Pharmacokinetic/pharmacodynamic modeling in drug development

Preclinical PK/PD modeling and human efficacious dose projection for a glucokinase activator in the treatment of diabetes

Human Hexokinase IV, or glucokinase (GK), is a regulator of glucose concentrations in the body. It plays a key role in pancreatic insulin secretion as well as glucose biotransformation in the liver, making it a potentially viable target for treatment of Type 2 diabetes. Allosteric activators of GK have been shown to decrease blood glucose concentrations in both animals and humans. Here, the development of a mathematical model is presented that describes glucose modulation in an ob/ob mouse model via administration of a potent GK activator, with the goal of projecting a human efficacious dose and plasma exposure. The model accounts for the allosteric interaction between GK, the activator, and glucose using a modified Hill function. Based on model simulations using data from the ob/ob mouse and in vitro studies, human projections of glucose response to the GK activator are presented, along with dose and regimen predictions to maintain clinically significant decreases in blood glucose in a Type 2 diabetic patient. This effort serves as a basis to build a detailed mechanistic understanding of GK and its role as a therapeutic target for Type 2 diabetes, and it highlights the benefits of using such an approach in a drug discovery setting.

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.

Onartuzumab (MetMAb): using nonclinical pharmacokinetic and concentration-effect data to support clinical development

PURPOSE

We characterized the pharmacokinetics of onartuzumab (MetMAb) in animals and determined a concentration-effect relationship in tumor-bearing mice to enable estimation of clinical pharmacokinetics and target doses.

EXPERIMENTAL DESIGN

A tumor growth inhibition model was used to estimate tumoristatic concentrations (TSC) in mice. Human pharmacokinetic parameters were projected from pharmacokinetics in cynomolgus monkeys by the species-invariant time method. Monte Carlo simulations predicted the percentage of patients achieving steady-state trough serum concentrations (Ctrough ss) ≥TSC for every 3-week (Q3W) dosing.

RESULTS

Onartuzumab clearance (CL) in the linear dose range was 21.1 and 12.2 mL/d/kg in mice and cynomolgus monkeys with elimination half-life at 6.10 and 3.37 days, respectively. The estimated TSC in KP4 pancreatic xenograft tumor-bearing mice was 15 μg/mL. Projected CL for humans in the linear dose range was 5.74 to 9.36 mL/d/kg with scaling exponents of CL at 0.75 to 0.9. Monte Carlo simulations projected a Q3W dose of 10 to 30 mg/kg to achieve Ctrough ss of 15 μg/mL in 95% or more of patients.

CONCLUSIONS

Onartuzumab pharmacokinetics differed from typical bivalent glycosylated monoclonal antibodies with approximately 2-times faster CL in the linear dose range. Despite this higher CL, xenograft efficacy data supported dose flexibility with Q1W to Q3W dose regimens in the clinical setting with a TSC of 15 μg/mL as the Ctrough ss target. The projected human efficacious dose of 10 to 30 mg/kg Q3W should achieve the target TSC of 15 μg/mL. These data show effective pharmacokinetic/pharmacodynamic modeling to project doses to be tested in the clinic.

Stochastic modeling of systems mapping in pharmacogenomics

As a basis of personalized medicine, pharmacogenetics and pharmacogenomics that aim to study the genetic architecture of drug response critically rely on dynamic modeling of how a drug is absorbed and transported to target tissues where the drug interacts with body molecules to produce drug effects. Systems mapping provides a general framework for integrating systems pharmacology and pharmacogenomics through robust ordinary differential equations. In this chapter, we extend systems mapping to more complex and more heterogeneous structure of drug response by implementing stochastic differential equations (SDE). We argue that SDE-implemented systems mapping provides a computational tool for pharmacogenetic or pharmacogenomic research towards personalized medicine.

Population pharmacokinetics of cyclosporine in transplant recipients

A number of classical pharmacokinetic studies have been conducted in transplant patients. However, they suffer from some limitations, for example, (1) the study design was limited to intense blood sampling in small groups of patients during a certain posttransplant period, (2) patient factors were evaluated one at a time to identify their association with the pharmacokinetic parameters, and (3) mean pharmacokinetic parameters often cannot be precisely estimated due to large intraindividual variability. Population pharmacokinetics provides a potential means of addressing these limitations and is a powerful tool to evaluate the magnitude and consistency of drug exposure. Population pharmacokinetic studies of cyclosporine focused solely on developing limited sampling strategies and Bayesian estimators to estimate drug exposure, have been summarized before, and are, therefore, not a subject of this review. The major focus of this review is to describe factors (demographic factors, hepatic and gastrointestinal functions, drug-drug interactions, genetic polymorphisms of drug metabolizing enzymes and transporters) that have been identified to contribute to the large portion of observed variability in the pharmacokinetics of cyclosporine in transplant patients. This review summarizes and interprets the conclusions as well as the nonlinear mixed-effects modeling methodologies used in such studies. A highly diversified collection of structural models, variability models, and covariate submodels have been evaluated and validated using internal or external validation methods. This review also highlights areas where additional research is warranted to improve the models since a portion of model variability still remains unexplained.

