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The International Council for Harmonisation revised the E14 guideline through the questions and answers process to allow concentration-QTc (C-QTc) modeling to be used as the primary analysis for assessing the QTc interval prolongation risk of new drugs. A well-designed and conducted QTc assessment based on C-QTc modeling in early phase 1 studies can be an alternative approach to a thorough QT study for some drugs to reliably exclude clinically relevant QTc effects. This white paper provides recommendations on how to plan and conduct a definitive QTc assessment of a drug using C-QTc modeling in early phase clinical pharmacology and thorough QT studies. Topics included are: important study design features in a phase 1 study; modeling objectives and approach; exploratory plots; the pre-specified linear mixed effects model; general principles for model development and evaluation; and expectations for modeling analysis plans and reports. The recommendations are based on current best modeling practices, scientific literature and personal experiences of the authors. These recommendations are expected to evolve as their implementation during drug development provides additional data and with advances in analytical methodology.

There are several antibody therapeutics in preclinical and clinical development, industry-wide, for the treatment of central nervous system (CNS) disorders. Due to the limited permeability of antibodies across brain barriers, the quantitative understanding of antibody exposure in the CNS is important for the design of antibody drug characteristics and determining appropriate dosing regimens. We have developed a minimal physiologically-based pharmacokinetic (mPBPK) model of the brain for antibody therapeutics, which was reduced from an existing multi-species platform brain PBPK model. All non-brain compartments were combined into a single tissue compartment and cerebral spinal fluid (CSF) compartments were combined into a single CSF compartment. The mPBPK model contains 16 differential equations, compared to 100 in the original PBPK model, and improved simulation speed approximately 11-fold. Area under the curve ratios for minimal versus full PBPK models were close to 1 across species for both brain and plasma compartments, which indicates the reduced model simulations are similar to those of the original model. The minimal model retained detailed physiological processes of the brain while not significantly affecting model predictability, which supports the law of parsimony in the context of balancing model complexity with added predictive power. The minimal model has a variety of applications for supporting the preclinical development of antibody therapeutics and can be expanded to include target information for evaluating target engagement to inform clinical dose selection. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09776-7.

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed. Supplementary Information The online version supplementary material available at 10.1007/s10928-021-09764-x.

Population pharmacokinetic/pharmacodynamic (PK/PD) analysis was performed for extensive data for differing dosage forms and routes for dexamethasone (DEX) and betamethasone (BET) in 48 healthy nonpregnant Indian women in a partial and complex cross-over design. Single doses of 6 mg dexamethasone phosphate (DEX-P), betamethasone phosphate (BET-P), or 1:1 mixture of betamethasone phosphate and acetate (BET-PA) were administered orally (PO) or intramuscularly (IM) where each woman enrolled in a two-period cross-over study. Plasma concentrations collected over 96 h were described with a two-compartment model with differing PO and IM first-order absorption inputs. Overall, BET exhibited slower clearance, similar volume of distribution, faster absorption, and longer persistence than DEX with BET acetate producing extremely slow absorption but full bioavailability of BET. Six biomarkers were assessed over a 24-h baseline period with four showing circadian rhythms with complex baselines. These baselines and the strong responses seen after drug dosing were fitted with various indirect response models using the Laplace estimation methods in NONMEM 7.4. Both the PK and six biomarker responses were well-described with modest variability likely due to the homogeneous ages, weights, and ethnicities of the women. The drugs either inhibited or stimulated the influx processes with some models requiring joint inclusion of drug effects on circadian cortisol suppression. The biomarkers and order of sensitivity (lowest IC50/SC50 to highest) were: cortisol, T-helper cells, basophils, glucose, neutrophils, and T-cytotoxic cells. DEX sensitivities were generally greater than BET with corresponding mean ratios for these biomarkers of 2.86, 1.27, 1.72, 1.27, 2.69, and 1.06. Overall, the longer PK (e.g. half-life) of BET, but lesser PD activity (e.g. higher IC50), produces single-dose response profiles that appear quite similar, except for the extended effects from BET-PA. This comprehensive population modeling effort provides the first detailed comparison of the PK profiles and six biomarker responses of five commonly used dosage forms of DEX and BET in healthy women.

Circadian rhythms are ubiquitous phenomena that recur daily in a self-sustaining, entrainable, and oscillatory manner, and orchestrate a wide range of molecular, physiological, and behavioral processes. Circadian clocks are comprised of a hierarchical network of central and peripheral clocks that generate, sustain, and synchronize the circadian rhythms. The functioning of the peripheral clock is regulated by signals from autonomic innervation (from the central clock), endocrine networks, feeding, and other external cues. The critical role played by circadian rhythms in maintaining both systemic and tissue-level homeostasis is well established, and disruption of the rhythm has direct consequence for human health, disorders, and diseases. Circadian oscillations in both pharmacokinetics and pharmacodynamic processes are known to affect efficacy and toxicity of several therapeutic agents. A variety of modeling approaches ranging from empirical to more complex systems modeling approaches have been applied to characterize circadian biology and its influence on drug actions, optimize time of dosing, and identify opportunities for pharmacological modulation of the clock mechanisms and their downstream effects. In this review, we summarize current understanding of circadian rhythms and its influence on physiology, pharmacology, and therapeutic interventions, and discuss the role of chronopharmacometrics in gaining new insights into circadian rhythms and its applications in chronopharmacology.

Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.

