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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.

A physiologically based model describing the dissolution, diffusion, and transfer of drug from the intra-articular (IA) space to the plasma, was developed for GastroPlus® v9.8. The model is subdivided into compartments representing the synovial fluid, synovium, and cartilage. The synovium is broken up into two sublayers. The intimal layer acts as a diffusion barrier between the synovial fluid and the subintimal layer. The subintimal layer of the synovium has fenestrated capillaries that allow the free drug to be transported into systemic circulation. The articular cartilage is broken up into 10 diffusion sublayers as it is much thicker than the synovium. The cartilage acts as a depot tissue for the drug to diffuse into from synovial fluid. At later times, the drug will diffuse from the cartilage back into synovial fluid once a portion of the dose enters systemic circulation. In this study, a listing of all relevant details and equations for the model is presented. Methotrexate was chosen as a case study to show the application and utility of the model, based on the availability of intravenous (IV), oral (PO) and IA administration data in patients presenting rheumatoid arthritis (RA) symptoms. Systemic disposition of methotrexate in RA patients was described by compartmental pharmacokinetic (PK) model with PK parameters extracted using the PKPlus™ module in GastroPlus®. The systemic PK parameters were validated by simulating PO administration of methotrexate before being used for simulation of IA administration. For methotrexate, the concentrations of drug in the synovial fluid and plasma were well described after adjustments of physiological parameters to account for RA disease state, and with certain assumptions about binding and diffusion. The results indicate that the model can correctly describe PK profiles resulting from administration in the IA space, however, additional cases studies will be required to evaluate ability of the model to scale between species and/or doses. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09781-w.

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.

Intravitreal (IVT) injection of pharmacological agents is an established and widely used procedure for the treatment of many posterior segment of the eye diseases. IVT injections permit drugs to reach high concentrations in the retina whilst limiting systemic exposure. Beyond the risk of secondary complications such as intraocular infection, the potential of systemic adverse events cannot be neglected. Therefore, a detailed understanding of the rules governing systemic exposure following IVT drug administration remains a prerequisite for the evaluation and development of new pharmacological agents intended for eye delivery. We present here a novel mathematical model to describe and predict circulating drug levels following IVT in the rabbit eye, a species which is widely used for drug delivery, pharmacokinetic, and pharmacodynamic studies. The mathematical expression was derived from a pharmacokinetic model that assumes the existence of a compartment between the vitreous humor compartment itself and the systemic compartment. We show that the model accurately describes circulating levels of THR-149, a plasma kallikrein inhibitor in development for the treatment of diabetic macular edema. We hypothesize that the model based on the rabbit eye has broader relevance to the human eye and can be used to analyze systemic exposure of a variety of drugs delivered in the eye.

Modeling of retrospectively collected multi-center data of a rare disease in pediatrics is challenging because laboratory data can stem from several decades measured with different assays. Here we present a retrospective pharmacometrics (PMX) based data analysis of the rare disease congenital hypothyroidism (CH) in newborns and infants. Our overall aim is to develop a model that can be applied to optimize dosing in this pediatric patient population since suboptimal treatment of CH during the first 2 years of life is associated with a reduced intelligence quotient between 10 and 14 years. The first goal is to describe a retrospectively collected dataset consisting of 61 newborns and infants with CH up to 2 years of age. Overall, 505 measurements of free thyroxine (FT4) and 510 measurements of thyrotropin or thyroid-stimulating hormone were available from patients receiving substitution treatment with levothyroxine (LT4). The second goal is to introduce a scale/location-scale normalization method to merge available FT4 measurements since 34 different postnatal age- and assay-specific laboratory reference ranges were applied. This method takes into account the change of the distribution of FT4 values over time, i.e. a transformation from right-skewed towards normality during LT4 treatment. The third goal is to develop a practical and useful PMX model for LT4 treatment to characterize FT4 measurements, which is applicable within a clinical setting. In summary, a time-dependent normalization method and a practical PMX model are presented. Since there is no on-going or planned development of new pharmacological approaches for CH, PMX based modeling and simulation can be leveraged to personalize dosing with the goal to enhance longer-term neurological outcome in children with the rare disease CH. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09765-w.

