Nonlinearity detection: advantages of nonlinear mixed-effects modeling

Development of a genetic algorithm and NONMEM workbench for automating and improving population pharmacokinetic/pharmacodynamic model selection

The current approach to selection of a population PK/PD model is inherently flawed as it fails to account for interactions between structural, covariate, and statistical parameters. Further, the current approach requires significant manual and redundant model modifications that heavily lend themselves to automation. Within the discipline of numerical optimization it falls into the "local search" category. Genetic algorithms are a class of algorithms inspired by the mathematics of evolution. GAs are general, powerful, robust algorithms and can be used to find global optimal solutions for difficult problems even in the presence of non-differentiable functions, as is the case in the discrete nature of including/excluding model components in search of the best performing mixed-effects PK/PD model. A genetic algorithm implemented in an R-based NONMEM workbench for identification of near optimal models is presented. In addition to the GA capabilities, the workbench supports modeling efforts by: (1) Organizing and displaying models in tabular format, allowing the user to sort, filter, edit, create, and delete models seamlessly, (2) displaying run results, parameter estimates and precisions, (3) integrating xpose4 and PsN to facilitate generation of model diagnostic plots and run PsN scripts, (4) running regression models between post-hoc parameter estimates and covariates. This approach will further facilitate the scientist to shift efforts to focus on model evaluation, hypotheses generation, and interpretation and applications of resulting models.

Theoretical Performance of Nonlinear Mixed-Effect Models Incorporating Saliva as an Alternative Sampling Matrix for Therapeutic Drug Monitoring in Pediatrics: A Simulation Study

BACKGROUND

Historically, pharmacokinetic (PK) studies and therapeutic drug monitoring (TDM) have relied on plasma as a sampling matrix. Noninvasive sampling matrices, such as saliva, can reduce the burden on pediatric patients. The variable plasma-saliva relationship can be quantified using population PK models (nonlinear mixed-effect models). However, criteria regarding acceptable levels of variability in such models remain unclear. In this simulation study, the authors aimed to propose a saliva TDM evaluation framework and evaluate model requirements in the context of TDM, with gentamicin and lamotrigine as model compounds.

METHODS

Two population pharmacokinetic models for gentamicin in neonates and lamotrigine in pediatrics were extended with a saliva compartment including a delay constant (kSALIVA), a saliva:plasma ratio, and between-subject variability (BSV) on both parameters. Subjects were simulated using a realistic covariate distribution. Bayesian maximum a posteriori TDM was applied to assess the performance of an increasing number of TDM saliva samples and varying levels of BSV and residual variability. Saliva TDM performance was compared with plasma TDM performance. The framework was applied to a known voriconazole saliva model as a case study.

RESULTS

TDM performed using saliva resulted in higher target attainment than no TDM, and a residual proportional error <25% on saliva observations led to saliva TDM performance comparable with plasma TDM. BSV on kSALIVA did not affect performance, whereas increasing BSV on saliva:plasma ratios by >25% for gentamicin and >50% for lamotrigine reduced performance. The simulated target attainment for voriconazole saliva TDM was >90%.

CONCLUSIONS

Saliva as an alternative matrix for noninvasive TDM is possible using nonlinear mixed-effect models combined with Bayesian optimization. This article provides a workflow to explore TDM performance for compounds measured in saliva and can be used for evaluation during model building.

Hybrid modelling for stroke care: Review and suggestions of new approaches for risk assessment and simulation of scenarios

Stroke is an example of a complex and multi-factorial disease involving multiple organs, timescales, and disease mechanisms. To deal with this complexity, and to realize Precision Medicine of stroke, mathematical models are needed. Such approaches include: 1) machine learning, 2) bioinformatic network models, and 3) mechanistic models. Since these three approaches have complementary strengths and weaknesses, a hybrid modelling approach combining them would be the most beneficial. However, no concrete approach ready to be implemented for a specific disease has been presented to date. In this paper, we both review the strengths and weaknesses of the three approaches, and propose a roadmap for hybrid modelling in the case of stroke care. We focus on two main tasks needed for the clinical setting: a) For stroke risk calculation, we propose a new two-step approach, where non-linear mixed effects models and bioinformatic network models yield biomarkers which are used as input to a machine learning model and b) For simulation of care scenarios, we propose a new four-step approach, which revolves around iterations between simulations of the mechanistic models and imputations of non-modelled or non-measured variables. We illustrate and discuss the different approaches in the context of Precision Medicine for stroke.

Efficacy, Safety, and Tolerability of a Novel Cyclosporine, a Formulation for Dry Eye Disease: A Multicenter Phase II Clinical Study

PURPOSE

The purpose of this study was to explore the efficacy, safety, and tolerability of a novel cyclosporine formulation for dry eye disease (DED).

METHODS

This is an exploratory, multicenter, single-blind, randomized, positive-controlled Phase II clinical trial between cyclosporine ophthalmic gel (CyclAGel) and an open-label comparator (Restasis, positive control). A total of 240 eligible patients with moderate to severe DED were randomized to 4 study groups: CyclAGel 0.05%/once daily (QD) (n = 59), CyclAGel 0.05%/BID (n = 60), CyclAGel 0.1%/QD (n = 60), and Restasis 0.05%/BID (n = 61). After receiving BID dosing of hypromellose eye drops during a 2-week run-in period, patients were randomized to the respective treatment group and dosed QD or BID for 12 weeks. Efficacy was assessed based on a number of sign and symptom end points, including eye dryness score (visual analog scale), 6 other parameters of symptoms for dryness (burning/stinging, itching, foreign body sensation, discomfort, sensitivity to light, and pain), and corneal fluorescein staining. The Schirmer test was used to assess dry eye symptoms (visual analog scale severity) at visit 3 (week 2), visit 4 (week 6), and visit 5 (week 12).