ASP8232 is a novel inhibitor of vascular adhesion protein-1 that was under evaluation for reducing residual albuminuria in patients with diabetic kidney disease. To characterize the pharmacokinetics (PK) of ASP8232 and its effect on vascular adhesion protein 1 (VAP-1) plasma activity and VAP-1 concentrations (pharmacodynamics, PD) in an integrated and quantitative manner, a target mediated drug disposition model was developed based on pooled data from four completed clinical trials with ASP8232 in healthy volunteers, and in patients with diabetic kidney disease and diabetic macular edema, respectively. In this model, the binding of ASP8232 to its soluble and membrane-bound target in the central and peripheral compartments were included. The model was able to adequately describe the non-linear PK and PD of ASP8232. The observed difference in PK between healthy volunteers and renally impaired patients could be explained by an effect of baseline estimated glomerular filtration rate on ASP8232 clearance and relative bioavailability. The relationship between ASP8232 concentration and VAP-1 inhibition was successfully established and can be applied to simulate drug exposure and degree of VAP-1 inhibition for any given dose of ASP8232 across the spectrum of renal function. Electronic supplementary material The online version of this article (10.1007/s10928-020-09717-w) contains supplementary material, which is available to authorized users.

The vascular adhesion protein-1 (VAP-1) inhibitor ASP8232 reduces albuminuria in patients with type 2 diabetes and chronic kidney disease. A mechanism-based model was developed to quantify the effects of ASP8232 on renal markers from a placebo-controlled Phase 2 study in diabetic kidney disease with 12 weeks of ASP8232 treatment. The model incorporated the available pharmacokinetic, pharmacodynamic (plasma VAP-1 concentration and activity), serum and urine creatinine, serum cystatin C, albumin excretion rate, urinary albumin-to-creatinine ratio, and urine volume information in an integrated manner. Drug-independent time-varying changes and different drug effects could be quantified for these markers using the model. Through simulations, this model provided the opportunity to dissect the relationship and longitudinal association between the estimated glomerular filtration rate and albuminuria and to quantify the pharmacological effects of ASP8232. The developed drug-independent model may be useful as a starting point for other compounds affecting the same biomarkers in a similar time scale. Electronic supplementary material The online version of this article (10.1007/s10928-020-09716-x) contains supplementary material, which is available to authorized users.

CYP3A plays an important role in drug metabolism and, thus, can be a considerable liability for drug-drug interactions. Population pharmacokinetics may be an efficient tool for detecting such drug-drug interactions. Multiple models have been developed for midazolam, the typical probe substrate for CYP3A activity, but no population pharmacokinetic models have been developed for use with inhibition or induction. The objective of the current analysis was to develop a composite parent-metabolite model for midazolam which could adequately describe CYP3A drug-drug interactions. As an exploratory objective, parameters were assessed for potential cut-points which may allow for determination of drug-drug interactions when a baseline profile is not available. The final interaction model adequately described midazolam and 1′-OH midazolam concentrations for constitutive, inhibited, and induced CYP3A activity. The model showed good internal and external validity, both with full profiles and limited sampling (2, 2.5, 3, and 4 h), and the model predicted parameters were congruent with values found in clinical studies. Assessment of potential cut-points for model predicted parameters to assess drug-drug interaction liability with a single profile suggested that midazolam clearance may reasonably be used to detect inhibition (4.82–16.4 L/h), induction (41.8–88.9 L/h), and no modulation (16.4–41.8 L/h), with sensitivities for potent inhibition and induction of 87.9% and 83.3%, respectively, and a specificity of 98.2% for no modulation. Thus, the current model and cut-points could provide efficient and accurate tools for drug-drug liability detection, both during drug development and in the clinic, following prospective validation in healthy volunteers and patient populations. Electronic supplementary material The online version of this article (10.1007/s10928-020-09704-1) contains supplementary material, which is available to authorized users.

Cardiac output (CO) is expected to affect elimination and distribution of highly extracted and perfusion rate-limited drugs. This work was undertaken to quantify the effect of CO measured by the pulse pressure method on pharmacokinetics and pharmacodynamics of propofol and fentanyl administrated during total intravenous anesthesia (TIVA). The data were obtained from 22 ASA III patients undergoing abdominal aortic surgery. Propofol was administered via target-controlled infusion system (Diprifusor) and fentanyl was administered at a dose of 2–3 µg/kg each time analgesia appeared to be inadequate. Hemodynamic measurements as well as bispectral index were monitored and recorded throughout the surgery. Data analysis was performed by using a non-linear mixed-effect population modeling (NONMEM 7.4 software). Three compartment models that incorporated blood flows as parameters were used to describe propofol and fentanyl pharmacokinetics. The delay of the anesthetic effect, with respect to plasma concentrations, was described using a biophase (effect) compartment. The bispectral index was linked to the propofol and fentanyl effect site concentrations through a synergistic Emax model. An empirical linear model was used to describe CO changes observed during the surgery. Cardiac output was identified as an important predictor of propofol and fentanyl pharmacokinetics. Consequently, it affected the depth of anesthesia and the recovery time after propofol-fentanyl TIVA infusion cessation. The model predicted (not observed) CO values correlated best with measured responses. Patients‘ age was identified as a covariate affecting the rate of CO changes during the anesthesia leading to age-related difference in individual patient’s responses to both drugs. Electronic supplementary material The online version of this article (10.1007/s10928-020-09712-1) contains supplementary material, which is available to authorized users.