Optimization of antibiotic administration helps minimizing cases of bacterial resistance. Dosages are often selected by trial and error using a pharmacokinetic (PK) model. However, this is limited to the range of tested dosages, restraining possible treatment choices, especially for the loading doses. Colistin is a last-resort antibiotic with a narrow therapeutic window; therefore, its administration should avoid subtherapeutic or toxic concentrations. This study formulates an optimal control problem for dosage selection of colistin based on a PK model, minimizing deviations of colistin concentration to a target value and allowing a specific dosage optimization for a given individual. An adjoint model was used to provide the sensitivity of concentration deviations to dose changes. A three-compartment PK model was adopted. The standard deviation between colistin plasma concentrations and a target set at 2 mg/L was minimized for some chosen treatments and sample patients. Significantly lower deviations from the target concentration are obtained for shorter administration intervals (e.g. every 8 h) compared to longer ones (e.g. every 24 h). For patients with normal or altered renal function, the optimal loading dose regimen should be divided into two or more administrations to attain the target concentration quickly, with a high first loading dose followed by much lower ones. This regimen is not easily obtained by trial and error, highlighting advantages of the method. The present method is a refined optimization of antibiotic dosage for the treatment of infections. Results for colistin suggest significant improvement in treatment avoiding subtherapeutic or toxic concentrations.

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.

Cemiplimab, a human monoclonal antibody targeting programmed cell death-1 (PD-1) receptor, demonstrated antitumor activity in patients with advanced malignancies and a safety profile comparable to other anti–PD-1 therapies. This population pharmacokinetics (PopPK) analysis of cemiplimab included 11,178 pharmacokinetics (PK) observations from 548 patients pooled from a first-in-human study (Study 1423; NCT02383212) in advanced malignancies and a Phase 2 study (Study 1540; NCT02760498) in advanced cutaneous squamous cell carcinoma (CSCC). Most patients (80.3%) received cemiplimab 3 mg/kg every 2 weeks (Q2W) intravenously (IV). A PopPK model was developed by evaluating two-compartment linear models with an empirical non-linear function describing time-varying change in cemiplimab clearance and covariates that improved goodness-of-fit. PopPK simulations were used to describe cemiplimab exposure generated by a fixed 350 mg every 3 weeks (Q3W) IV dose regimen. PopPK modeling showed that a two-compartment model with zero-order IV infusion rate and first-order elimination rate well described individual concentrations of cemiplimab. Although several covariates, including baseline body weight and albumin concentrations, had a modest impact on cemiplimab exposure, the magnitude of influence was within the typical observed PK variability of approximately 30%. Based on PopPK simulation results, the 350 mg Q3W dose regimen was selected for further studies in advanced malignancies, including advanced CSCC. Similarity in observed cemiplimab exposure at the fixed 350 mg Q3W and the weight-based 3 mg/kg Q2W dose regimens confirmed this fixed dose selection. A robust PopPK model was developed to describe cemiplimab concentrations and supported use of the fixed 350 mg Q3W IV dose regimen. Supplementary Information The online version of this article (10.1007/s10928-021-09739-y) contains supplementary material, which is available to authorized users.