A general model-based design of experiments approach to achieve practical identifiability of pharmacokinetic and pharmacodynamic models

The use of pharmacokinetic (PK) and pharmacodynamic (PD) models is a common and widespread practice in the preliminary stages of drug development. However, PK-PD models may be affected by structural identifiability issues intrinsically related to their mathematical formulation. A preliminary structural identifiability analysis is usually carried out to check if the set of model parameters can be uniquely determined from experimental observations under the ideal assumptions of noise-free data and no model uncertainty. However, even for structurally identifiable models, real-life experimental conditions and model uncertainty may strongly affect the practical possibility to estimate the model parameters in a statistically sound way. A systematic procedure coupling the numerical assessment of structural identifiability with advanced model-based design of experiments formulations is presented in this paper. The objective is to propose a general approach to design experiments in an optimal way, detecting a proper set of experimental settings that ensure the practical identifiability of PK-PD models. Two simulated case studies based on in vitro bacterial growth and killing models are presented to demonstrate the applicability and generality of the methodology to tackle model identifiability issues effectively, through the design of feasible and highly informative experiments.

Scaling of pharmacokinetics across paediatric populations: the lack of interpolative power of allometric models

AIM

The objective of this investigation was to assess the performance of an allometric model as the basis for interpolating drug exposure in the context of pharmacokinetic bridging across paediatric subpopulations.

METHODS

Midazolam was selected as a paradigm compound. Two nonlinear mixed effects models were developed to describe midazolam pharmacokinetics in infants, toddlers and adults (model 1) and in children and adolescents (model 2). Subsequently, systemic drug exposure, expressed in terms of the area under the concentration vs. time curve (AUC), in children and adolescents was interpolated based on pharmacokinetic parameter distributions obtained from the model describing infants, toddlers and adults (model 1). Results were compared with the values obtained from modelling of the data in the corresponding population (model 2).

RESULTS

The two pharmacokinetic models accurately described midazolam exposure in the population on which they were built. However, the model based on data from infants, toddlers and adults failed to predict the exposure observed in children and adolescents: the mean difference between the predicted and estimated AUC(0-180) was of -17.8%, with a range of -6.8 to -38.4%.The discrepancy between estimated and interpolated exposure increased proportionally with body weight.

CONCLUSIONS

The current results indicate that irrespective of whether extrapolation or interpolation methods are to be applied during paediatric drug development, model predictions beyond the range of the data used for parameter estimation may be biased. For accurate inter- or extrapolation to different populations, the assumption of identical parameter-covariate correlations across age groups may not be taken for granted.

Dose selection using a semi-mechanistic integrated glucose-insulin-glucagon model: designing phase 2 trials for a novel oral glucokinase activator

Selecting dosing regimens for phase 2 studies for a novel glucokinase activator LY2599506 is challenging due to the difficulty in modeling and assessing hypoglycemia risk. A semi-mechanistic integrated glucose-insulin-glucagon (GIG) model was developed in NONMEM based on pharmacokinetic, glucose, insulin, glucagon, and meal data obtained from a multiple ascending dose study in patients with Type 2 diabetes mellitus treated with LY2599506 for up to 26 days. The series of differential equations from the NONMEM model was translated into an R script to prospectively predict 24-h glucose profiles following LY2599506 treatment for 3 months for a variety of doses and dosing regimens. The reduction in hemoglobin A1c (HbA1c) at the end of the 3-month treatment was estimated using a transit compartment model based on the simulated fasting glucose values. Two randomized phase 2 studies, one with fixed dosing and the other employing conditional dose titration were conducted. The simulation suggested that (1) Comparable HbA1c lowering with lower hypoglycemia risk occurs with titration compared to fixed-dosing; and (2) A dose range of 50-400 mg BID provides either greater efficacy or lower hypoglycemia incidence or both than glyburide. The predictions were in reasonable agreement with the observed clinical data. The model predicted HbA1c reduction and hypoglycemia risk provided the basis for the decision to focus on the dose-titration trial and for the selection of doses for the demonstration of superiority of LY2599506 to glyburide. The integrated GIG model represented a valuable tool for the evaluation of hypoglycemia incidence.