The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: $$2*{\kern 1pt} \,{\ln}\left( {{\Pr}\left( X \right)/\left( {1 - {\Pr}\left( X \right)} \right)} \right)$$ 2 ∗ ln Pr X / 1 - Pr X , Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ($$r=0.9$$ r = 0.9 ), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is 80% but

Population pharmacokinetic analysis is used to estimate pharmacokinetic parameters and their variability from concentration data. Due to data sparseness issues, available datasets often do not allow the estimation of all parameters of the suitable model. The PRIOR subroutine in NONMEM supports the estimation of some or all parameters with values from previous models, as an alternative to fixing them or adding data to the dataset. From a literature review, the best practices were compiled to provide a practical guidance for the use of the PRIOR subroutine in NONMEM. Thirty-three articles reported the use of the PRIOR subroutine in NONMEM, mostly in special populations. This approach allowed fast, stable and satisfying modelling. The guidance provides general advice on how to select the most appropriate reference model when there are several previous models available, and to implement and weight the selected parameter values in the PRIOR function. On the model built with PRIOR, the similarity of estimates with the ones of the reference model and the sensitivity of the model to the PRIOR values should be checked. Covariates could be implemented a priori (from the reference model) or a posteriori, only on parameters estimated without prior (search for new covariates). Graphic abstract Electronic supplementary material The online version of this article (10.1007/s10928-020-09695-z) contains supplementary material, which is available to authorized users.

A phase 1 clinical trial in healthy male volunteers was conducted with a somatostatin-dopamine chimera (BIM23B065), from which information could be obtained on the concentration-effect relationship of the inhibition of pulsatile endogenous growth hormone and prolactin secretion. Endogenous growth hormone profiles were analyzed using a two-step deconvolution-analysis-informed population pharmacodynamic modeling approach, which was developed for the analyses of pulsatile profiles. Prolactin concentrations were modelled using a population pool model with a circadian component on the prolactin release. During treatment with BIM23B065, growth hormone secretion was significantly reduced (maximal effect [EMAX] = − 64.8%) with significant reductions in the pulse frequency in two out of three multiple ascending dose cohorts. A circadian component in prolactin secretion was identified, modelled using a combination of two cosine functions with 24 h and 12 h periods. Dosing of BIM23B065 strongly inhibited (EMAX = − 91%) the prolactin release and demonstrated further reduction of prolactin secretion after multiple days of dosing. This study quantified the concentration-effect relationship of BIM23B065 on the release of two pituitary hormones, providing proof of pharmacology of the chimeric actions of BIM23B065. Electronic supplementary material The online version of this article (10.1007/s10928-020-09683-3) contains supplementary material, which is available to authorized users.

Dexmedetomidine (DEX) is a fairly new alfa2-agonist which has been increasingly used in recent years for analgosedation, mostly because it offers a unique ability of providing both moderate level of sedation and analgesia without respiratory depression. Despite of many papers published, there are still only a few concerning the PK of the drug given as long-term infusion in ICU patients. The aim of this work was to characterize the population pharmacokinetics of dexmedetomidine and to investigate the potential benefits of individualization of drug dosing based on patient characteristics in the heterogeneous group of medical and surgical patients staying in intensive care unit. This study was performed in the group of 17 males and 10 females patients with a median age of 59.5 years and median body weight of 75 kg. Blood samples for dexmedetomidine assay were collected from arterial catheter, during and after discontinuation of a standard infusion, that ranged from 24 to 102 h. The following covariates were examined to influence dexmedetomidine PK: age, sex, body weight, patients’ health status described by Sequential Organ Failure Assessment Score (SOFA), inotropes usage, and infusion duration. The dexmedetomidine PK was best described by a two-compartment model. The typical values of PK parameters were estimated as 27 L for the volume of the central compartment, 87.6 L for the volume of the peripheral compartment, 38.5 L/h (9.2 mL/min/kg for a 70 kg patient) for systemic clearance and 46.4 L/h for the distribution clearance. Those values are consistent with literature findings. We were unable to show any significant relationship between collected covariates and dexmedetomidine PK. This study does not provide sufficient evidence to support the individualization of dexmedetomidine dosing based on age, sex, body weight, SOFA, and infusion duration. Electronic supplementary material The online version of this article (10.1007/s10928-017-9564-7) contains supplementary material, which is available to authorized users.

Physiologically based pharmacokinetic (PBPK) models are an important type of systems model used commonly in drug development before commencement of first-in-human studies. Due to structural complexity, these models are not easily utilised for future data-driven population pharmacokinetic (PK) analyses that require simpler models. In the current study we aimed to explore and automate methods of simplifying PBPK models using a proper lumping technique. A linear 17-state PBPK model for fentanyl was identified from the literature. Four methods were developed to search the optimal lumped model, including full enumeration (the reference method), non-adaptive random search (NARS), scree plot plus NARS, and simulated annealing (SA). For exploratory purposes, it was required that the total area under the fentanyl arterial concentration–time curve (AUC) between the lumped and original models differ by 0.002% at maximum. In full enumeration, a 4-state lumped model satisfying the exploratory criterion was found. In NARS, a lumped model with the same number of lumped states was found, requiring a large number of random samples. The scree plot provided a starting lumped model to NARS and the search completed within a short time. In SA, a 4-state lumped model was consistently delivered. In simplify an existing linear fentanyl PBPK model, SA was found to be robust and the most efficient and may be suitable for general application to other larger-scale linear systems. Ultimately, simplified PBPK systems with fundamental mechanisms may be readily used for data-driven PK analyses. Electronic supplementary material The online version of this article (10.1007/s10928-019-09644-5) contains supplementary material, which is available to authorized users.