Verinurad, a uric acid transporter 1 (URAT1) inhibitor, lowers serum uric acid by promoting its urinary excretion. Co-administration with a xanthine oxidase inhibitor (XOI) to simultaneously reduce uric acid production rate reduces the potential for renal tubular precipitation of uric acid, which can lead to acute kidney injury. The combination is currently in development for chronic kidney disease and heart failure. The aim of this work was to apply and extend a previously developed semi-mechanistic exposure–response model for uric acid kinetics to include between-subject variability to verinurad and its combinations with XOIs, and to provide predictions to support future treatment strategies. The model was developed using data from 12 clinical studies from a total of 434 individuals, including healthy volunteers, patients with hyperuricemia, and renally impaired subjects. The model described the data well, taking into account the impact of various patient characteristics such as renal function, baseline fractional excretion of uric acid, and race. The potencies (EC50s) of verinurad (reducing uric acid reuptake), febuxostat (reducing uric acid production), and oxypurinol (reducing uric acid production) were: 29, 128, and 13,030 ng/mL, respectively. For verinurad, symptomatic hyperuricemic (gout) subjects showed a higher EC50 compared with healthy volunteers (37 ng/mL versus 29 ng/mL); while no significant difference was found for asymptomatic hyperuricemic patients. Simulations based on the uric acid model were performed to assess dose–response of verinurad in combination with XOI, and to investigate the impact of covariates. The simulations demonstrated application of the model to support dose selection for verinurad. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09747-y.

Population analysis of pharmacokinetic data for five differing dosage forms and routes for dexamethasone and betamethasone in 48 healthy nonpregnant Indian women was performed that accounted for 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). Plasma concentrations collected for two periods over 96 h were described with a two-compartment model with differing PO and IM first-order absorption inputs. Clearances and volumes were divided by the IM bioavailability $${F}_{IM}$$ F IM . The homogeneous ages, body weights, and ethnicity of the women obviated covariate analysis. Parameter estimates were obtained by the Laplace estimation method implemented in NONMEM 7.4. Typical values for dexamethasone were clearance ($${CL/F}_{IM})$$ C L / F IM ) of 9.29 L/h, steady-state volume ($${{V}_{ss}/F}_{IM})$$ V ss / F IM ) of 56.4 L, IM absorption constant $$\left({k}_{aIM}\right)$$ k aIM of 0.460 1/h and oral absorption constant ($${k}_{aPO})$$ k aPO ) of 0.936 1/h. Betamethasone parameters were CL/FIM of 5.95 L/h, $${Vss/F}_{IM}$$ V s s / F IM of 72.4 L, $${k}_{aIM}$$ k aIM of 0.971 1/h, and $${k}_{aPO}$$ k aPO of 1.21 1/h. The PO to IM F values were close to 1.0 for both drugs. The terminal half-lives averaged about 7.5 h for DEX, 17 h for BET, and 78 h for BET from BET-PA with the latter reflecting very slow release of BET from the acetate ester. Overall, BET exhibited slower clearance, larger volume of distribution, faster absorption, and longer persistence than DEX. These data may be useful in considering exposures when substituting one form of corticosteroid for another.

This article highlights some numerical challenges when implementing the bounded integer model for composite score modeling and suggests an improved implementation. The improvement is based on an approximation of the logarithm of the error function. After presenting the derivation of the improved implementation, the article compares the performance of the algorithm to a naive implementation of the log-likelihood using both simulations and a real data example. In the simulation setting, the improved algorithm yielded more precise and less biased parameter estimates when the within-subject variability was small and estimation was performed using the Laplace algorithm. The estimation results did not differ between implementations when the SAEM algorithm was used. For the real data example, bootstrap results differed between implementations with the improved implementation producing identical or better objective function values. Based on the findings in this article, the improved implementation is suggested as the new default log-likelihood implementation for the bounded integer model. Electronic supplementary material The online version of this article (10.1007/s10928-020-09727-8) contains supplementary material, which is available to authorized users.

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.