A generalisation of T-optimality for discriminating between competing models with an application to pharmacokinetic studies

The T-optimality criterion is used in optimal design to derive designs for model selection. To set up the method, it is required that one of the models is considered to be true. We term this local T-optimality. In this work, we propose a generalisation of T-optimality (termed robust T-optimality) that relaxes the requirement that one of the candidate models is set as true. We then show an application to a nonlinear mixed effects model with two candidate non-nested models and combine robust T-optimality with robust D-optimality. Optimal design under local T-optimality was found to provide adequate power when the a priori assumed true model was the true model but poor power if the a priori assumed true model was not the true model. The robust T-optimality method provided adequate power irrespective of which model was true. The robust T-optimality method appears to have useful properties for nonlinear models, where both the parameter values and model structure are required to be known a priori, and the most likely model that would be applied to any new experiment is not known with certainty.

Merging systems biology with pharmacodynamics

The emerging discipline of systems pharmacology aims to combine analysis and computational modeling of cellular regulatory networks with quantitative pharmacology approaches to drive the drug discovery processes, predict rare adverse events, and catalyze the practice of personalized precision medicine. Here, we introduce the concept of enhanced pharmacodynamic (ePD) models, which synergistically combine the desirable features of systems biology and current PD models within the framework of ordinary or partial differential equations. ePD models that analyze regulatory networks involved in drug action can account for a drug's multiple targets and for the effects of genomic, epigenomic, and posttranslational changes on the drug efficacy. This new knowledge can drive drug discovery and shape precision medicine.

Role of modelling and simulation: a European regulatory perspective

Modelling and simulation (M&S) of clinical data, e.g. pharmacokinetic, pharmacodynamic and clinical endpoints, is a useful approach for more efficient interpretation of collected data and for extrapolation of knowledge to the entire target population. This type of documentation is included in the majority of marketing authorization applications for new medicinal products. This article summarizes the current status of regulatory review with respect to the role of M&S in Europe from the perspective of the Swedish Medical Products Agency. At present, regulatory bodies in Europe encourage the application of the M&S approach during drug development. However, there is a lack of consensus and transparent guidance documents. The main regulatory usage is in the evaluation of dose choices in sub-populations and as support for the dosing regimen in general. The regulatory review of conestat alfa illustrates how the dose recommendation was revised during the approval procedure based on M&S information. A survey of marketing authorization applications for new medicinal products approved in 2010 revealed that the use of the information gained from M&S documentation varies with respect to both regulatory review and the applicants' presentation of the data in the submitted dossier. Increased utilization and broadened application of M&S is anticipated in pharmaceutical development, where one area of focus is medicines for paediatric patients. Accordingly, the regulatory agencies will need to increase their capability to assess and utilize this type of information, and an interactive process among regulatory agencies is warranted to provide more unified regulatory assessment and guidance. Moreover, applicants are encouraged to expand on the usage of exposure-response models to map the systemic exposure range that yields safe and efficacious treatment and to improve the presentation of the gained knowledge in summary documents of the marketing authorization applications.

Structural identifiability analysis and reparameterisation (parameter reduction) of a cardiovascular feedback model

Structural identifiability should be considered when developing mathematical models. A globally or at least locally identifiable model has to be obtained in order to have some chance of obtaining unique parameter estimates when real data are available. An indicator of structural unidentifiability may be that some unknown parameter estimates are found to be not well determined from parameter estimation of a model. An example is discussed in this paper to illustrate the procedures involved when such situations arise. Problems with parameter estimation were observed for a PKPD model for an α1A/1L-adrenoceptor partial agonist developed for the treatment of stress urinary incontinence The regulation of the side effects of the increased peripheral resistance, induced by the constriction of the blood vessels, was modelled by adapting a previous cardiovascular nonlinear PKPD model proposed by Franchetau and co-workers. Structural identifiability analysis confirmed that the model was unidentifiable. The model was then reparameterised (parameter list reduction) to obtain a globally identifiable model. Simulation studies confirm the superiority of the reduced parameterisation with respect to parameter estimation. The simulation study also confirms the models behave indistinguishably with respect to the input-output behaviour. The example demonstrates the importance of recognising an unidentifiable model and illustrates step by step identifiability analysis, reparameterisation and validation of reparameterised model against the original model.