FINDINGS

CyclAGel showed a consistent improvement in eye dryness score and the 6 other parameters of symptoms for dryness, corneal fluorescein staining, breakup time, and Schirmer test scores compared with Restasis over the 12-week treatment period. However, there were no statistically significant differences between CyclAGel and Restasis after baseline corrections were made, and the results of the full analysis set remained consistent with those of the per-protocol set (P > 0.05). Moreover, each CyclAGel-treated group (0.05%/QD, 0.05%/BID, and 0.1%/QD) exerted better effects than the Restasis group, and CyclAGel 0.05%/QD showed the most significant improvement. The number of ocular-related treatment-emergent adverse events was low in all treatment groups, with no serious drug-related treatment-emergent adverse events.

IMPLICATIONS

CyclAGel showed excellent safety, tolerability, and comfort profiles at 2 concentrations and frequency in moderate to severe DED.

A Clinical Phase II Study to Assess Efficacy, Safety, and Tolerability of Waterfree Cyclosporine Formulation for Treatment of Dry Eye Disease

Purpose:

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Results:

Conclusions:

Examining the neurochemical underpinnings of animal models of risky choice: Methodological and analytic considerations

Because risky choice is associated with several psychiatric conditions, recent research has focused on examining the underlying neurochemical processes that control risk-based decision-making. Not surprisingly, several tasks have been developed to study the neural mechanisms involved in risky choice. The current review will briefly discuss the major tasks used to measure risky choice and will summarize the contribution of several major neurotransmitter systems to this behavior. To date, the most common measures of risky choice are the probability discounting task, the risky decision task, and the rat gambling task. Across these three tasks, the contribution of the dopaminergic system has been most studied, although the effects of serotonergic, adrenergic, cholinergic, and glutamatergic ligands will be discussed. Drug effects across these tasks have been inconsistent, which makes determining the precise role of neurotransmitter systems in risky choice somewhat difficult. Furthermore, procedural differences can modulate drug effects in these procedures, and the way data are analyzed can alter the interpretations one makes concerning pharmacological manipulations. By taking these methodological/analytic considerations into account, we may better elucidate the neurochemistry of risky decision-making. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Dissecting drug effects in preclinical models of impulsive choice: emphasis on glutamatergic compounds

RATIONALE

Impulsive choice is often measured with delay discounting paradigms. Because there are multiple discounting procedures, as well as different statistical analyses that can be applied to data generated from these paradigms, there are some inconsistencies in the literature regarding drug effects on impulsive choice.

OBJECTIVES

The goal of the current paper is to review the methodological and analytic approaches used to measure discounting and to discuss how these differences can account for differential drug effects observed across studies.

RESULTS

Because some procedures/analyses use a single data point as the dependent variable, changes in this value following pharmacological treatment may be interpreted as alterations in sensitivity to delayed reinforcement, but when other procedures/analyses are used, no changes in behavior are observed. Even when multiple data points are included, some studies show that the statistical analysis (e.g., ANOVA on raw proportion of responses vs. using hyperbolic/exponential functions) can lead to different interpretations. Finally, procedural differences (e.g., delay presentation order, signaling the delay to reinforcement, etc.) in the same discounting paradigm can alter how drugs affect sensitivity to delayed reinforcement.

CONCLUSIONS

Future studies should utilize paradigms that allow one to observe alterations in responding at each delay (e.g., concurrent-chains schedules). Concerning statistical analyses, using parameter estimates derived from nonlinear functions or incorporating the generalized matching law can allow one to determine if drugs affect sensitivity to delayed reinforcement or impair discrimination of the large and small magnitude reinforcers. Using these approaches can help further our understanding of the neurochemical underpinnings of delay discounting.

An Algorithm and R Program for Fitting and Simulation of Pharmacokinetic and Pharmacodynamic Data

BACKGROUND AND OBJECTIVES

Pharmacokinetic/pharmacodynamic link models are widely used in dose-finding studies. By applying such models, the results of initial pharmacokinetic/pharmacodynamic studies can be used to predict the potential therapeutic dose range. This knowledge can improve the design of later comparative large-scale clinical trials by reducing the number of participants and saving time and resources. However, the modeling process can be challenging, time consuming, and costly, even when using cutting-edge, powerful pharmacological software. Here, we provide a freely available R program for expediently analyzing pharmacokinetic/pharmacodynamic data, including data importation, parameter estimation, simulation, and model diagnostics.

METHODS

First, we explain the theory related to the establishment of the pharmacokinetic/pharmacodynamic link model. Subsequently, we present the algorithms used for parameter estimation and potential therapeutic dose computation. The implementation of the R program is illustrated by a clinical example. The software package is then validated by comparing the model parameters and the goodness-of-fit statistics generated by our R package with those generated by the widely used pharmacological software WinNonlin.

