential to the reporting of clinical pharmacokinetic studies. When applied to the 100 most recently published clinical pharmacokinetic studies, 45 were determined to be compliant with at least 80 % of the checklist items. Explanatory text was prepared using examples of compliant reporting from these and other relevant studies.

CONCLUSIONS

The reader's ability to judge the validity of pharmacokinetic research can be greatly compromised by the incomplete reporting of study information. Using consensus methods, we have developed a tool to guide transparent and accurate reporting of clinical pharmacokinetic studies. Endorsement and implementation of these guidelines by researchers, clinicians and journals would promote more consistent reporting of these studies and allow for better assessment of utility for clinical applications.

A strategy for residual error modeling incorporating scedasticity of variance and distribution shape

Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of commonly used models. In this work, two strategies are proposed to extend and unify residual error modeling: a dynamic transform-both-sides approach combined with a power error model (dTBS) capable of handling skewed and/or heteroscedastic residuals, and a t-distributed residual error model allowing for symmetric heavy tails. Ten published pharmacokinetic and pharmacodynamic models as well as stochastic simulation and estimation were used to evaluate the two approaches. dTBS always led to significant improvements in objective function value, with most examples displaying some degree of right-skewness and variances proportional to predictions raised to powers between 0 and 1. The t-distribution led to significant improvement for 5 out of 10 models with degrees of freedom between 3 and 9. Six models were most improved by the t-distribution while four models benefited more from dTBS. Changes in other model parameter estimates were observed. In conclusion, the use of dTBS and/or t-distribution models provides a flexible and easy-to-use framework capable of characterizing all commonly encountered residual error distributions.

Tramadol and o-desmethyl tramadol clearance maturation and disposition in humans: a pooled pharmacokinetic study

BACKGROUND AND OBJECTIVES

We aimed to study the impact of size, maturation and cytochrome P450 2D6 (CYP2D6) genotype activity score as predictors of intravenous tramadol disposition.

METHODS

Tramadol and O-desmethyl tramadol (M1) observations in 295 human subjects (postmenstrual age 25 weeks to 84.8 years, weight 0.5-186 kg) were pooled. A population pharmacokinetic analysis was performed using a two-compartment model for tramadol and two additional M1 compartments. Covariate analysis included weight, age, sex, disease characteristics (healthy subject or patient) and CYP2D6 genotype activity. A sigmoid maturation model was used to describe age-related changes in tramadol clearance (CLPO), M1 formation clearance (CLPM) and M1 elimination clearance (CLMO). A phenotype-based mixture model was used to identify CLPM polymorphism.

RESULTS

Differences in clearances were largely accounted for by maturation and size. The time to reach 50 % of adult clearance (TM50) values was used to describe maturation. CLPM (TM50 39.8 weeks) and CLPO (TM50 39.1 weeks) displayed fast maturation, while CLMO matured slower, similar to glomerular filtration rate (TM50 47 weeks). The phenotype-based mixture model identified a slow and a faster metabolizer group. Slow metabolizers comprised 9.8 % of subjects with 19.4 % of faster metabolizer CLPM. Low CYP2D6 genotype activity was associated with lower (25 %) than faster metabolizer CLPM, but only 32 % of those with low genotype activity were in the slow metabolizer group.

CONCLUSIONS

Maturation and size are key predictors of variability. A two-group polymorphism was identified based on phenotypic M1 formation clearance. Maturation of tramadol elimination occurs early (50 % of adult value at term gestation).

Omeprazole, pantoprazole, and CYP2C19 effects on clopidogrel pharmacokinetic-pharmacodynamic relationships in stable coronary artery disease patients

PURPOSE

Proton-pump Inhibitors use and CYP2C19 loss-of-function alleles are associated with reduced responsiveness to standard clopidogrel doses and increased cardiovascular events.

METHODS

Post-myocardial infarction patients heterozygous (wild type [wt]/*2, n = 41) or homozygous (*2/*2, n = 7) for the CYP2C19*2 genetic variant were matched with patients not carrying the variant (wt/wt, n = 58). All patients were randomized to a 300- or 900-mg clopidogrel loading dose. A PK/PD model was defined using the variation of the P2Y12 reaction unit relative to baseline.