Covariate pharmacokinetic model building in oncology and its potential clinical relevance

When modeling pharmacokinetic (PK) data, identifying covariates is important in explaining interindividual variability, and thus increasing the predictive value of the model. Nonlinear mixed-effects modeling with stepwise covariate modeling is frequently used to build structural covariate models, and the most commonly used software-NONMEM-provides estimations for the fixed-effect parameters (e.g., drug clearance), interindividual and residual unidentified random effects. The aim of covariate modeling is not only to find covariates that significantly influence the population PK parameters, but also to provide dosing recommendations for a certain drug under different conditions, e.g., organ dysfunction, combination chemotherapy. A true covariate is usually seen as one that carries unique information on a structural model parameter. Covariate models have improved our understanding of the pharmacology of many anticancer drugs, including busulfan or melphalan that are part of high-dose pretransplant treatments, the antifolate methotrexate whose elimination is strongly dependent on GFR and comedication, the taxanes and tyrosine kinase inhibitors, the latter being subject of cytochrome p450 3A4 (CYP3A4) associated metabolism. The purpose of this review article is to provide a tool to help understand population covariate analysis and their potential implications for the clinic. Accordingly, several population covariate models are listed, and their clinical relevance is discussed. The target audience of this article are clinical oncologists with a special interest in clinical and mathematical pharmacology.

Modelling and simulation in the pharmaceutical industry--some reflections

Modelling and simulation (M&S) is increasingly being applied in (clinical) drug development. It provides an opportune area for the community of pharmaceutical statisticians to pursue. In this article, we highlight useful principles behind the application of M&S. We claim that M&S should be focussed on decisions, tailored to its purpose and based in applied sciences, not relying entirely on data-driven statistical analysis. Further, M&S should be a continuous process making use of diverse information sources and applying Bayesian and frequentist methodology, as appropriate. In addition to forming a basis for analysing decision options, M&S provides a framework that can facilitate communication between stakeholders. Besides the discussion on modelling philosophy, we also describe how standard simulation practice can be ineffective and how simulation efficiency can often be greatly improved.

Translational PK-PD modelling of molecular target modulation for the AMPA receptor positive allosteric modulator Org 26576

INTRODUCTION

The α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptor potentiator Org 26576 represents an interesting pharmacological tool to evaluate the utility of glutamatergic enhancement towards the treatment of psychiatric disorders. In this study, a rat-human translational pharmacokinetic-pharmacodynamic (PK-PD) model of AMPA receptor modulation was used to predict human target engagement and inform dose selection in efficacy clinical trials.

METHODS

Modelling and simulation was applied to rat plasma and cerebrospinal fluid (CSF) pharmacokinetic and pharmacodynamic measurements to identify a target concentration (EC(80)) for AMPA receptor modulation. Human plasma pharmacokinetics was determined from 33 healthy volunteers and eight major depressive disorder patients. From four out of these eight patients, CSF PK was also determined. Simulations of human CSF levels were performed for several doses of Org 26576.

RESULTS

Org 26576 (0.1-10 mg/kg, i.v.) potentiated rat hippocampal AMPA receptor responses in an exposure-dependant manner. The rat plasma and CSF PK data were fitted by one-compartment model each. The rat CSF PK-PD model yielded an EC(80) value of 593 ng/ml (90% confidence interval 406.8, 1,264.1). The human plasma and CSF PK data were simultaneously well described by a two-compartment model. Simulations showed that in humans at 100 mg QD, CSF levels of Org 26576 would exceed the EC(80) target concentration for about 2 h and that 400 mg BID would engage AMPA receptors for 24 h.

CONCLUSION

The modelling approach provided useful insight on the likely human dose-molecular target engagement relationship for Org 26576. Based on the current analysis, 100 and 400 mg BID would be suitable to provide 'phasic' and 'continuous' AMPA receptor engagement, respectively.