RESULTS

The pharmacokinetic and pharmacodynamic parameters as well as the potential recommended therapeutic dose can be acquired with the R package. The validation process shows that the parameters estimated using our package are satisfactory.

CONCLUSIONS

The R program developed and presented here provides pharmacokinetic researchers with a simple and easy-to-access tool for pharmacokinetic/pharmacodynamic analysis on personal computers.

Invasiveness of pharmacokinetic studies in children: a systematic review

OBJECTIVES

To explore whether pharmacokinetic (PK) studies in paediatric patients are becoming less invasive. This will be evaluated by analysing the number of samples and volume of blood collected for each study within four different decades.

METHODS

A systematic literature review was performed to identify PK papers describing number of samples and volume of blood collected in studies of children aged 0-18 years. The following databases were searched: MEDLINE (1946 to December 2015), EMBASE (1974 to December 2015), International Pharmaceutical Abstracts (1970 to December 2015), CINAHL and Cochrane Library.

RESULTS

A total of 549 studies were identified between 1974 and 2015. There were 52 studies between 1976 and 1985, 105 between 1986 and 1995, 201 between 1996 and 2005 and 191 between 2006 and 2015. The number of blood samples collected per participant increased between the first two decades (p=0.013), but there was a decrease in the number of samples in the subsequent two decades (p=0.044 and p<0.001, respectively). Comparing the first and last decades, there has been no change in the number of blood samples collected. There were no significant differences in volume collected per sample or total volume per child in any of the age groups. There was however a significant difference in the frequency of blood sampling between population PK studies (median 5 (IQR 3-7)) and non-population PK studies (median 8 (IQR 6-10); p=<0.001).

CONCLUSIONS

The number of blood samples collected for PK studies in children rose in 1985-1995 and subsequently declined. There was no overall change in the volume of blood collected over the 4 decades. The usage of population PK methods reduces the frequency of blood sampling in children.

Children in clinical trials: towards evidence-based pediatric pharmacotherapy using pharmacokinetic-pharmacodynamic modeling

INTRODUCTION

In pediatric pharmacotherapy, many drugs are still used off-label, and their efficacy and safety is not well characterized. Different efficacy and safety profiles in children of varying ages may be anticipated, due to developmental changes occurring across pediatric life.

AREAS COVERED

Beside pharmacokinetic (PK) studies, pharmacodynamic (PD) studies are urgently needed. Validated PKPD models can be used to derive optimal dosing regimens for children of different ages, which can be evaluated in a prospective study before implementation in clinical practice. Strategies should be developed to ensure that formularies update their drug dosing guidelines regularly according to the most recent advances in research, allowing for clinicians to integrate these guidelines in daily practice. Expert commentary: We anticipate a trend towards a systems-level approach in pediatric modeling to optimally use the information gained in pediatric trials. For this approach, properly designed clinical PKPD studies will remain the backbone of pediatric research.

Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models

Context

Mathematical models may help the analysis of biological systems by providing estimates of otherwise un-measurable quantities such as concentrations and fluxes. The variability in such systems makes it difficult to translate individual characteristics to group behavior. Mixed effects models offer a tool to simultaneously assess individual and population behavior from experimental data. Lipoproteins and plasma lipids are key mediators for cardiovascular disease in metabolic disorders such as diabetes mellitus type 2. By the use of mathematical models and tracer experiments fluxes and production rates of lipoproteins may be estimated.

Results

We developed a mixed effects model to study lipoprotein kinetics in a data set of 15 healthy individuals and 15 patients with type 2 diabetes. We compare the traditional and the mixed effects approach in terms of group estimates at various sample and data set sizes.

Conclusion

We conclude that the mixed effects approach provided better estimates using the full data set as well as with both sparse and truncated data sets. Sample size estimates showed that to compare lipoprotein secretion the mixed effects approach needed almost half the sample size as the traditional method.

Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it

Background

Studies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty. Like much high-quality data, single-cell data is best analysed using a systems biology approach. The most common systems biology approach to single-cell data is the standard two-stage (STS) approach. In STS, data from each cell is analysed in a separate sub-problem, meaning that only data from the same cell is used to calculate the parameter values within that cell. Because only parts of the data are considered, problems with parameter unidentifiability are exaggerated in STS. In contrast, a related approach to data analysis has been developed for the studies of patient-to-patient variations. This approach, called nonlinear mixed-effects modelling (NLME), makes use of all data, when estimating the patient-specific parameters. NLME would therefore be advantageous compared to STS also for the study of cell-to-cell variation. However, no such systematic evaluation of the two approaches exists.

Results

Herein, such a systematic comparison between STS and NLME has been performed. Different examples, both linear and nonlinear, and both simulated and real experimental data, have been examined. With informative data, there is no significant difference in the results for either parameter or noise estimation. However, when data becomes uninformative, NLME is significantly superior to STS. These results hold independently of whether the loss of information is due to a low signal-to-noise ratio, too few data points, or a bad input signal. The improvement is shown to come from both the consideration of a joint likelihood (JLH) function, describing all parameters and data, and from an a priori postulated form of the population parameters. Finally, we provide a small tutorial that shows how to use NLME for single-cell analysis, using the free and user-friendly software Monolix.

Conclusions

When considering uninformative single-cell data, NLME yields more accurate parameter and noise estimates, compared to more traditional approaches, such as STS and JLH.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0203-x) contains supplementary material, which is available to authorized users.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

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.