The assumption of interindividual variability being unimodally distributed in nonlinear mixed effects models does not hold when the population under study displays multimodal parameter distributions. Mixture models allow the identification of parameters characteristic to a subpopulation by describing these multimodalities. Visual predictive check (VPC) is a standard simulation based diagnostic tool, but not yet adapted to account for multimodal parameter distributions. Mixture model analysis provides the probability for an individual to belong to a subpopulation (IPmix) and the most likely subpopulation for an individual to belong to (MIXEST). Using simulated data examples, two implementation strategies were followed to split the data into subpopulations for the development of mixture model specific VPCs. The first strategy splits the observed and simulated data according to the MIXEST assignment. A shortcoming of the MIXEST-based allocation strategy was a biased allocation towards the dominating subpopulation. This shortcoming was avoided by splitting observed and simulated data according to the IPmix assignment. For illustration purpose, the approaches were also applied to an irinotecan mixture model demonstrating 36% lower clearance of irinotecan metabolite (SN-38) in individuals with UGT1A1 homo/heterozygote versus wild-type genotype. VPCs with segregated subpopulations were helpful in identifying model misspecifications which were not evident with standard VPCs. The new tool provides an enhanced power of evaluation of mixture models. Electronic supplementary material The online version of this article (10.1007/s10928-019-09632-9) contains supplementary material, which is available to authorized users.

A mechanism-based biomarker model of TNFα-response, including different external provocations of LPS challenge and test compound intervention, was developed. The model contained system properties (such as kt, kout), challenge characteristics (such as ks, kLPS, Km, LPS, Smax, SC50) and test-compound-related parameters (Imax, IC50). The exposure to test compound was modelled by means of first-order input and Michaelis–Menten type of nonlinear elimination. Test compound potency was estimated to 20 nM with a 70% partial reduction in TNFα-response at the highest dose of 30 mg·kg−1. Future selection of drug candidates may focus the estimation on potency and efficacy by applying the selected structure consisting of TNFα system and LPS challenge characteristics. A related aim was to demonstrate how an exploratory (graphical) analysis may guide us to a tentative model structure, which enables us to better understand target biology. The analysis demonstrated how to tackle a biomarker with a baseline below the limit of detection. Repeated LPS-challenges may also reveal how the rate and extent of replenishment of TNFα pools occur. Lack of LPS exposure-time courses was solved by including a biophase model, with the underlying assumption that TNFα-response time courses, as such, contain kinetic information. A transduction type of model with non-linear stimulation of TNFα release was finally selected. Typical features of a challenge experiment were shown by means of model simulations. Experimental shortcomings of present and published designs are identified and discussed. The final model coupled to suggested guidance rules may serve as a general basis for the collection and analysis of pharmacological challenge data of future studies. Electronic supplementary material The online version of this article (10.1007/s10928-019-09622-x) contains supplementary material, which is available to authorized users.

The quantitative description of individual observations in non-linear mixed effects models over time is complicated when the studied biomarker has a pulsatile release (e.g. insulin, growth hormone, luteinizing hormone). Unfortunately, standard non-linear mixed effects population pharmacodynamic models such as turnover and precursor response models (with or without a cosinor component) are unable to quantify these complex secretion profiles over time. In this study, the statistical power of standard statistical methodology such as 6 post-dose measurements or the area under the curve from 0 to 12 h post-dose on simulated dense concentration–time profiles of growth hormone was compared to a deconvolution-analysis-informed modelling approach in different simulated scenarios. The statistical power of the deconvolution-analysis-informed approach was determined with a Monte-Carlo Mapped Power analysis. Due to the high level of intra- and inter-individual variability in growth hormone concentrations over time, regardless of the simulated effect size, only the deconvolution-analysis informed approach reached a statistical power of more than 80% with a sample size of less than 200 subjects per cohort. Furthermore, the use of this deconvolution-analysis-informed modelling approach improved the description of the observations on an individual level and enabled the quantification of a drug effect to be used for subsequent clinical trial simulations.

Gerhard Levy started his investigations on the “Kinetics of Drug Action in Disease States” in the fall of 1980. The objective of his research was to study inter-individual variation in pharmacodynamics. To this end, theoretical concepts and experimental approaches were introduced, which enabled assessment of the changes in pharmacodynamics per se, while excluding or accounting for the cofounding effects of concomitant changes in pharmacokinetics. These concepts were applied in several studies. The results, which were published in 45 papers in the years 1984–1994, showed considerable variation in pharmacodynamics. These initial studies on kinetics of drug action in disease states triggered further experimental research on the relations between pharmacokinetics and pharmacodynamics. Together with the concepts in Levy’s earlier publications “Kinetics of Pharmacologic Effects” (Clin Pharmacol Ther 7(3): 362–372, 1966) and “Kinetics of pharmacologic effects in man: the anticoagulant action of warfarin” (Clin Pharmacol Ther 10(1): 22–35, 1969), they form a significant impulse to the development of physiology-based pharmacodynamic (PBPD) modeling as novel discipline in the pharmaceutical sciences. This paper reviews Levy’s research on the “Kinetics of Drug Action in Disease States”. Next it addresses the significance of his research for the evolution of PBPD modeling as a scientific discipline. PBPD models contain specific expressions to characterize in a strictly quantitative manner processes on the causal path between exposure (in terms of concentration at the target site) and the drug effect (in terms of the change in biological function). Pertinent processes on the causal path are: (1) target site distribution, (2) target binding and activation and (3) transduction and homeostatic feedback.