RESULTS

Carriage of CYP2C19*2 allele and the use of omeprazole/esomeprazole were associated with the inter-individual variability in the active metabolite clearance. The relationship between inhibition of platelet aggregation (IPA, %) and the active metabolite AUC (h*μg/L) was described by a sigmoid function (Emax 56 ± 5%; EAUC50 15.9 ± 0.8 h*μg/L) with a gamma exponent (7.04 ± 2.26).

CONCLUSION

This on/off shape explains that a small variation of exposure may have a clinical relevance.

A general purpose pharmacokinetic model for propofol

BACKGROUND

Pharmacokinetic (PK) models are used to predict drug concentrations for infusion regimens for intraoperative displays and to calculate infusion rates in target-controlled infusion systems. For propofol, the PK models available in the literature were mostly developed from particular patient groups or anesthetic techniques, and there is uncertainty of the accuracy of the models under differing patient and clinical conditions. Our goal was to determine a PK model with robust predictive performance for a wide range of patient groups and clinical conditions.

METHODS

We aggregated and analyzed 21 previously published propofol datasets containing data from young children, children, adults, elderly, and obese individuals. A 3-compartmental allometric model was estimated with NONMEM software using weight, age, sex, and patient status as covariates. A predictive performance metric focused on intraoperative conditions was devised and used along with the Akaike information criteria to guide model development.

RESULTS

The dataset contains 10,927 drug concentration observations from 660 individuals (age range 0.25-88 years; weight range 5.2-160 kg). The final model uses weight, age, sex, and patient versus healthy volunteer as covariates. Parameter estimates for a 35-year, 70-kg male patient were: 9.77, 29.0, 134 L, 1.53, 1.42, and 0.608 L/min for V1, V2, V3, CL, Q2, and Q3, respectively. Predictive performance is better than or similar to that of specialized models, even for the subpopulations on which those models were derived.

CONCLUSIONS

We have developed a single propofol PK model that performed well for a wide range of patient groups and clinical conditions. Further prospective evaluation of the model is needed.

Pharmacokinetics of dexmedetomidine combined with therapeutic hypothermia in a piglet asphyxia model

Background

The highly selective α₂-adrenoreceptor agonist, dexmedetomidine, exerts neuroprotective, analgesic, anti-inflammatory and sympatholytic properties that may be beneficial for perinatal asphyxia. The optimal safe dose for pre-clinical newborn neuroprotection studies is unknown.

Methods

Following cerebral hypoxia-ischaemia, dexmedetomidine was administered to nine newborn piglets in a de-escalation dose study in combination with hypothermia (whole body cooling to 33.5°C). Dexmedetomidine was administered with a loading dose of 1 μg/kg and maintenance infusion at doses from 10 to 0.6 μg/kg/h. One additional piglet was not subjected to hypoxia-ischaemia. Blood for pharmacokinetic analysis was sampled pre-insult and frequently post-insult. A one-compartment linear disposition model was used to fit data. Population parameter estimates were obtained using non-linear mixed effects modelling.

Results

All dexmedetomidine infusion regimens led to plasma concentrations above those associated with sedation in neonates and children (0.4–0.8 μg/l). Seven out of the nine piglets with hypoxia-ischaemia experienced periods of bradycardia, hypotension, hypertension and cardiac arrest; all haemodynamic adverse events occurred in piglets with plasma concentrations greater than 1 μg/l. Dexmedetomidine clearance was 0.126 l/kg/h [coefficient of variation (CV) 46.6.%] and volume of distribution was 3.37 l/kg (CV 191%). Dexmedetomidine clearance was reduced by 32.7% at a temperature of 33.5°C. Dexmedetomidine clearance was reduced by 55.8% following hypoxia-ischaemia.

Conclusions

Dexmedetomidine clearance was reduced almost tenfold compared with adult values in the newborn piglet following hypoxic-ischaemic brain injury and subsequent therapeutic hypothermia. Reduced clearance was related to cumulative effects of both hypothermia and exposure to hypoxia. High plasma levels of dexmedetomidine were associated with major cardiovascular complications.