Population pharmacodynamic analysis of erythropoiesis in preterm infants for determining the anemia treatment potential of erythropoietin

A population pharmacokinetics/pharmacodynamic (PK/PD) model was developed to describe changes in erythropoiesis as a function of plasma erythropoietin (EPO) concentration over the first 30 days of life in preterm infants who developed severe anemia requiring red blood cell (RBC) transfusion. Several covariates were tested as possible factors influencing the responsiveness to EPO. Discarded blood samples in 27 ventilated preterm infants born at 24-29 wk of gestation were used to construct plasma EPO, hemoglobin (Hb), and RBC concentration-time profiles. The amount of Hb removed for laboratory testing and that transfused throughout the study period were recorded. A population PK/PD model accounting for the dynamic Hb changes experienced by these infants was simultaneously fitted to plasma EPO, Hb, and RBC concentrations. A covariate analysis suggested that the erythropoietic efficacy of EPO is increased for preterm infants at later gestational ages. The PD analysis showed a sevenfold difference in maximum Hb production rate dependent on gestational age and indicated that preterm infants, when stimulated by EPO, have the capacity to produce additional Hb that may result in a decrease in RBC transfusions. The present model has utility in clinical trial simulations investigating the treatment potential of erythropoietic stimulating agents in the treatment of anemia of prematurity.

Pharmacokinetics, safety, and tolerability of GLPG0259, a mitogen-activated protein kinase-activated protein kinase 5 (MAPKAPK5) inhibitor, given as single and multiple doses to healthy male subjects

BACKGROUND AND OBJECTIVES

GLPG0259 is a small-molecule inhibitor of mitogen-activated protein kinase-activated protein kinase 5 (MAPKAPK5), a kinase enzyme that plays a role in important inflammatory pathways. The main objectives of the phase I clinical studies in early development were to characterize the pharmacokinetics, tolerability, and safety of GLPG0259 in healthy subjects, including the development of a solid dosage form (free-base pellets and fumarate salt capsules) and the potential for interaction of GLPG0259 with methotrexate.

SUBJECTS AND METHODS

Four phase I studies were initiated. Study 1 was a randomized, double-blind, placebo-controlled study to evaluate the safety, tolerability, and pharmacokinetics of single ascending doses (1.5-150 mg) and multiple oral doses (20 and 50 mg once daily) of GLPG0259 in healthy male subjects (n = 34). Study 2 was a randomized, double-blind, placebo-controlled study to evaluate the safety, tolerability, and pharmacokinetics of oral multiple ascending doses of GLPG0259 (25-75 mg once daily) given for 14 days to healthy male subjects, and to get preliminary information on the potential pharmacokinetic interaction between GLPG0259 and methotrexate (n = 24). Studies 3 and 4 were open-label, randomized, crossover studies to compare the oral bioavailability of two solid dosage forms of GLPG0259 (a capsule) relative to an oral solution after a 100 mg or 50 mg single dose and to evaluate the effect of food on these formulations (n = 12 for each study).

MAIN OUTCOME MEASURES

The non-compartmental pharmacokinetic parameters for plasma concentrations of GLPG0259 were determined, and a population pharmacokinetic model of GLPG0259 was developed to support the planning of the number and timing of the sparse samples to be taken per patient in the phase II study. Safety and tolerability data are also summarized.

RESULTS

The absorption of GLPG0259 was slow, with a decrease in the absorption rate with increasing dose, and there was decreased elimination, with an apparent terminal elimination half-life of 26.0 hours. On the basis of statistical analysis of variance, the exposure to GLPG0259 increased in proportion to the dose over a 30-150 mg single-dose range and a 25-75 mg repeated-dose range. Between- and within-subject variability in GLPG0259 pharmacokinetics was low/moderate (coefficient of variation [CV] 16-30%). After once-daily repeated dosing, steady-state plasma concentrations were reached at between 5 and 8 dosing days, which is consistent with the long apparent elimination half-life of GLPG0259. Food increased the bioavailability of GLPG0259 given in a solid dosage form. Co-administration of GLPG0259 with a single dose of methotrexate 7.5 mg did not result in any change in the pharmacokinetic profiles of either GLPG0259 or methotrexate.

CONCLUSION

In summary, the investigation of safety/tolerability and pharmacokinetics in the early development phase showed that single and repeated doses of GLPG0259 were safe and well tolerated. The most common adverse event reported was mild gastrointestinal discomfort. The pharmacokinetics characterized in healthy male subjects showed no major obstacles and supports a once-daily oral regimen in patients.

Nonlinear population pharmacokinetics of sirolimus in patients with advanced cancer

Sirolimus, the prototypical inhibitor of the mammalian target of rapamycin, has substantial antitumor activity. In this study, sirolimus showed nonlinear pharmacokinetic characteristics over a wide dose range (from 1 to 60 mg/week). The objective of this study was to develop a population pharmacokinetic (PopPK) model to describe the nonlinearity of sirolimus. Whole blood concentration data, obtained from four phase I clinical trials, were analyzed using a nonlinear mixed-effects modeling (NONMEM) approach. The influence of potential covariates was evaluated. Model robustness was assessed using nonparametric bootstrap and visual predictive check approaches. The data were well described by a two-compartment model incorporating a saturable Michaelis–Menten kinetic absorption process. A covariate analysis identified hematocrit as influencing the oral clearance of sirolimus. The visual predictive check indicated that the final pharmacokinetic model adequately predicted observed concentrations. The pharmacokinetics of sirolimus, based on whole blood concentrations, appears to be nonlinear due to saturable absorption.