The role of artificial intelligence (AI) in healthcare for pregnant women. To assess the role of AI in women’s health, discover gaps, and discuss the future of AI in maternal health. A systematic review of English articles using EMBASE, PubMed, and SCOPUS. Search terms included pregnancy and AI. Research articles and book chapters were included, while conference papers, editorials and notes were excluded from the review. Included papers focused on pregnancy and AI methods, and pertained to pharmacologic interventions. We identified 376 distinct studies from our queries. A final set of 31 papers were included for the review. Included papers represented a variety of pregnancy concerns and multidisciplinary applications of AI. Few studies relate to pregnancy, AI, and pharmacologics and therefore, we review carefully those studies. External validation of models and techniques described in the studies is limited, impeding on generalizability of the studies. Our review describes how AI has been applied to address maternal health, throughout the pregnancy process: preconception, prenatal, perinatal, and postnatal health concerns. However, there is a lack of research applying AI methods to understand how pharmacologic treatments affect pregnancy. We identify three areas where AI methods could be used to improve our understanding of pharmacological effects of pregnancy, including: (a) obtaining sound and reliable data from clinical records (15 studies), (b) designing optimized animal experiments to validate specific hypotheses (1 study) to (c) implementing decision support systems that inform decision-making (11 studies). The largest literature gap that we identified is with regards to using AI methods to optimize translational studies between animals and humans for pregnancy-related drug exposures. Electronic supplementary material The online version of this article (10.1007/s10928-020-09685-1) contains supplementary material, which is available to authorized users.

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.

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The GPC, E2 and NC models were applied to a total of 148 serum samples drawn from 20 min to 72 h following bolus intravenous metformin in seven healthy mongrel dogs. 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The GPC models of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C yielded metformin \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values that were 84.8% of total renal plasma flow (RPF) as estimated from meta-analysis. The GPC \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values were significantly less than the corresponding NC and E2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values of 104.7% and 123.7% of RPF, respectively. The GPC plasma/serum only model predicted 78.9% drug \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M average urinary recovery at 72 h; similar to prior human urine drug \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M collection results. The GPC model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd, were asymptotically proportional to elapsed time, with a constant limiting \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 ratio of M/C averaging 7.0 times, a result in keeping with prior simultaneous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C and urine \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M collection studies and exhibiting a rate of apparent volume growth of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 with elapsing time, effects that have been observed experimentally during same-dose multidosing. The GPC heavy-tailed models explained multiple documented phenomena that were unexplained with lighter-tailed models. Electronic supplementary material The online version of this article (10.1007/s10928-019-09666-z) contains supplementary material, which is available to authorized users.

Graphic abstract Lack of data is an obvious limitation to what can be modelled. However, aggregate data in the form of means and possibly (co)variances, as well as previously published pharmacometric models, are often available. Being able to use all available data is desirable, and therefore this paper will outline several methods for using aggregate data as the basis of parameter estimation. The presented methods can be used for estimation of parameters from aggregate data, and as a computationally efficient alternative for the stochastic simulation and estimation procedure. They also allow for population PK/PD optimal design in the case when the data-generating model is different from the data-analytic model, a scenario for which no solutions have previously been available. Mathematical analysis and computational results confirm that the aggregate-data FO algorithm converges to the same estimates as the individual-data FO and yields near-identical standard errors when used in optimal design. The aggregate-data MC algorithm will asymptotically converge to the exactly correct parameter estimates if the data-generating model is the same as the data-analytic model. The performance of the aggregate-data methods were also compared to stochastic simulations and estimations (SSEs) when the data-generating model is different from the data-analytic model. The aggregate-data FO optimal design correctly predicted the sampling distributions of 200 models fitted to simulated datasets with the individual-data FO method. Supplementary Information The online version contains supplementary material available at 10.1007/s10928-021-09760-1.

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.

Population model-based (pharmacometric) approaches are widely used for the analyses of phase IIb clinical trial data to increase the accuracy of the dose selection for phase III clinical trials. On the other hand, if the analysis is based on one selected model, model selection bias can potentially spoil the accuracy of the dose selection process. In this paper, four methods that assume a number of pre-defined model structure candidates, for example a set of dose–response shape functions, and then combine or select those candidate models are introduced. The key hypothesis is that by combining both model structure uncertainty and model parameter uncertainty using these methodologies, we can make a more robust model based dose selection decision at the end of a phase IIb clinical trial. These methods are investigated using realistic simulation studies based on the study protocol of an actual phase IIb trial for an oral asthma drug candidate (AZD1981). Based on the simulation study, it is demonstrated that a bootstrap model selection method properly avoids model selection bias and in most cases increases the accuracy of the end of phase IIb decision. Thus, we recommend using this bootstrap model selection method when conducting population model-based decision-making at the end of phase IIb clinical trials. Electronic supplementary material The online version of this article (doi:10.1007/s10928-017-9550-0) 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.