A modeling and simulation approach was used for quantitative comparison of a new generation HER2 antibody drug conjugate (ADC, PF-06804103) with trastuzumab-DM1 (T-DM1). To compare preclinical efficacy, the pharmacokinetic (PK)/pharmacodynamic (PD) relationship of PF-06804103 and T-DM1 was determined across a range of mouse tumor xenograft models, using a tumor growth inhibition model. The tumor static concentration was assigned as the minimal efficacious concentration. PF-06804103 was concluded to be more potent than T-DM1 across cell lines studied. TSCs ranged from 1.0 to 9.8 µg/mL (n = 7) for PF-06804103 and from 4.7 to 29 µg/mL (n = 5) for T-DM1. Two experimental models which were resistant to T-DM1, responded to PF-06804103 treatment. A mechanism-based target mediated drug disposition (TMDD) model was used to predict the human PK of PF-06804103. This model was constructed and validated based on T-DM1 which has non-linear PK at doses administered in the clinic, driven by binding to shed HER2. Non-linear PK is predicted for PF-06804103 in the clinic and is dependent upon circulating HER2 extracellular domain (ECD) concentrations. The models were translated to human and suggested greater efficacy for PF-06804103 compared to T-DM1. In conclusion, a fit-for-purpose translational PK/PD strategy for ADCs is presented and used to compare a new generation HER2 ADC with T-DM1. Electronic supplementary material The online version of this article (10.1007/s10928-020-09702-3) contains supplementary material, which is available to authorized users.

Drug–target binding kinetics (as determined by association and dissociation rate constants, kon and koff) can be an important determinant of the kinetics of drug action. However, the effect compartment model is used most frequently instead of a target binding model to describe hysteresis. Here we investigate when the drug–target binding model should be used in lieu of the effect compartment model. The utility of the effect compartment (EC), the target binding kinetics (TB) and the combined effect compartment–target binding kinetics (EC–TB) model were tested on either plasma (ECPL, TBPL and EC–TBPL) or brain extracellular fluid (ECF) (ECECF, TBECF and EC–TBECF) morphine concentrations and EEG amplitude in rats. It was also analyzed when a significant shift in the time to maximal target occupancy (TmaxTO) with increasing dose, the discriminating feature between the TB and EC model, occurs in the TB model. All TB models assumed a linear relationship between target occupancy and drug effect on the EEG amplitude. All three model types performed similarly in describing the morphine pharmacodynamics data, although the EC model provided the best statistical result. The analysis of the shift in TmaxTO (∆TmaxTO) as a result of increasing dose revealed that ∆TmaxTO is decreasing towards zero if the koff is much smaller than the elimination rate constant or if the target concentration is larger than the initial morphine concentration. The results for the morphine PKPD modelling and the analysis of ∆TmaxTO indicate that the EC and TB models do not necessarily lead to different drug effect versus time curves for different doses if a delay between drug concentrations and drug effect (hysteresis) is described. Drawing mechanistic conclusions from successfully fitting one of these two models should therefore be avoided. Since the TB model can be informed by in vitro measurements of kon and koff, a target binding model should be considered more often for mechanistic modelling purposes. Electronic supplementary material The online version of this article (10.1007/s10928-018-9593-x) contains supplementary material, which is available to authorized users.

This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Amlodipine, a commonly prescribed anti-hypertensive drug, shows increased systemic exposure with cytochrome P450 (CYP) 3A inhibitors. Ritonavir (RTV) is a potent mechanism-based and reversible CYP3A inhibitor and moderate inducer that is used as a pharmacokinetic enhancer in several antiviral treatment regimens. Drug–drug interaction (DDI) between RTV and amlodipine is due to mixed inhibition and induction of CYP3A4, which is challenging to predict without a mechanistic model that accounts for the complexity of both mechanisms occurring simultaneously. A novel physiologically-based pharmacokinetic (PBPK) model was developed for amlodipine, and the model was verified using published clinical PK and DDI data. The verified amlodipine PBPK model was linked to a pharmacodynamics model that describes changes in systolic blood pressure (SBP) during and after co-administration with RTV. The magnitude and time course of RTV effects on amlodipine plasma exposures and SBP were evaluated, to provide guidance on dose adjustment of amlodipine during and after co-administration with RTV-containing regimens. Model simulations suggested that the increase in amlodipine’s plasma exposure by RTV diminishes by approximately 80% within 5 days after the last dose of RTV. PBPK simulations suggested that resuming a full dose of amlodipine [5 mg once daily (QD)] immediately after RTV’s last dose would decrease daily average SBP by a maximum of 3.3 mmHg, while continuing with the reduced dose (2.5 mg QD) for 5 days after the last dose of RTV would increase daily average SBP by a maximum of 5.8 mmHg. Based on these results, either approach of resuming amlodipine’s full dose could be appropriate when combined with appropriate clinical monitoring. Electronic supplementary material The online version of this article (10.1007/s10928-018-9574-0) contains supplementary material, which is available to authorized users.

Proteins are an increasingly important class of drugs used as therapeutic as well as diagnostic agents. A generic physiologically based pharmacokinetic (PBPK) model was developed in order to represent at whole body level the fundamental mechanisms driving the distribution and clearance of large molecules like therapeutic proteins. The model was built as an extension of the PK-Sim model for small molecules incorporating (i) the two-pore formalism for drug extravasation from blood plasma to interstitial space, (ii) lymph flow, (iii) endosomal clearance and (iv) protection from endosomal clearance by neonatal Fc receptor (FcRn) mediated recycling as especially relevant for antibodies. For model development and evaluation, PK data was used for compounds with a wide range of solute radii. The model supports the integration of knowledge gained during all development phases of therapeutic proteins, enables translation from pre-clinical species to human and allows predictions of tissue concentration profiles which are of relevance for the analysis of on-target pharmacodynamic effects as well as off-target toxicity. The current implementation of the model replaces the generic protein PBPK model available in PK-Sim since version 4.2 and becomes part of the Open Systems Pharmacology Suite. Electronic supplementary material The online version of this article (10.1007/s10928-017-9559-4) contains supplementary material, which is available to authorized users.

