Training the next generation of pharmacometric modelers: a multisector perspective.

The current demand for pharmacometricians outmatches the supply provided by academic institutions and considerable investments are made to develop the competencies of these scientists on-the-job. Even with the observed increase in academic programs related to pharmacometrics, this need is unlikely to change in the foreseeable future, as the demand and scope of pharmacometrics applications keep expanding. Further, the field of pharmacometrics is changing. The field largely started when Lewis Sheiner and Stuart Beal published their seminal papers on population pharmacokinetics in the late 1970's and early 1980's and has continued to grow in impact and use since its inception. Physiological-based pharmacokinetics and systems pharmacology have grown rapidly in scope and impact in the last decade and machine learning is just on the horizon. While all these methodologies are categorized as pharmacometrics, no one person can be an expert in everything. So how do you train future pharmacometricians? Leading experts in academia, industry, contract research organizations, clinical medicine, and regulatory gave their opinions on how to best train future pharmacometricians. Their opinions were collected and synthesized to create some general recommendations.

A Model-Informed Drug Development (MIDD) Approach for a Low Dose of Empagliflozin in Patients with Type 1 Diabetes.

In clinical trials, sodium-glucose co-transporter (SGLT) inhibitor use as adjunct to insulin therapy in type 1 diabetes (T1D) provides glucometabolic benefits while diabetic ketoacidosis risk is increased. The SGLT2 inhibitor empagliflozin was evaluated in two phase III trials: EASE-2 and EASE-3. A low, 2.5-mg dose was included in EASE-3 only. As the efficacy of higher empagliflozin doses (i.e., 10 and 25 mg) in T1D has been established in EASE-2 and EASE-3, a modeling and simulation approach was used to generate additional supportive evidence on efficacy for the 2.5-mg dose. We present the methodology behind the development and validation of two modeling and simulation frameworks: M-EASE-1, a semi-mechanistic model integrating information on insulin, glucose, and glycated hemoglobin; and M-EASE-2, a descriptive model informed by prior information. Both models were developed independently of data from EASE-3. Simulations based on these models assessed efficacy in untested clinical trial scenarios. In this manner, the models provide supportive evidence for efficacy of low-dose empagliflozin 2.5 mg in patients with T1D, illustrating how pharmacometric analyses can support efficacy assessments in the context of limited data.

Quantification of the Impact of Partition Coefficient Prediction Methods on Physiologically Based Pharmacokinetic Model Output Using a Standardized Tissue Composition.

Tissue:plasma partition coefficients are key parameters in physiologically based pharmacokinetic (PBPK) models, yet the coefficients are challenging to measure in vivo. Several mechanistic-based equations have been developed to predict partition coefficients using tissue composition information and the compound's physicochemical properties, but it is not clear which, if any, of the methods is most appropriate under given circumstances. Complicating the evaluation, each prediction method was developed, and is typically employed, using a different set of tissue composition information, thereby making a controlled comparison impossible. This study proposed a standardized tissue composition for humans that can be used as a common input for each of the five frequently used prediction methods. These methods were implemented in R and were used to predict partition coefficients for 11 drugs, classified as strong bases, weak bases, acids, neutrals, and zwitterions. PBPK models developed in R (mrgsolve) for each drug and each set of partition coefficient predictions were compared with respective observed plasma concentration data. Percent root mean square error and half-life percent error were used to evaluate the accuracy of the PBPK model predictions using each partition coefficient method as summarized by strong bases, weak bases, acids, neutrals, and zwitterions characterization. The analysis indicated that no partition coefficient method consistently yielded the most accurate PBPK model predictions. As such, PBPK model predictions using all partition coefficient methods should be considered during drug development. SIGNIFICANCE STATEMENT: Several mechanistic-based methods exist to predict tissue:plasma partition coefficients critical to PBPK modeling. Controlled comparisons are confounded by the use of different tissue composition values for each method; a standardized tissue composition was proposed. Resulting assessments indicated that no method was consistently superior; therefore, sensitivity of PBPK predictions to each method may be warranted prior to model optimization.

Toward Progress in Quantitative Translational Medicine: A Call to Action.

Quantitative translational medicine (QTM) is envisioned as a multifaceted discipline that will galvanize the path from idea to medicine through quantitative translation across the discovery, development, regulatory, and utilization spectrum. Here, we summarize results of an American Society for Clinical Pharmacology and Therapeutics (ASCPT) survey on barriers relevant to the advancement of QTM and propose opportunities for its deployment. Importantly, we offer a call to action to break down these barriers through patient-centered stewardship, effective communication, cross-sector collaboration, and a modernized educational curriculum.

Low-dose empagliflozin as adjunct-to-insulin therapy in type 1 diabetes: A valid modelling and simulation analysis to confirm efficacy.