Mechanism-based population pharmacokinetic modelling in diabetes: vildagliptin as a tight binding inhibitor and substrate of dipeptidyl peptidase IV

AIMS

To assess the pharmacokinetics of vildagliptin at different doses and build a mechanism-based population model that simultaneously describes vildagliptin pharmacokinetics and its effects on DPP-4 activity based on underlying physiology and biology.

METHODS

Vildagliptin concentrations and DPP-4 activity vs. time from 13 type 2 diabetic patients after oral vildagliptin 10, 25 or 100 mg and placebo twice daily for 28 days were co-modelled. NONMEM VI and S-ADAPT were utilized for population modelling.

RESULTS

A target-mediated drug disposition (TMDD) model accounting for capacity-limited high affinity binding of vildagliptin to DPP-4 in plasma and tissues had good predictive performance. Modelling the full time course of the vildagliptin-DPP-4 interaction suggested parallel vildagliptin dissociation from DPP-4 by a slow first-order process and hydrolysis by DPP-4 to an inactive metabolite as a disposition mechanism. Due to limited amounts of DPP-4, vildagliptin concentrations increased slightly more than dose proportionally. This newly proposed model and the parameter estimates are supported by published in vitro studies. Mean parameter estimates (inter-individual coefficient of variation) were: non-saturable clearance 36 l h−1 (25%), central volume of distribution 22 l (37%), half-life of dissociation from DPP-4 1.1 h (94%) and half-life of hydrolysis 6.3 h (81%).

CONCLUSIONS

Vildagliptin is both an inhibitor and substrate for DPP-4. By utilizing the TMDD approach, slow dissociation of vildagliptin from DPP-4 was found in patients and the half-life of hydrolysis by DPP-4 estimated. This model can be used to predict DPP-4 inhibition effects of other dosage regimens and be modified for other DPP-4 inhibitors to differentiate their properties.

Deciding when to "cash in" when outcomes are continuously improving: an escalating interest task

A first-person shooter video game was adapted for the study of choice between smaller sooner and larger later outcomes. Participants chose when to fire a weapon that increased in damage potential over a 10s interval, an escalating interest situation. Across two experiments, participants demonstrated sensitivity to the nature of the mathematical function that defined the relationship between waiting and damage potential. In Experiment 1, people tended to wait longer when doing so allowed them to eliminate targets more quickly. In Experiment 2, people tended to wait longer to increase the probability of a constant magnitude outcome than to increase the magnitude of a 100% certain outcome that was matched for the same expected value (i.e., probability times magnitude). The two experiments demonstrated sensitivity to the way in which an outcome improves when the outcome is continuously available. The results also demonstrate that this new video game task is useful for generating sensitivity to delay to reinforcement over time scales that are typically used in nonhuman animal studies.

Performance and robustness of the Monte Carlo importance sampling algorithm using parallelized S-ADAPT for basic and complex mechanistic models

The Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm can approximate the true log-likelihood as precisely as needed and is efficiently parallelizable. Our objectives were to evaluate an importance sampling version of the MC-PEM algorithm for mechanistic models and to qualify the default estimation settings in SADAPT-TRAN. We assessed bias, imprecision and robustness of this algorithm in S-ADAPT for mechanistic models with up to 45 simultaneously estimated structural parameters, 14 differential equations, and 10 dependent variables (one drug concentration and nine pharmacodynamic effects). Simpler models comprising 15 parameters were estimated using three of the ten dependent variables. We set initial estimates to 0.1 or 10 times the true value and evaluated 30 bootstrap replicates with frequent or sparse sampling. Datasets comprised three dose levels with 16 subjects each. For simultaneous estimation of the full model, the ratio of estimated to true values for structural model parameters (median [5-95% percentile] over 45 parameters) was 1.01 [0.94-1.13] for means and 0.99 [0.68-1.39] for between-subject variances for frequent sampling and 1.02 [0.81-1.47] for means and 1.02 [0.47-2.56] for variances for sparse sampling. Imprecision was ≤25% for 43 of 45 means for frequent sampling. Bias and imprecision was well comparable for the full and simpler models. Parallelized estimation was 23-fold (6.9-fold) faster using 48 threads (eight threads) relative to one thread. The MC-PEM algorithm was robust and provided unbiased and adequately precise means and variances during simultaneous estimation of complex, mechanistic models in a 45 dimensional parameter space with rich or sparse data using poor initial estimates.

Population pharmacokinetic analysis of voriconazole plasma concentration data from pediatric studies

Voriconazole is a potent triazole with broad-spectrum antifungal activity against clinically significant and emerging pathogens. The present population pharmacokinetic analysis evaluated voriconazole plasma concentration-time data from three studies of pediatric patients of 2 to <12 years of age, incorporating a range of single or multiple intravenous (i.v.) and/or oral (p.o.) doses. An appropriate pharmacokinetic model for this patient population was created using the nonlinear mixed-effect modeling approach. The final model described voriconazole elimination by a Michaelis-Menten process and distribution by a two-compartment model. It also incorporated a statistically significant (P < 0.001) influence of the CYP2C19 genotype and of the alanine aminotransferase level on clearance. The model was used in a number of deterministic simulations (based on various fixed, mg/kg of body weight, and individually adjusted doses) aimed at finding suitable i.v. and p.o. voriconazole dosing regimens for pediatric patients. As a result, 7 mg/kg twice a day (BID) i.v. or 200 mg BID p.o., irrespective of body weight, was recommended for this patient population. At these doses, the pediatric area-under-the-curve (AUC) distribution exhibited the least overall difference from the adult AUC distribution (at dose levels used in clinical practice). Loading doses or individual dosage adjustments according to baseline covariates are not considered necessary in administering voriconazole to children.