Non-small cell lung cancer (NSCLC) patients greatly benefit from the treatment with tyrosine kinase inhibitors (TKIs) targeting the epidermal growth factor receptor (EGFR). However, emergence of acquired resistance inevitable occurs after long-term treatment in most patients and limits clinical improvement. In the present study, resistance to drug treatment in patient-derived NSCLC xenograft mice was assessed and modeling and simulation was applied to understand the dynamics of drug resistance as a basis to explore more beneficial drug regimen. Two semi-mechanistic models were fitted to tumor growth inhibition profiles during and after treatment with erlotinib or gefitinib. The base model proposes that as a result of drug treatment, tumor cells stop proliferating and undergo several stages of damage before they eventually die. The acquired resistance model adds a resistance term to the base model which assumes that resistant cells are emerging from the pool of damaged tumor cells. As a result, tumor cells sensitive to drug treatment will either die or be converted to a drug resistant cell population which is proliferating at a slower growth rate as compared to the sensitive cells. The observed tumor growth profiles were better described by the resistance model and emergence of resistance was concluded. In simulation studies, the selection of resistant cells was explored as well as the time-variant fraction of resistant over sensitive cells. The proposed model provides insight into the dynamic processes of emerging resistance. It predicts tumor regrowth during treatment driven by the selection of resistant cells and explains why faster tumor regrowth may occur after discontinuation of TKI treatment. Finally, it is shown how the semi-mechanistic model can be used to explore different scenarios and to identify optimal treatment schedules in clinical trials. Electronic supplementary material The online version of this article (10.1007/s10928-017-9553-x) contains supplementary material, which is available to authorized users.

Drug-discovery has become a complex discipline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathematics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be transformed into their equilibrium concentration-response (target or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response-time dataset; when what-if? predictions beyond the observational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged. These four examples are typical situations when standard approaches known to the general community of pharmacokineticists prove to be inadequate.

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc–FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague–Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{\text{max}}$$\end{document}Imax model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu {\text{M}}}$$\end{document}μM, respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}∼2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

We explore the impact of saturable distribution over the central and the peripheral compartment in pharmacokinetic models, whilst assuming that back flow into the central compartiment is linear. Using simulations and analytical methods we demonstrate characteristic tell-tale differences in plasma concentration profiles of saturable versus linear distribution models, which can serve as a guide to their practical applicability. For two extreme cases, relating to (i) the size of the peripheral compartment with respect to the central compartment and (ii) the magnitude of the back flow as related to direct elimination from the central compartment, we derive explicit approximations which make it possible to give quantitative estimates of parameters. In three appendices we give detailed explanations of how these estimates are derived. They demonstrate how singular perturbation methods can be successfully employed to gain insight in the dynamics of multi-compartment pharmacokinetic models. These appendices are also intended to serve as an introductory tutorial to these ideas.

Knowledge of the uncertainty in model parameters is essential for decision-making in drug development. Contrarily to other aspects of nonlinear mixed effects models (NLMEM), scrutiny towards assumptions around parameter uncertainty is low, and no diagnostic exists to judge whether the estimated uncertainty is appropriate. This work aims at introducing a diagnostic capable of assessing the appropriateness of a given parameter uncertainty distribution. The new diagnostic was applied to case bootstrap examples in order to investigate for which dataset sizes case bootstrap is appropriate for NLMEM. The proposed diagnostic is a plot comparing the distribution of differences in objective function values (dOFV) of the proposed uncertainty distribution to a theoretical Chi square distribution with degrees of freedom equal to the number of estimated model parameters. The uncertainty distribution was deemed appropriate if its dOFV distribution was overlaid with or below the theoretical distribution. The diagnostic was applied to the bootstrap of two real data and two simulated data examples, featuring pharmacokinetic and pharmacodynamic models and datasets of 20–200 individuals with between 2 and 5 observations on average per individual. In the real data examples, the diagnostic indicated that case bootstrap was unsuitable for NLMEM analyses with around 70 individuals. A measure of parameter-specific “effective” sample size was proposed as a potentially better indicator of bootstrap adequacy than overall sample size. In the simulation examples, bootstrap confidence intervals were shown to underestimate inter-individual variability at low sample sizes. The proposed diagnostic proved a relevant tool for assessing the appropriateness of a given parameter uncertainty distribution and as such it should be routinely used.

The effect of subcutaneous (SC) peginterferon β-1a exposure on reduction of gadolinium-enhanced (Gd+) lesion count over time was evaluated in patients with relapsing-remitting multiple sclerosis (RRMS) in a Phase 3 study (ADVANCE). Patients were randomized to receive SC injections of placebo (n = 500), 125 mcg every-2-weeks (n = 512), or 125 mcg every-4-weeks (n = 500) for 1 year, and then active treatment in the second year. Steady state 4-week AUC (AUCss) was derived for each individual based on sparse pharmacokinetic (PK) sample and a population PK model. Several longitudinal count models, including marginal, mixed effect, and mixture models, were compared to explore the relationship between AUCss and Gd+ lesion count (or T2 lesion count). A mixture model which divided subjects into two subpopulations by low and high baseline lesion activity was found to yield best goodness-of-fit for the data. In this model, the point estimate and 95 % CI for drug effect slope on log(λ) are −0.0256 (−0.0304, −0.0216) for Gd+ lesion and −0.0147 (−0.0170, −0.0124) for T2 lesion. This suggested that reduction of Gd+ lesion (or T2 lesion) count over time is significantly related to SC peginterferon β-1a exposure, and that the increased reduction lesion count with the every-2-week regimen versus the every-4-week regimen was driven by the higher exposure achieved in that treatment arm (mean Gd+ lesion count 0.2 and 0.7 at Year 2, respectively). The every-2-week regimen produced an exposure range that was close to the plateau range of the exposure–response curve, supporting its selection as the regulatory approved dosage. Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9477-x) contains supplementary material, which is available to authorized users.