Methods to detect non-compliance and reduce its impact on population PK parameter estimates

This work proposes and evaluates two methods (CM1 and CM2) for detecting non-compliance using concentration-time data and for obtaining estimates of population pharmacokinetic model parameters in a population with prevalent non-compliance. CM1 estimates individual residual variability (RV) and identifies subjects with higher than average RV as non-compliant. Exclusion of subjects with high RV from the analysis dataset reduces the bias in the estimates of the model parameters. Various methods of identification and exclusion of non-compliant subjects were tested, compared, and shown to reduce or eliminate bias in parameter estimates associated with non-compliance. The tested methods were (i) a pre-defined cutoff value of the random effect on RV, (ii) sequential exclusion of subjects with the highest RV percentiles, and (iii) use of a mixture model for RV. CM2 is applicable for the data with a specific sampling pattern that includes a potentially non-compliant outpatient part with several trough samples followed by a dense profile after the inpatient (compliant) dose. It relies only on the doses known to be administered (e.g., inpatient doses). In this method, all concentration measurements during the outpatient part of the study (except the trough value immediately preceding the inpatient dose) are removed from the dataset and an additional parameter (individual relative bioavailability of the outpatient doses) is introduced. For a number of simulated datasets with various sampling schemes and non-compliance patterns the proposed methods allowed to identify subjects with compliance problems and to reduce or eliminate bias in the estimates of the model parameters.

Exploring population pharmacokinetic modeling with resampling visualization

Background. In the last decade, population pharmacokinetic (PopPK) modeling has spread its influence in the whole process of drug research and development. While targeting the construction of the dose-concentration of a drug based on a population of patients, it shows great flexibility in dealing with sparse samplings and unbalanced designs. The resampling approach has been considered an important statistical tool to assist in PopPK model validation by measuring the uncertainty of parameter estimates and evaluating the influence of individuals. Methods. The current work describes a graphical diagnostic approach for PopPK models by visualizing resampling statistics, such as case deletion and bootstrap. To examine resampling statistics, we adapted visual methods from multivariate analysis, parallel coordinate plots, and multidimensional scaling. Results. Multiple models were fitted, the information of parameter estimates and diagnostics were extracted, and the results were visualized. With careful scaling, the dependencies between different statistics are revealed. Using typical examples, the approach proved to have great capacity to identify influential outliers from the statistical perspective, which deserves special attention in a dosing regimen. Discussion. By combining static graphics with interactive graphics, we are able to explore the multidimensional data from an integrated and systematic perspective. Complementary to current approaches, our proposed method provides a new way for PopPK modeling analysis.

Use of a linearization approximation facilitating stochastic model building

The objective of this work was to facilitate the development of nonlinear mixed effects models by establishing a diagnostic method for evaluation of stochastic model components. The random effects investigated were between subject, between occasion and residual variability. The method was based on a first-order conditional estimates linear approximation and evaluated on three real datasets with previously developed population pharmacokinetic models. The results were assessed based on the agreement in difference in objective function value between a basic model and extended models for the standard nonlinear and linearized approach respectively. The linearization was found to accurately identify significant extensions of the model's stochastic components with notably decreased runtimes as compared to the standard nonlinear analysis. The observed gain in runtimes varied between four to more than 50-fold and the largest gains were seen for models with originally long runtimes. This method may be especially useful as a screening tool to detect correlations between random effects since it substantially quickens the estimation of large variance-covariance blocks. To expedite the application of this diagnostic tool, the linearization procedure has been automated and implemented in the software package PsN.

Population pharmacokinetics of paracetamol across the human age-range from (pre)term neonates, infants, children to adults

In order to characterize the variation in pharmacokinetics of paracetamol across the human age span, we performed a population pharmacokinetic analysis from preterm neonates to adults with specific focus on clearance. Concentration-time data obtained in 220 neonates (post-natal age 1-76 days, gestational age 27-42 weeks), infants (0.11-1.33 yrs), children (2-7 yrs) and adults (19-34 yrs) were analyzed using NONMEM 7.2. In the covariate analysis, linear functions, power functions, and a power function with a bodyweight-dependent exponent were tested. Between preterm neonates and adults, linear bodyweight functions were identified for Q2, Q3, V1, V2, and V3, while for CL a power function with a bodyweight-dependent exponent k was identified (CLi  = CLp  × (BW/70)(k) ). The exponent k was found to decrease in a sigmoidal manner with bodyweight from 1.2 to 0.75, with half the decrease in exponent reached at 12.2 kg. No other covariates such as age were identified. A pharmacokinetic model for paracetamol characterizing changes in pharmacokinetic parameters across the pediatric age-range was developed. Clearance was found to change in a nonlinear manner with bodyweight. Based on the final model, dosing guidelines are proposed from preterm neonates to adolescents resulting in similar exposure across all age ranges.