Structural models describing placebo treatment effects in schizophrenia and other neuropsychiatric disorders

Large variation in placebo response within and among clinical trials can substantially affect conclusions about the efficacy of new medications in psychiatry. Developing a robust placebo model to describe the placebo response is important to facilitate quantification of drug effects, and eventually to guide the design of clinical trials for psychiatric treatment via a model-based simulation approach. In addition, high dropout rates are very common in the placebo arm of psychiatric clinical trials. While developing models to evaluate the effect of placebo response, the data from patients who drop out of the trial should be considered for accurate interpretation of the results. The objective of this paper is to review the various empirical and semi-mechanistic models that have been used to quantify the placebo response in schizophrenia trials. Pros and cons of each placebo model are discussed. Additionally, placebo models used in other neuropsychiatric disorders like depression, Alzheimer's disease and Parkinson's disease are also reviewed with the objective of finding those placebo models that could be useful for clinical studies of both acute and chronic schizophrenic disease conditions. Better understanding of the patterns of dropout and the factors leading to dropouts are crucial in identifying the true placebo response. We therefore also review dropout models that are used in the development of models for treatment effects and in the optimization of clinical trials by simulation approaches. The use of an appropriate modelling strategy that is capable of identifying the potential sources of variable placebo responses and dropout rates is recommended for improving the sensitivity in discriminating between the effects of active treatment and placebo.

The value of population pharmacokinetics and simulation for postmarketing safety evaluation of dosing guidelines for drugs with a narrow therapeutic index: buflomedil as a case study

Population pharmacokinetics and simulation techniques currently play an important role in new drug development. This paper illustrates the potential value of those methods in postmarketing safety assessment, using buflomedil in elderly patients as an example. We retrospectively assessed the risk of buflomedil overdosing associated with the latest dosing recommendations of the French Drug Agency (AFSSAPS). First, buflomedil concentrations measured in 24 elderly patients were analysed with a nonparametric population approach. Then, the pharmacokinetic model was used to perform a 1000-patient Monte Carlo simulation for the two recommended buflomedil dosage regimens. The maximum concentrations calculated after 10 days of therapy were compared with levels observed in reported cases of toxicity to assess the probability of overdosing. A three-compartment model best fit concentration data. Population predictions showed little bias (-0.14 mg/L) and good precision (8.73 mg(2) /L(2)). Overall results of the simulation study showed that the application of the two recommended dosage regimens of buflomedil was associated with overdosing (C(max) > 10 mg/L) and potential toxicity in 2.9% of geriatric patients. In patients with mild renal impairment, who may receive the higher-dosage regimen by therapeutic error, the probability of overdosing was 6.2%. Despite specific dosing recommendations in case of renal impairment, this study shows that the use of buflomedil could be associated with significant risk of overdosing in geriatric patients. Such results might have enhanced decision-making when buflomedil safety was reassessed by AFSSAPS in 2006. The retrospective case of buflomedil illustrates how these methods may be valuable in postmarketing safety evaluation of potentially toxic drugs.

Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models

Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or changing between periods. We use the expected standard errors of treatment effect to compute the power for the Wald test of comparison or equivalence and the number of subjects needed for a given power. We perform various simulations mimicking crossover two-period trials to show the relevance of these developments. We then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3.2 of the r function PFIM.

Adherence to medications: insights arising from studies on the unreliable link between prescribed and actual drug dosing histories

Satisfactory adherence to aptly prescribed medications is essential for good outcomes of patient care and reliable evaluation of competing modes of drug treatment. The measure of satisfactory adherence is a dosing history that includes timely initiation of dosing plus punctual and persistent execution of the dosing regimen throughout the specified duration of treatment. Standardized terminology for initiation, execution, and persistence of drug dosing is essential for clarity of communication and scientific progress. Electronic methods for compiling drug dosing histories are now the recognized standard for quantifying adherence, the parameters of which support model-based, continuous projections of drug actions and concentrations in plasma that are confirmable by intermittent, direct measurements at single time points. The frequency of inadequate adherence is usually underestimated by pre-electronic methods and thus is clinically unrecognized as a frequent cause of failed treatment or underestimated effectiveness. Intermittent lapses in dosing are potential sources of toxicity through hazardous rebound effects or recurrent first-dose effects.

Understanding the time course of pharmacological effect: a PKPD approach

The key concepts that underpin the choice of drug and dosing regimen are an understanding of the drugs' effectiveness, the potential for adverse effects, and the expected time course over which both desired and adverse effects are likely to occur. Research in clinical pharmacology should therefore address three fundamental questions: (1) What is the magnitude of drug effects (beneficial or adverse) from a given dose? (2) How quickly will any given effects occur? (3) How long will these effects last? Under steady-state conditions, only the magnitude of drug effects can be examined. This requires researchers to consider non-steady-state conditions, which require more complex models and an understanding of the mechanisms that drive the time course of drug effect. The aim of this review is to provide a conceptual framework for understanding the time course of drug effects using pharmacokinetic-pharmacodynamic models. Key examples will illustrate how this can inform the optimal use of drugs in the clinic.