The purpose of this study was to assess the pharmacokinetics of dexmedetomidine in the ICU settings during the prolonged infusion and to compare it with the existing literature data using the Bayesian population modeling with literature-based informative priors. Thirty-eight patients were included in the analysis with concentration measurements obtained at two occasions: first from 0 to 24 h after infusion initiation and second from 0 to 8 h after infusion end. Data analysis was conducted using WinBUGS software. The prior information on dexmedetomidine pharmacokinetics was elicited from the literature study pooling results from a relatively large group of 95 children. A two compartment PK model, with allometrically scaled parameters, maturation of clearance and t-student residual distribution on a log-scale was used to describe the data. The incorporation of time-dependent (different between two occasions) PK parameters improved the model. It was observed that volume of distribution is 1.5-fold higher during the second occasion. There was also an evidence of increased (1.3-fold) clearance for the second occasion with posterior probability equal to 62 %. This work demonstrated the usefulness of Bayesian modeling with informative priors in analyzing pharmacokinetic data and comparing it with existing literature knowledge. Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9474-0) contains supplementary material, which is available to authorized users.

Bronchoalveolar lavage (BAL) is a pulmonary sampling technique for characterization of drug concentrations in epithelial lining fluid and alveolar cells. Two hypothetical drugs with different pulmonary distribution rates (fast and slow) were considered. An optimized BAL sampling design was generated assuming no previous information regarding the pulmonary distribution (rate and extent) and with a maximum of two samples per subject. Simulations were performed to evaluate the impact of the number of samples per subject (1 or 2) and the sample size on the relative bias and relative root mean square error of the parameter estimates (rate and extent of pulmonary distribution). The optimized BAL sampling design depends on a characterized plasma concentration time profile, a population plasma pharmacokinetic model, the limit of quantification (LOQ) of the BAL method and involves only two BAL sample time points, one early and one late. The early sample should be taken as early as possible, where concentrations in the BAL fluid ≥ LOQ. The second sample should be taken at a time point in the declining part of the plasma curve, where the plasma concentration is equivalent to the plasma concentration in the early sample. Using a previously described general pulmonary distribution model linked to a plasma population pharmacokinetic model, simulated data using the final BAL sampling design enabled characterization of both the rate and extent of pulmonary distribution. The optimized BAL sampling design enables characterization of both the rate and extent of the pulmonary distribution for both fast and slowly equilibrating drugs. Electronic supplementary material The online version of this article (doi:10.1007/s10928-015-9438-9) contains supplementary material, which is available to authorized users.

The purpose of this work was to develop a consolidated set of guiding principles for reporting of population pharmacokinetic (PK) analyses based on input from a survey of practitioners as well as discussions between industry, consulting and regulatory scientists. The survey found that identification of population covariate effects on drug exposure and support for dose selection (where population PK frequently serves as preparatory analysis to exposure–response modeling) are the main areas of influence for population PK analysis. The proposed guidelines consider two main purposes of population PK reports (1) to present key analysis findings and their impact on drug development decisions, and (2) as documentation of the analysis methods for the dual purpose of enabling review of the analysis and facilitating future use of the models. This work also identified two main audiences for the reports: (1) a technically competent group responsible for in-depth review of the data, methodology, and results, and (2) a scientifically literate, but not technically adept group, whose main interest is in the implications of the analysis for the broader drug development program. We recommend a generalized question-based approach with six questions that need to be addressed throughout the report. We recommend eight sections (Synopsis, Introduction, Data, Methods, Results, Discussion, Conclusions, Appendix) with suggestions for the target audience and level of detail for each section. A section providing general expectations regarding population PK reporting from a regulatory perspective is also included. We consider this an important step towards industrialization of the field of pharmacometrics such that non-technical audience also understands the role of pharmacometrics analyses in decision making. Population PK reports were chosen as representative reports to derive these recommendations; however, the guiding principles presented here are applicable for all pharmacometric reports including PKPD and simulation reports. Electronic supplementary material The online version of this article (doi:10.1007/s10928-015-9417-1) contains supplementary material, which is available to authorized users.

Nonadherence to prescribed medication is a common barrier to effective treatment, and current options to determine adherence are limited. This study describes development of an aggregate adherence measure based on population pharmacokinetics (PK), and its comparison to a subjective questionnaire, the Morisky 8-item medication adherence scale (MMAS8), in a trial of psychiatric patients on stable doses of oral aripiprazole. A comprehensive model was first built using plasma drug concentration data from 24 clinical studies comprising 448 patients with over 13,500 observations. Application of this model to independent patient profiles for a given drug-dosing regimen were used to generate the primary aggregate adherence metric, a ratio of observed versus expected plasma exposures at steady-state. Although the metric is capable of comparing relative adherence across groups, simulations showed that the metric is not sufficiently sensitive as an individual diagnostic in all cases. There were no trends observed between results from calculated aggregate adherence metrics and total scores from MMAS8 in a single-visit clinical trial of 47 patients with bipolar 1 disorder or schizophrenia who were on stable doses of aripiprazole, although a strong association was observed for one MMAS8 question. The range of the metric calculated for patients was between 0.16 and 3.15. The described approach of a novel “reverse” application of population PK to quantify relative adherence with an aggregate measure may be influential for both clinical and pharmacometric communities. Electronic supplementary material The online version of this article (doi:10.1007/s10928-015-9414-4) contains supplementary material, which is available to authorized users.