Chronic obstructive pulmonary disease (COPD) is a chronic obstructive disease of the airways. An exacerbation of COPD is defined as shortness of breath, cough, and sputum production. New therapies for COPD exacerbations are examined in clinical trials frequently based on the number of exacerbations that implies long-term study due to the high variability in occurrence and duration of the events. In this work, we expanded the two-state model developed by Cook et al. where the patient transits from an asymptomatic (state 1) to a symptomatic state (state 2) and vice versa, through investigating different semi-Markov models in a Bayesian context using data from actual clinical trials. Of the four models tested, the log-logistic model was shown to adequately characterize the duration and number of COPD exacerbations. The patient disease stage was found a significant covariate with an effect of accelerating the transition from asymptomatic to symptomatic state. In addition, the best dropout model (log-logistic) was incorporated in the final two-state model to describe the dropout mechanism. Simulation based diagnostics such as posterior predictive check (PPC) and visual predictive check (VPC) were used to assess the behaviour of the model. The final model was applied in three clinical trial data to investigate its ability to detect the drug effect: the drug effect was captured in all three datasets and in both directions (from state 1 to state 2 and vice versa). A practical design investigation was also carried out and showed the limits of reducing the number of subjects and study length on the drug effect identification. Finally, clinical trial simulation confirmed that the model can potentially be used to predict medium term (6–12 months) clinical trial outcome using the first 3 months data, but at the expense of showing a non-significant drug effect. Electronic supplementary material The online version of this article (10.1007/s10928-019-09643-6) contains supplementary material, which is available to authorized users.

Fanhdi/Alphanate is a plasma derived factor VIII concentrate used for treating hemophilia A, for which there has not been any dedicated model describing its pharmacokinetics (PK). A population PK model was developed using data extracted from the Web-Accessible Population Pharmacokinetic Service-Hemophilia (WAPPS-Hemo) project. WAPPS-Hemo provided individual PK profiles for hemophilia patients using sparse observations as provided in routine clinical care by hemophilia centers. Plasma factor activity measurements and covariate data from hemophilia A patients on Fanhdi/Alphanate were extracted from the WAPPS-Hemo database. A population PK model was developed using NONMEM and evaluated for suitability for Bayesian forecasting using prediction-corrected visual predictive check (pcVPC), cross validation, limited sampling analysis and external evaluation against a population PK model developed on rich sampling data. Plasma factor activity measurements from 92 patients from 12 centers were used to derive the model. The PK was best described by a 2-compartment model including between subject variability on clearance and central volume, fat free mass as a covariate on clearance, central and peripheral volumes, and age as covariate on clearance. Evaluations showed that the developed population PK model could predict the PK parameters of new individuals based on limited sampling analysis and cross and external evaluations with acceptable precision and bias. This study shows the feasibility of using real-world data for the development of a population PK model. Evaluation and comparison of the model for Bayesian forecasting resulted in similar results as a model developed using rich sampling data. Electronic supplementary material The online version of this article (10.1007/s10928-019-09637-4) 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.

Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. These fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research combines adaptive chaos synchronization and grid search to estimate physiological and pharmacological systems with emergent properties by exploring deterministic methods that are more appropriate and have potentially superior performance than classical numerical approaches, which minimize the sum of squares or maximize the likelihood. We illustrate these issues with an established model of cortisol in human with nonlinear dynamics. The model describes cortisol kinetics over time, including its chaotic oscillations, by a delay differential equation. We demonstrate that chaos synchronization helps to avoid the tendency of the gradient-based optimization algorithms to end up in a local minimum. The subsequent analysis illustrates that the hybrid adaptive chaos synchronization for estimation of linear parameters with coarse-to-fine grid search for optimal values of non-linear parameters can be applied iteratively to accurately estimate parameters and effectively track trajectories for a wide class of noisy chaotic systems. Electronic supplementary material The online version of this article (10.1007/s10928-019-09629-4) contains supplementary material, which is available to authorized users.