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

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

Bayesian population modeling of phase I dose escalation studies: Gaussian process versus parametric approaches

The early stages of the drug development process are often characterized by a limited number of subjects participating the study and a limited number of measurements per individual that can be collected, mainly due to technical, ethical, and cost reasons. The so-called dose escalation studies, performed during phase I, usually involve about 40 subjects or less, and feature observations at no more than three (rarely four or five) dose levels-per-subject. Depending on the complexity of the underlying pharmacokinetics, simple linear models or nonlinear ones (e.g., power, E(max) models) may be appropriate to describe the relationship between the metrics of systemic exposure to the drug (C(max), AUC) and the administered dose. However, in such data-poor scenarios, formulating models based on parametric descriptions is generally hard, and may easily result in model misspecification. Hence, nonparametric or "model-free" solutions, borrowed from the machine learning field, are deemed appealing. We resort to Gaussian process theory to work out Bayesian posterior expectations of a population (a.k.a mixed-effects) regression problem, namely Population Smoothing Splines (PSS). We show that in seven experimental dose escalation studies, Population Smoothing Splines improve on three widely used parametric population methods. Superiority of the model-free technique is confirmed by a simulated benchmark: Population Smoothing Splines compare very favorably even with the true parametric model structure underlying the simulated data.

Model-based drug development survey finds pharmacometrics impacting decision making in the pharmaceutical industry

During the past decade, the pharmaceutical industry has seen the increasing application of pharmacometrics approaches in drug development. However, the full potential of incorporating model-based approaches in drug development and its impact on decision making has not been fully realized to date. In 2009, a survey on model-based drug development (MBDD) was conducted (1) to further understand the current state of MBDD in the pharmaceutical industry and (2) to identify opportunities to realize the full potential of MBDD. Ten large and mid-sized pharmaceutical companies provided responses to this survey. The results indicate that MBDD is achieving broad application in early and late development and is positively affecting both internal and regulatory decisions. Senior leadership (vice president and higher) within the companies indicated widely accepted utility for dose selection and gaining acceptance for study design and regulatory interactions but limited acceptance in discovery and commercial/pipeline decisions. Mounting appreciation for the impact of MBDD on internal and regulatory decision-making bodes well for the future of the pharmacometric discipline and the growth of opportunities to realize the full potential of MBDD.

Model-based drug development: strengths, weaknesses, opportunities, and threats for broad application of pharmacometrics in drug development

Systematic implementation of model-based drug development (MBDD) to drug discovery and development has the potential to significantly increase the rate of medical breakthroughs and make available new and better treatments to patients. An analysis of the strengths, weaknesses, opportunities, and threats (ie, SWOT) was conducted through focus group discussions that included 24 members representing 8 pharmaceutical companies to systematically assess the challenges to implementing MBDD into the drug development decision-making process. The application of the SWOT analysis to the successful implementation of MBDD yielded 19 strengths, 27 weaknesses, 34 opportunities, and 22 threats, which support the following conclusions. The shift from empirical drug development to MBDD requires a question-based mentality; early, proactive planning; dynamic access to multisource data; quantitative knowledge integration; multidisciplinary collaboration; effective communication and leadership skills; and innovative, impactful application of pharmacometrics focused on enhancing quantitative decision making. The ultimate goal of MBDD is to streamline discovery and development of innovative medicines to benefit patients.

Pharmacokinetics of teriparatide (rhPTH[1-34]) and calcium pharmacodynamics in postmenopausal women with osteoporosis

Teriparatide (rhPTH[1-34]) affects calcium metabolism in a pattern consistent with the known actions of endogenous parathyroid hormone (PTH). This report describes the pharmacokinetics and resulting serum calcium response to teriparatide in postmenopausal women with osteoporosis. Pharmacokinetic samples for this analysis were obtained from 360 women who participated in the Fracture Prevention Trial. Postmenopausal women with osteoporosis received daily subcutaneous injections of either teriparatide 20 μg (4.86 μmol) or placebo, median 21 months' treatment. Serum teriparatide and calcium concentrations were measured throughout the study. An indirect-response model was developed to describe the pharmacokinetic-pharmacodynamic relationship between teriparatide concentrations and serum calcium response. The pharmacokinetics of teriparatide were characterized by rapid absorption (maximum concentration achieved within 30 min) and rapid elimination (half-life of 1 h), resulting in a total duration of exposure to the peptide of approximately 4 h. Teriparatide transiently increased serum calcium, with the maximum effect observed at approximately 4.25 h (median increase 0.4 mg/dl [0.1 mmol/l]). Calcium concentrations returned to predose levels by 16-24 h after each dose. Persistent hypercalcemia was not observed; one teriparatide 20 μg-treated patient had a predose serum calcium value above the normal range but <11.0 mg/dl (2.75 mmol/l). Following once-daily subcutaneous administration, teriparatide produces a modest but transient increase in serum calcium, consistent with the known effects of endogenous PTH on mineral metabolism. The excursion in serum calcium is brief, due to the short length of time that teriparatide concentrations are elevated.