Parameter Estimation of Population Pharmacokinetic Models with Stochastic Differential Equations: Implementation of an Estimation Algorithm

Population pharmacokinetic (PPK) models play a pivotal role in quantitative pharmacology study, which are classically analyzed by nonlinear mixed-effects models based on ordinary differential equations. This paper describes the implementation of SDEs in population pharmacokinetic models, where parameters are estimated by a novel approximation of likelihood function. This approximation is constructed by combining the MCMC method used in nonlinear mixed-effects modeling with the extended Kalman filter used in SDE models. The analysis and simulation results show that the performance of the approximation of likelihood function for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for the analysis of population pharmacokinetic data.

Busulfan in infant to adult hematopoietic cell transplant recipients: a population pharmacokinetic model for initial and Bayesian dose personalization

PURPOSE

Personalizing intravenous busulfan doses to a target plasma concentration at steady state (Css) is an essential component of hematopoietic cell transplantation (HCT). We sought to develop a population pharmacokinetic model to predict i.v. busulfan doses over a wide age spectrum (0.1-66 years) that accounts for differences in age and body size.

EXPERIMENTAL DESIGN

A population pharmacokinetic model based on normal fat mass and maturation based on postmenstrual age was built from 12,380 busulfan concentration time points obtained after i.v. busulfan administration in 1,610 HCT recipients. Subsequently, simulation results of the initial dose necessary to achieve a target Css with this model were compared with pediatric-only models.

RESULTS

A two-compartment model with first-order elimination best fit the data. The population busulfan clearance was 12.4 L/h for an adult male with 62 kg normal fat mass (equivalent to 70 kg total body weight). Busulfan clearance, scaled to body size-specifically normal fat mass, is predicted to be 95% of the adult clearance at 2.5 years postnatal age. With a target Css of 770 ng/mL, a higher proportion of initial doses achieved the therapeutic window with this age- and size--dependent model (72%) compared with dosing recommended by the U.S. Food and Drug Administration (57%) or the European Medicines Agency (70%).

CONCLUSION

This is the first population pharmacokinetic model developed to predict initial i.v. busulfan doses and personalize to a target Css over a wide age spectrum, ranging from infants to adults.

Establishing best practices and guidance in population modeling: an experience with an internal population pharmacokinetic analysis guidance

This tutorial describes the development of a population pharmacokinetic (Pop PK) analysis guidance within Pfizer, which strives for improved consistency and efficiency, and a more systematic approach to model building. General recommendations from the Pfizer internal guidance and a suggested workflow for Pop PK model building are discussed. A description is also provided for mechanisms by which conflicting opinions were captured and resolved across the organization to arrive at the final guidance.

CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e51; doi:10.1038/psp.2013.26; advance online publication 3 July 2013

An Integrated Model for Glucose and Insulin Regulation in Healthy Volunteers and Type 2 Diabetic Patients Following Intravenous Glucose Provocations

An integrated model for the regulation of glucose and insulin concentrations following intravenous glucose provocations in healthy volunteers and type 2 diabetic patients was developed. Data from 72 individuals were included. Total glucose, labeled glucose, and insulin concentrations were determined. Simultaneous analysis of all data by nonlinear mixed effect modeling was performed in NONMEM. Integrated models for glucose, labeled glucose, and insulin were developed. Control mechanisms for regulation of glucose production, insulin secretion, and glucose uptake were incorporated. Physiologically relevant differences between healthy volunteers and patients were identified in the regulation of glucose production, elimination rate of glucose, and secretion of insulin. The model was able to describe the insulin and glucose profiles well and also showed a good ability to simulate data. The features of the present model are likely to be of interest for analysis of data collected in antidiabetic drug development and for optimization of study design.