This population pharmacokinetics analysis evaluated the target-mediated drug disposition of inotuzumab ozogamicin (InO) through an empirical time-dependent clearance (CLt) term and identified potential covariates that may be important predictors of variability in InO distribution and elimination. This analysis was conducted by pooling data from 2 studies of single-agent InO in patients with relapsed or refractory (R/R) B cell acute lymphoblastic leukemia (ALL), 3 studies of single-agent InO, 5 studies of InO plus rituximab (R-InO), and 1 study of R-InO plus chemotherapy in patients with R/R B-cell non-Hodgkin lymphoma (NHL). Pharmacokinetic data included 8361 InO concentration–time observations that were modeled using nonlinear mixed-effects analysis. Covariate relations were identified using generalized additive modeling on base model parameters and then tested in a stepwise manner via covariate modeling. InO concentration was described with a 2-compartment model with linear and time-dependent clearance components. Based on the final model, baseline body surface area was a covariate of the linear and time-dependent clearance components and volume of distribution in the central compartment; baseline percentage of blasts in the peripheral blood was a covariate of the decay coefficient of the time-dependent clearance term (CLt); and concomitant rituximab treatment was a covariate of the linear clearance component (CL1). The magnitude of change of each pharmacokinetic parameter due to these covariates was not considered clinically relevant. Therefore, no dose adjustment of InO for the treatment of patients with R/R B-cell ALL or NHL is needed on the basis of selected covariates. Electronic supplementary material The online version of this article (10.1007/s10928-018-9614-9) 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 World Health Organization recommends exclusive breastfeeding (EBF) for the first 6 months after birth. The deuterium oxide dose-to-the-mother (DTM) technique is used to distinguish EBF based on a cut-off (

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.

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery. Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9467-z) contains supplementary material, which is available to authorized users.

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.

Ulcerative Colitis (UC) is an inflammatory bowel disease typically affecting the colon. Patients with active UC have elevated tumor necrosis factor (TNF) concentrations in serum and colonic tissue. Infliximab is a monoclonal antibody directed against TNF and binds with high affinity. Target-mediated drug disposition (TMDD) is reported for monoclonal antibodies meaning that their pharmacokinetics are affected by high target affinity. Here, a TMDD model is proposed to describe the interaction between infliximab and TNF in UC patients. Data from 20 patients with moderate to severe UC was used. Patients received standard infliximab induction therapy (5 mg kg−1) at week 0, followed by infusions at week 2 and 6. IFX, anti-drug antibodies and TNF serum concentrations were measured at day 0 (1 h after infusion), 1, 4, 7, 11, 14, 18, 21, 28 and 42. A binding model, TMDD model, and a quasi-steady state (QSS) approximation were evaluated using nonlinear mixed effects modeling (NONMEM). A two-compartment model best described the concentration–time profiles of infliximab. Typical clearance of infliximab was 0.404 L day−1 and increased with the presence of anti-drug antibodies and with lower albumin concentrations. The TMDD-QSS model best described the pharmacokinetic and pharmacodynamics data. Estimate for TNF baseline (Bmax was 19.8 pg mL−1 and the dissociation constant (Kss) was 13.6 nM. This model could eventually be used to investigate the relationship between suppression of TNF and the response to IFX therapy. Electronic supplementary material The online version of this article (10.1007/s10928-019-09652-5) contains supplementary material, which is available to authorized users.