Quantitative clinical pharmacology is transforming drug regulation

Prior to 1970s, development and regulation of new drugs was devoid of a fully quantitative, pathophysiological conceptual foundation. Malcolm Rowland pioneered, in collaboration with colleagues and friends, our modern understanding of drug clearance concepts, and equipped drug development and regulatory scientists with key investigative tools such as physiologically-based pharmacokinetic (PBPK) modeling, standardized approaches to characterizing drug metabolism, and microdosing. From the 1970s to the present, Malcolm Rowland has contributed to key advances in pharmacokinetics that have had transformational impacts on drug regulatory science. These advances include concepts that have led to the fundamental understanding that mechanistically derived, quantitative variations in drug concentrations, rather than assigned dosage alone, drive pharmacodynamic effects (PKPD)-including disease biomarkers and clinical outcomes. This body of knowledge has transformed drug development and regulatory science theory and practice from naïve empiricism to a mechanism/model-based, quantitative scientific discipline. As a result, it is now possible to incorporate pre-clinical in vitro data on drug physico-chemical properties, metabolizing enzymes, transporters and permeability properties into PBPK-based simulations of expected PK distributions and drug-drug interactions in human populations. The most comprehensive application of PK-PD is in the modeling and simulation of clinical trials in the context of model-based drug development and regulation, imbedded in the "learn-confirm paradigm". Regulatory agencies have embraced these advances and incorporated them into regulatory requirements, approval acceleration pathways and regulatory decisions. These developments are reviewed here, with emphasis on key contributions of Malcolm Rowland that facilitated this transformation.

Quantification of apixaban's therapeutic utility in prevention of venous thromboembolism: selection of phase III trial dose

A model-based approach was used to integrate data from a phase II study in order to provide a quantitative rationale for selecting the apixaban dosage regimen for a phase III trial. The exposure-response models demonstrated that an increase in daily steady-state area under the plasma concentration-vs.-time curve (AUC(ss)) of 1 microg x h/ml would increase the odds ratio for major bleeding by 0.118 and decrease the odds ratio for venous thromboembolism (VTE) by 0.0499. The therapeutic utility index (TUI) was used to integrate the efficacy and safety predictions to quantify apixaban's efficacy/safety balance as a function of AUC(ss). Of the apixaban dosage regimens tested in phase II, the 2.5 mg twice-daily (b.i.d.) dosage regimen had the highest TUI (86.2%). This was also higher than the TUI for either 30 mg b.i.d. enoxaparin (82.5%) or for warfarin (71.8%). Subjects with moderate renal impairment are expected to have a 43% increase in apixaban exposure; however, apixaban's TUI suggests that dose adjustment is not needed in these subjects with renal impairment.

Proposals for model-based paediatric medicinal development within the current European Union regulatory framework

The new paediatric European Union (EU) regulation and the consequent demand for paediatric studies on one hand and the ethical need for minimizing the burden of studies in children on the other hand necessitate optimal techniques in the assessment of safety/efficacy and use of drugs in children. Modelling and simulation (M&S) is one way to circumvent some difficulties in developing medicinal products in children. M&S allows the quantitative use of sparse sampling, characterization and prediction of pharmacokinetics/pharmacodynamics (PK/PD), extrapolation from adults to children, interpolation between paediatric age subsets, optimal use of scientific literature and in vitro/preclinical data. Together, industry, academia and regulators recognize the usefulness of modelling and simulation in this setting. However, even if M&S is an emerging science, its integration in the EU regulatory decision making is for the time being deficient and M&S expertise is concentrated in big pharmaceutical companies and academic institutions. The European Medicines Agency, acknowledging all the above conditions, organized and hosted a Workshop on Modelling in Paediatric Medicines. The article presents the personal views of the authors on the issues presented and discussed in the workshop.We attempt to identify the regulatory framework for the use of M&S in paediatric medicinal development and to make proposals for model-based paediatric medicinal development. The objective is to open the discussion between industry, academia, paediatricians and regulators on the optimal use of M&S in paediatric medicinal development.