Population pharmacodynamic model of bronchodilator response to inhaled albuterol in children and adults with asthma

BACKGROUND

Because interpatient variability in bronchodilation from inhaled albuterol is large and clinically important, we characterized the albuterol dose/response relationship by pharmacodynamic modeling and quantified variability.

METHODS

Eighty-one patients with asthma (24% African American [AA]; 8 to 65 years old; baseline FEV1, 40 to 80% of predicted) received 180 microg of albuterol from a metered-dose inhaler (MDI), and then 90 microg every 15 min until maximum improvement or 540 microg was administered; all then received 2.5 mg of nebulized albuterol. FEV1 was measured 15 min after each dose. The population cumulative dose/response data were fitted with a sigmoid maximum effect of albuterol (Emax) [maximum percentage of predicted FEV1 effect] model by nonlinear mixed-effects modeling. The influence of covariates on maximum percentage of predicted FEV1 reached after albuterol administration (Rmax) and cumulative dose of albuterol required to bring about 50% of maximum effect of albuterol (ED50) and differences between AA and white patients were explored.

RESULTS

ED50 was 141 microg, and Emax was 24.0%. Coefficients of variation for ED50 and Emax were 40% and 56%, respectively. Ethnicity was a statistically significant covariate (p < 0.05). AA and white patients reached 82.4% and 91.9% of predicted FEV1, respectively (p = 0.0004); and absolute improvement in percentage of predicted FEV1 was 16.6% in AA patients vs 26.7% in white patients (p < 0.0003). There were no baseline characteristic differences between AA and white patients. Nebulized albuterol increased FEV1 > or = 200 mL in 21% of participants. Heart rate and BP were unchanged from baseline after maximal albuterol doses.

CONCLUSIONS

Our model predicts that 180 microg of albuterol by MDI produces a 14.4% increase in percentage of predicted FEV1 over baseline (11.7% in AA patients, and 17.5% in white patients). Emax varies widely between asthmatic patients. AA patients are less responsive to maximal doses of inhaled albuterol than white patients.

Randomized exposure-controlled trials; impact of randomization and analysis strategies

AIMS

In the literature, five potential benefits of randomizing clinical trials on concentration levels, rather than dose, have been proposed: (i) statistical study power will increase; (ii) study power will be less sensitive to high variability in the pharmacokinetics (PK); (iii) the power of establishing an exposure-response relationship will be robust to correlations between PK and pharmacodynamics (PD); (iv) estimates of the exposure-response relationship are likely to be less biased; and (v) studies will provide a better control of exposure in situations with toxicity issues. The main aim of this study was to investigate if these five statements are valid when the trial results are evaluated using a model-based analysis.

METHODS

Quantitative relationships between drug dose, concentration, biomarker and clinical end-point were defined using pharmacometric models. Three randomization schemes for exposure-controlled trials, dose-controlled (RDCT), concentration-controlled (RCCT) and biomarker-controlled (RBCT), were simulated and analysed according to the models.

RESULTS

(i) The RCCT and RBCT had lower statistical power than RDCT in a model-based analysis; (ii) with a model-based analysis the power for an RDCT increased with increasing PK variability; (iii) the statistical power in a model-based analysis was robust to correlations between CL and EC(50) or E(max); (iv) under all conditions the bias was negligible (<3%); and (v) for studies with equal power RCCT could produce either more or fewer adverse events compared with an RDCT.

CONCLUSION

Alternative randomization schemes may not have the proposed advantages if a model-based analysis is employed.

Population Pharmacokinetics of Troxacitabine, a Novel Dioxolane Nucleoside Analogue

PURPOSE

To develop and validate a population pharmacokinetic model for troxacitabine, a novel l-nucleoside analogue, administered by short infusion; to characterize clinical covariates that influence pharmacokinetic variability; and to design a dosage rate for continuous infusion administration to achieve low micromolar concentrations, which may be more efficacious than shorter infusions.

EXPERIMENTAL DESIGN

Plasma samples from 111 cancer patients receiving troxacitabine (0.12-12.5 mg/m(2)) as a 30-minute infusion in phase I trials were used to develop the model with NONMEM. Clinical covariates evaluated included creatinine clearance, body surface area, age, and sex. From the model, a troxacitabine dosage rate of 2.0 to 3.0 mg/m(2)/d was expected to achieve a target concentration of 0.1 micromol/L; plasma samples were obtained during the infusion from eight patients receiving troxacitabine as a 3-day infusion.