Modeling and simulations were used to support body weight-based dose selection for eslicarbazepine acetate (ESL) in pediatric subjects aged 4–17 years with partial-onset seizures. A one-compartment pediatric population pharmacokinetic model with formulation-specific first-order absorption, first-order elimination, and weight-based allometric scaling of clearance and distribution volume was developed with PK data from subjects 2–18 years of age treated with ESL 5–30 mg/kg/day. Covariate analysis was performed to quantify the effects of key demographic and clinical covariates (including body weight and concomitant use of carbamazepine, levetiracetam, and phenobarbital-like antiepileptic drugs [AEDs]) on variability in PK parameters. Model evaluation performed using a simulation-based visual predictive check and a non-parametric bootstrap procedure indicated no substantial bias in the overall model and in the accuracy of estimates. The model estimated that concomitant use of carbamazepine or phenobarbital-like AEDs with ESL would decrease the exposure of eslicarbazepine, and that concomitant use of levetiracetam with ESL would increase the exposure of eslicarbazepine, although the small effect of levetiracetam may not represent a true difference. Model-based simulations were subsequently performed to apply target exposure matching of selected ESL doses for pediatric subjects (aged 4–17 years) to attain eslicarbazepine exposures associated with effective and well-tolerated ESL doses in adults. Overall, model-based exposure matching allowed for extrapolation of efficacy to support pediatric dose selection as part of the submission to obtain FDA approval for ESL (adjunctive therapy and monotherapy) in subjects aged 4–17 years, without requiring an additional clinical study.

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.

Evolocumab, a novel human monoclonal antibody, inhibits proprotein convertase subtilisin/kexin type 9, a protein that targets low-density lipoprotein-cholesterol (LDL-C) receptors for the treatment of hyperlipidemia. The primary objective of this analysis was to characterize the population pharmacokinetics (popPK) and exposure–response relationship of evolocumab to assess if dose adjustment is needed across differing patient populations. Data were pooled for 5474 patients in 11 clinical studies who received evolocumab doses of 7–420 mg at various frequencies, either intravenously or subcutaneously. Evolocumab area under concentration–time curve from 8 to 12 weeks (AUCwk8–12) was simulated for individuals using the popPK model and was used to predict the LDL-C response in relation to AUCwk8–12. Evolocumab was eliminated through nonspecific (linear) and target-mediated (nonlinear) clearance. PopPK parameters and associated variabilities of evolocumab were similar to those of other monoclonal antibodies. The exposure–response model predicted a maximal 66% reduction in LDL-C from baseline to the mean of weeks 10 and 12 for doses of evolocumab 140 mg subcutaneously every 2 weeks or 420 mg subcutaneously once monthly. After inclusion of statistically significant covariates in an uncertainty-based simulation, LDL-C reduction from baseline at the mean of weeks 10 and 12 was predicted to be within 74% to 126% of the reference patient for all simulated patient groups. Evolocumab had nonlinear pharmacokinetics. The range of responses based on intrinsic and extrinsic factors was not predicted to be sufficiently different from the reference patient to warrant evolocumab dose adjustment.

Olopatadine is an antihistamine and mast cell stabilizer used for treating allergic conjunctivitis. Olopatadine 0.7% has been recently approved for daily dosing in the US, which supersedes the previously approved 0.2% strength. The objective of this analysis was to characterize patients who have better itching relief at 24 h when taking olopatadine 0.7% treatment instead of olopatadine 0.2% (in terms of proportions of responses) and relate this to the severity of baseline itching as an indirect metric of a patient’s sensitivity to antihistamines. A differential odds model was developed using data from two conjunctival allergen challenge (CAC) studies to characterize individual-level and population-level response to ocular itching following olopatadine treatment and the data was analyzed retrospectively. This modeling analysis was designed to predict 24 h ocular itching scores and to quantify the differences in 24 h itching relief following treatment with olopatadine 0.2% versus 0.7% in patients with moderate-to-high baseline itching. A one-compartment kinetic-pharmacodynamic Emax model was used to determine the effect of olopatadine. Impact of baseline itching severity, vehicle effect and the drug effect on the overall itching scores post-treatment were explicitly incorporated in the model. The model quantified trends observed in the clinical data with regards to both mean scores and the proportions of patients responding to olopatadine treatment. The model predicts a higher proportion of patients in the olopatadine 0.7% versus 0.2% group will experience relief within 24 h. This prediction was confirmed with retrospective clinical data analysis. The number of allergy patients relieved with olopatadine 0.7% increased with higher baseline itching severity scores, when compared to olopatadine 0.2%.

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.