Pharmacokinetic/pharmacodynamic modeling and simulation to determine effective dosage regimens for doripenem

The aim of this study was to obtain information on effective dosage regimens of doripenem by a modeling and simulation approach based on pharmacokinetic (PK)/pharmacodynamic (PD) theory. The PK/PD model we have already developed was modified to explain in vitro bactericidal kinetics of doripenem for several Pseudomonas aeruginosa strains. Time-course profiles of bacterial counts in patients infected with P. aeruginosa were simulated for typical clinical dosage regimens in Japan considering the variability of PK and the patients' backgrounds by a Monte Carlo simulation. Moreover, time-course profiles of probability achieving the criterion (log(CFU/mL) < 0) were predicted for the evaluation of antibacterial efficacy by renal function. The in vitro bacterial profiles at various dosage regimens could be well explained by the PK/PD model. The simulations suggested the dependence of antibacterial efficacy on the frequency of administration, indicating time-dependent antibacterial activity. It was also suggested that 500 mg t.i.d. showed significant bacterial reduction in patients for any degree of renal function and any severities in 2 weeks after the start of treatment. Our approach to simulate time-course profiles of bacterial counts should be useful for determining and examining effective dosage regimens, including the treatment period, in drug development.

A model for glucose, insulin, and beta-cell dynamics in subjects with insulin resistance and patients with type 2 diabetes

Type 2 diabetes mellitus (T2DM) is a progressive, metabolic disorder characterized by reduced insulin sensitivity and loss of beta-cell mass (BCM), resulting in hyperglycemia. Population pharmacokinetic-pharmacodynamic (PKPD) modeling is a valuable method to gain insight into disease and drug action. A semi-mechanistic PKPD model incorporating fasting plasma glucose (FPG), fasting insulin, insulin sensitivity, and BCM in patients at various disease stages was developed. Data from 3 clinical trials (phase II/III) with a peroxisome proliferator-activated receptor agonist, tesaglitazar, were used to develop the model. In this, a modeling framework proposed by Topp et al was expanded to incorporate the effects of treatment and impact of disease, as well as variability between subjects. The model accurately described FPG and fasting insulin data over time. The model included a strong relation between insulin clearance and insulin sensitivity, predicted 40% to 60% lower BCM in T2DM patients, and realistic improvements of BCM and insulin sensitivity with treatment. The treatment response on insulin sensitivity occurs within the first weeks, whereas the positive effects on BCM arise over several months. The semi-mechanistic PKPD model well described the heterogeneous populations, ranging from nondiabetic, insulin-resistant subjects to long-term treated T2DM patients. This model also allows incorporation of clinical-experimental studies and actual observations of BCM.

Population pharmacokinetic/pharmacodynamic model for C.E.R.A. in both ESA-naive and ESA-treated chronic kidney disease patients with renal anemia

This study aimed to develop a population pharmacokinetic/pharmacodynamic (PK/PD) model for C.E.R.A., a continuous erythropoietin receptor activator. C.E.R.A. is administered via intravenous (IV) and subcutaneous (SC) routes once every 2 weeks (Q2W) or once every 4 weeks (Q4W), respectively, to correct or maintain hemoglobin levels in chronic kidney disease (CKD) patients. Population models were specified to describe C.E.R.A. (PK) and hemoglobin (PD) concentrations over time, using data from 3 phase III, open-label, randomized, parallel-group, multicenter studies that examined IV or SC C.E.R.A. administration Q2W and Q4W in erythropoiesis-stimulating agent (ESA)-naive and ESA-treated patients. C.E.R.A. PK was described by a 1-compartment model: drug clearance = 0.75 L/d, volume of distribution = 4.72 L, and half-life = 105 hours in accordance with previous reported values. The PD model, a life span sequential PK/PD model, adequately described hemoglobin data. Dosing schedule, administration route, and study type did not affect drug-related PD parameters or system-specific parameters (eg, red blood cell life span). This model adequately described C.E.R.A.'s PK and PD properties according to C.E.R.A. posology, thus permitting simulations exploring alternative drug administration scenarios. It supports use of C.E.R.A. IV and SC; Q2W for anemia correction in ESA-Naïve CKD patients and monthly administration in the hemoglobin maintenance phase.