RESULTS

Troxacitabine pharmacokinetics were characterized by a three-compartment linear model. The mean value for systemic clearance [interindividual variability (CV%)] from the covariate-free model was 9.1 L/h (28%). Creatinine clearance and body surface area accounted for 36% of intersubject variation in clearance. Troxacitabine 2.0 mg/m(2)/d (n = 3) and 3.0 mg/m(2)/d (n = 5) for 3 days produced mean +/- SD end of infusion concentrations of 0.12 +/- 0.03 and 0.15 +/- 0.03 micromol/L, respectively.

CONCLUSIONS

Renal function and body surface area were identified as sources of troxacitabine pharmacokinetic variability. The population pharmacokinetic model model-derived dosage rates for continuous infusion administration successfully achieved predetermined target plasma concentrations. The present model may be used to optimize treatment with troxacitabine by developing a dosing strategy based on both renal function and body size.

Population pharmacokinetics/pharmacodynamics of anesthetics

In this article we review how population pharmacokinetic/pharmacodynamic (PD) modeling has evolved in the specialty of anesthesiology, how anesthesiology benefited from the mixed-effects approach, and which features of modeling need careful attention. Key articles from the anesthesiology literature are selected to discuss the modeling of typical anesthesiological PD end points, such as level of consciousness and analgesia, interactions between hypnotics and analgesics, estimation with poor and sometimes rich data sets from populations of various sizes, covariate detection, covariances between random effects, and Bayesian forecasting.

Population pharmacokinetic modelling of BIBN 4096 BS, the first compound of the new class of calcitonin gene-related peptide receptor antagonists

Pharmacokinetics (PK) of the calcitonin gene-related (CGRP) peptide receptor antagonist BIBN 4096 BS, the first compound of this new class tested in humans, has been evaluated combining the data from a phase I study performed in healthy volunteers and a phase IIa study conducted in migraine patients. A total of 94 individuals with a total of 556 plasma samples contributed to the analysis. Subjects received a single dose of 0.25, 0.5, 1, 2.5, 5 or 10 mg BIBN 4096 BS administered in a 10 min i.v. infusion. Blood samples were obtained at selected times up to 12 h. Disposition of BIBN 4096 BS was best described with a three compartment body model with first order elimination. BIBN 4096 BS showed a moderate degree (between 30 and 50%) of inter-subject variability in the apparent volume of distribution of the central compartment (V1), total plasma clearance (CL), distribution clearance between the central and deep compartment, and the apparent volume of distribution of the shallow compartment. Typical estimates of V1 were significantly (P <0.01) lower in healthy volunteers (7.16 versus 9.95 L), and typical estimates of CL were significantly lower in subjects receiving oral contraceptives (11.4 versus 17.1 L/h), although the absolute reduction in the unexplained inter-subject variability was negligible (4%). Computer simulations showed that the above mentioned covariates lack clinical significance. In conclusion, the pharmacokinetics of BIBN 4096 BS was independent of the dose and not altered by the tested covariates to a clinically significant degree.

Using Stochastic Differential Equations for PK/PD Model Development

A method for PK/PD model development based on stochastic differential equation models is proposed. The new method has a number of advantages compared to conventional methods. In particular, the new method avoids the exhaustive trial-and-error based search often conducted to determine the most appropriate model structure, because it allows information about the appropriate model structure to be extracted directly from data. This is accomplished through quantification of the uncertainty of the individual parts of an initial model, by means of which tools for performing model diagnostics can be constructed and guidelines for model improvement provided. Furthermore, the new method allows time-variations in key parameters to be tracked and visualized graphically, which allows important functional relationships to be revealed. Using simulated data, the performance of the new method is demonstrated by means of two examples. The first example shows how, starting from a simple assumption of linear PK, the method can be used to determine the correct nonlinear model for describing the PK of a drug following an oral dose. The second example shows how, starting from a simple assumption of no drug effect, the method can be used to determine the correct model for the nonlinear effect of a drug with known PK in an indirect response model.

The back-step method--method for obtaining unbiased population parameter estimates for ordered categorical data

A significant bias in parameters, estimated with the proportional odds model using the software NONMEM, has been reported. Typically, this bias occurs with ordered categorical data, when most of the observations are found at one extreme of the possible outcomes. The aim of this study was to assess, through simulations, the performance of the Back-Step Method (BSM), a novel approach for obtaining unbiased estimates when the standard approach provides biased estimates. BSM is an iterative method involving sequential simulation-estimation steps. BSM was compared with the standard approach in the analysis of a 4-category ordered variable using the Laplacian method in NONMEM. The bias in parameter estimates and the accuracy of model predictions were determined for the 2 methods on 3 conditions: (1) a nonskewed distribution of the response with low interindividual variability (IIV), (2) a skewed distribution with low IIV, and (3) a skewed distribution with high IIV. An increase in bias with increasing skewness and IIV was shown in parameters estimated using the standard approach in NONMEM. BSM performed without appreciable bias in the estimates under the 3 conditions, and the model predictions were in good agreement with the original data. Each BSM estimation represents a random sample of the population; hence, repeating the BSM estimation reduces the imprecision of the parameter estimates. The BSM is an accurate estimation method when the standard modeling approach in NONMEM gives biased estimates.