Modeling and simulation (M&S) is increasingly used in drug development to characterize pharmacokinetic-pharmacodynamic (PKPD) relationships and support various efforts such as target feasibility assessment, molecule selection, human PK projection, and preclinical and clinical dose and schedule determination. While model development typically require mathematical modeling expertise, model exploration and simulations could in many cases be performed by scientists in various disciplines to support the design, analysis and interpretation of experimental studies. To this end, we have developed a versatile graphical user interface (GUI) application to enable easy use of any model constructed in SimBiology® to execute various common PKPD analyses. The MATLAB®-based GUI application, called gPKPDSim, has a single screen interface and provides functionalities including simulation, data fitting (parameter estimation), population simulation (exploring the impact of parameter variability on the outputs of interest), and non-compartmental PK analysis. Further, gPKPDSim is a user-friendly tool with capabilities including interactive visualization, exporting of results and generation of presentation-ready figures. gPKPDSim was designed primarily for use in preclinical and translational drug development, although broader applications exist. gPKPDSim is a MATLAB®-based open-source application and is publicly available to download from MATLAB® Central™. We illustrate the use and features of gPKPDSim using multiple PKPD models to demonstrate the wide applications of this tool in pharmaceutical sciences. Overall, gPKPDSim provides an integrated, multi-purpose user-friendly GUI application to enable efficient use of PKPD models by scientists from various disciplines, regardless of their modeling expertise. Electronic supplementary material The online version of this article (10.1007/s10928-017-9562-9) contains supplementary material, which is available to authorized users.

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

The purpose of this study was to develop a whole-body physiologically based pharmacokinetic (WB-PBPK) model for ciprofloxacin for ICU patients, based on only plasma concentration data. In a next step, tissue and organ concentration time profiles in patients were predicted using the developed model. The WB-PBPK model was built using a non-linear mixed effects approach based on data from 102 adult intensive care unit patients. Tissue to plasma distribution coefficients (Kp) were available from the literature and used as informative priors. The developed WB-PBPK model successfully characterized both the typical trends and variability of the available ciprofloxacin plasma concentration data. The WB-PBPK model was thereafter combined with a pharmacokinetic–pharmacodynamic (PKPD) model, developed based on in vitro time-kill data of ciprofloxacin and Escherichia coli to illustrate the potential of this type of approach to predict the time-course of bacterial killing at different sites of infection. The predicted unbound concentration–time profile in extracellular tissue was driving the bacterial killing in the PKPD model and the rate and extent of take-over of mutant bacteria in different tissues were explored. The bacterial killing was predicted to be most efficient in lung and kidney, which correspond well to ciprofloxacin’s indications pneumonia and urinary tract infections. Furthermore, a function based on available information on bacterial killing by the immune system in vivo was incorporated. This work demonstrates the development and application of a WB-PBPK–PD model to compare killing of bacteria with different antibiotic susceptibility, of value for drug development and the optimal use of antibiotics . Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9486-9) contains supplementary material, which is available to authorized users.

Current toxicity protocols relate measures of systemic exposure (i.e. AUC, Cmax) as obtained by non-compartmental analysis to observed toxicity. A complicating factor in this practice is the potential bias in the estimates defining safe drug exposure. Moreover, it prevents the assessment of variability. The objective of the current investigation was therefore (a) to demonstrate the feasibility of applying nonlinear mixed effects modelling for the evaluation of toxicokinetics and (b) to assess the bias and accuracy in summary measures of systemic exposure for each method. Here, simulation scenarios were evaluated, which mimic toxicology protocols in rodents. To ensure differences in pharmacokinetic properties are accounted for, hypothetical drugs with varying disposition properties were considered. Data analysis was performed using non-compartmental methods and nonlinear mixed effects modelling. Exposure levels were expressed as area under the concentration versus time curve (AUC), peak concentrations (Cmax) and time above a predefined threshold (TAT). Results were then compared with the reference values to assess the bias and precision of parameter estimates. Higher accuracy and precision were observed for model-based estimates (i.e. AUC, Cmax and TAT), irrespective of group or treatment duration, as compared with non-compartmental analysis. Despite the focus of guidelines on establishing safety thresholds for the evaluation of new molecules in humans, current methods neglect uncertainty, lack of precision and bias in parameter estimates. The use of nonlinear mixed effects modelling for the analysis of toxicokinetics provides insight into variability and should be considered for predicting safe exposure in humans. Electronic supplementary material The online version of this article (doi:10.1007/s10928-015-9413-5) contains supplementary material, which is available to authorized users.

A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q1 = 4.9 % and q3 = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data. Electronic supplementary material The online version of this article (doi:10.1007/s10928-012-9258-0) contains supplementary material, which is available to authorized users.

PF-05231023, a long-acting FGF21 analogue, is a promising potential pharmacotherapy for the treatment of obesity and associated comorbidities. Previous studies have shown the potential of FGF21 and FGF21-like compounds to decrease body weight in mice, non-human primates, and humans; the precise mechanisms of action remain unclear. In particular, there have been conflicting reports on the degree to which FGF21-induced weight loss in non-human primates is attributable to a decrease in food intake versus an increase in energy expenditure. Here, we present a semi-mechanistic mathematical model of energy balance and body composition developed from similar work in mice. This model links PF-05231023 administration and washout to changes in food intake, which in turn drives changes in body weight. The model is calibrated to and compared with recently published data from cynomolgus macaques treated with PF-05231023, demonstrating its accuracy in describing pharmacotherapy-induced weight loss in these animals. The results are consistent with the hypothesis that PF-05231023 decreases body weight in cynomolgus macaques solely by a reduction in food intake, with no direct effect on energy expenditure.