The Bayesian population approach to physiological toxicokinetic-toxicodynamic models--an example using the MCSim software

The calibration of physiologically based toxicokinetic models against experimental data encompasses the merging of prior knowledge with information present in the data. This prior knowledge is manifested in the scientific literature and associated with various degrees of uncertainty. The most convenient way to combine these sources of information is via the use of Bayesian statistical methods. Furthermore, toxicokinetic models are subject to both inter- and intra-individual variability. This variability may be handled statistically by the use of a population model. The MCSim software, which is available for free download on the Internet, permits the use of a population model in combination with a Bayesian statistical approach. An example of the use of MCSim in a recent model-based risk assessment of dichloromethane (DCM) is given and discussed.

Model of chemotherapy-induced myelosuppression with parameter consistency across drugs

PURPOSE

To develop a semimechanistic pharmacokinetic-pharmacodynamic model describing chemotherapy-induced myelosuppression through drug-specific parameters and system-related parameters, which are common to all drugs.

PATIENTS AND METHODS

Patient leukocyte and neutrophil data after administration of docetaxel, paclitaxel, and etoposide were used to develop the model, which was also applied to myelosuppression data from 2'-deoxy-2'-methylidenecytidine (DMDC), irinotecan (CPT-11), and vinflunine administrations. The model consisted of a proliferating compartment that was sensitive to drugs, three transit compartments that represented maturation, and a compartment of circulating blood cells. Three system-related parameters were estimated: baseline, mean transit time, and a feedback parameter. Drug concentration-time profiles affected the proliferation of sensitive cells by either an inhibitory linear model or an inhibitory E(max) model. To evaluate the model, system-related parameters were fixed to the same values for all drugs, which were based on the results from the estimations, and only drug-specific parameters were estimated. All modeling was performed using NONMEM software.

RESULTS

For all investigated drugs, the model successfully described myelosuppression. Consecutive courses and different schedules of administration were also well characterized. Similar system-related parameter estimates were obtained for the different drugs and also for leukocytes compared with neutrophils. In addition, when system-related parameters were fixed, the model well characterized chemotherapy-induced myelosuppression for the different drugs.

CONCLUSION

This model predicted myelosuppression after administration of one of several different chemotherapeutic drugs. In addition, with fixed system-related parameters to proposed values, and only drug-related parameters estimated, myelosuppression can be predicted. We propose that this model can be a useful tool in the development of anticancer drugs and therapies.

Gastric acid secretion in the dog: a mechanism-based pharmacodynamic model for histamine stimulation and irreversible inhibition by omeprazole

A mechanism-based pharmacodynamic model was used to describe the inhibitory effect by omeprazole on gastric acid secretion measured after histamine stimulation in the dog. The model identifies parameters that are related to the physiological system, the histamine stimulation, and the irreversible effect of omeprazole on the H+, K(+)-ATPase enzyme. Four different experiments with omeprazole (Exps. 1-4) and two placebo experiments were performed in each of the four Heidenhain pouch dogs used. For placebo and experiments 1-3, saline or omeprazole 0.81 mumol/kg was infused during 3 hr with measurements of histamine-stimulated gastric acid secretion in two periods of 3.5-6.5 hr, one period starting just before the omeprazole infusion and a second later period up to 29 hr post infusion. In experiment 4, 0.18 mumol/kg of omeprazole was infused for 22.5 min and gastric juice was collected for 5 hr post infusion. The response data was well described by the model. Similar parameter estimates were obtained by three different analysis methods; naïve pooling, two-stage method and nonlinear mixed effects modeling. The elimination rate constant for the H+, K(+)-ATPase enzyme, kout, was estimated to be 0.040 hr-1, corresponding to a half-life of about 17 hr. This rate constant determines the duration of omeprazole inhibition after long-term exposure. For short-term omeprazole exposure the duration is determined by the rate constant for transfer of enzymes from active to resting state, estimated to be 1.88 hr-1. The second-order rate constant for histamine stimulation was estimated to be 0.064 hr-1 per histamine concentration unit and the maximum acid secretion was estimated to be 5.0 mmol H+/30 min. The second-order rate constant for the irreversible binding of omeprazole to H+, K(+)-ATPase, kome, was estimated to be 2.39 L/mumol.hr. By modeling the histamine-induced baseline response simultaneously with active treatment, predictions of the response are possible not only following different dosing regimens of omeprazole, but also following different degrees of histamine stimulation.

Physiologically based modeling of the inhalation kinetics of styrene in humans using a bayesian population approach

Animal studies have implicated styrene as toxic to the central nervous system and its major metabolite styrene-7,8-oxide as a carcinogen. Therefore, a reliable estimate of the metabolic capacity for styrene in humans is of interest. However, the available models describing styrene kinetics in humans lack rigorous statistical validation and also ignore the population variability in metabolism. The population variability may be estimated by the use of population models. Furthermore, the statistical validation of pharmacokinetic models may be improved by use of Bayesian methods. These two approaches may be combined and recently have been gaining interest in the toxicology literature. A population-based physiologically based pharmacokinetic (PBPK) model for styrene was developed. The model was calibrated to extensive human toxicokinetic data from three previous studies in which 24 volunteers were exposed to 50-386 ppm of styrene at rest and various levels of exercise. Model fitting was performed in a Bayesian framework using Markov chain Monte Carlo simulation. The uncertainty around the partition coefficients and metabolic parameters for styrene was reduced. The metabolic capacity for styrene in humans was estimated to be 0.92 micromol/l kg(-1), with a lognormal standard deviation of 1.66. The estimated Vmax is 40% higher than previously estimated, whereas the population standard deviation is estimated for the first time.