AIM: To confirm the observed reduction in HbA1c for the 2.5 mg dose in EASE-3 by modelling and simulation analyses. MATERIALS AND METHODS: Independent of data from EASE-3 that tested 2.5 mg, we simulated the effect of a 2.5 mg dose through patient-level, exposure-response modelling in the EASE-2 clinical study. A primary semi-mechanistic model evaluated efficacy considering clinical insulin dose adjustments made after treatment initiation that potentially limited HbA1c reductions. The model was informed by pharmacokinetic, insulin dose, mean daily glucose and HbA1c data, and was verified by comparing the simulations with the observed HbA1c change in EASE-3. One of two empagliflozin phase 3 trials in type 1 diabetes (EASE-3 but not EASE-2) included a lower 2.5 mg dose. A placebo-corrected HbA1c reduction of 0.28% was demonstrated without the increased risk of diabetic ketoacidosis observed at higher doses (10 mg and 25 mg). Since only one trial included the lower dose, we aimed to confirm the observed reduction in HbA1c for the 2.5 mg dose by modelling and simulation analyses. RESULTS: The simulated 26-week mean HbA1c change was -0.41% without insulin dose adjustment and -0.29% at 26 weeks with insulin dose adjustment. A simplified (descriptive) model excluding insulin dose and mean daily glucose confirmed the -0.29% HbA1c change that would have been observed had the EASE-2 population received a 2.5 mg dose for 26/52 weeks. CONCLUSIONS: The HbA1c benefit of low-dose empagliflozin directly observed in the EASE-3 trial was confirmed by two modelling and simulation approaches.

Quantitative Systems Pharmacology and Physiologically-Based Pharmacokinetic Modeling With mrgsolve: A Hands-On Tutorial.

mrgsolve is an open-source R package available on the Comprehensive R Archive Network. It combines R and C++ coding for simulation from hierarchical, ordinary differential equation-based models. Its efficient simulation engine and integration into a parallelizable, R-based workflow makes mrgsolve a convenient tool both for simple and complex models and thus is ideal for physiologically-based pharmacokinetic (PBPK) and quantitative systems pharmacology (QSP) model. This tutorial will first introduce the basics of the mrgsolve simulation workflow, including model specification, the introduction of interventions (dosing events) into the simulation, and simulated results postprocessing. An applied simulation example is then presented using a PBPK model for voriconazole, including a model validation step against adult and pediatric data sets. A final simulation example is then presented using a previously published QSP model for mitogen-activated protein kinase signaling in colorectal cancer, illustrating population simulation of different combination therapies.

Pharmacometrics and systems pharmacology for metabolic bone diseases.

Mathematical modelling and simulation (M&S) of drug concentrations, pharmacologic effects and the (patho)physiologic systems within which they interact can be powerful tools for the preclinical, translational and clinical development of drugs. Indeed, the Prescription Drug User Fee Act (PDUFA VI), incorporated as part of the FDA Reauthorization Act of 2017 (FDARA), highlights the goal of advancing model-informed drug development (MIDD). MIDD can benefit development across many drug classes, including for metabolic bone diseases such as osteoporosis, cancer-related and numerous rare metabolic bone diseases; conditions characterized by significant morbidity and mortality. A drought looms in terms of the availability of new drugs to better treat these devastating diseases. This review provides an overview of several M&S approaches ranging from simple pharmacokinetic to integrated pharmacometric and systems pharmacology modelling. Examples are included to illustrate the use of these approaches during the development of several drugs for metabolic bone diseases such as bisphosphonates, denosumab, teriparatide and sclerostin inhibitors (romosozumab and blosozumab).

A model of fracture risk used to examine the link between bone mineral density and the impact of different therapeutic mechanisms on fracture outcomes in patients with osteoporosis.

A hazard model of fracture was developed using individual patient data (IPD) from the NHANES (2005-2008) database and summary-level data from an aggregate dataset (AD). The AD was built by performing a comprehensive and systematic literature search of clinical studies published from 1995 to 2015, recording fracture rate and bone mineral density (BMD) for both treatment and placebo arms. The search resulted in a metadata set comprised of 21 studies investigating the effects of various bisphosphonates, teriparatide, denosumab, and raloxifene in 65,254 patients over a cumulative 56.75 years of study. The IPD was used to augment an AD in a model-based meta-analysis (MBMA) hierarchical modeling approach. The resulting model predicts the probability of fracture events in patients with osteoporosis. The object of model building using this approach was to promote understanding of the impact of therapeutic drug effects on the probability of fracture together with, or independent of their effects on BMD. Candidate models were evaluated by deviance information criteria and posterior predictive check. The model with covariates for lumbar spine BMD with interaction with a drug effect on BMD, and patient body mass index, years post-menopause, fracture measure method (clinical or radiological) and an additional drug effect outperformed those models without interaction and without additional drug effects. The model quantitatively supports the widely held notion that changes in bone microarchitecture, which cannot be measured by areal BMD elicited by therapy contribute in a significant way to a reduction in fracture. Furthermore, this model can be used to simulate fracture risk in a clinical cohort similar to those contained in the MBMA.

Model-based meta-analysis for comparing Vitamin D2 and D3 parent-metabolite pharmacokinetics.

Association of Vitamin D (D3 & D2) and its 25OHD metabolite (25OHD3 & 25OHD2) exposures with various diseases is an active research area. D3 and D2 dose-equivalency and each form's ability to raise 25OHD concentrations are not well-defined. The current work describes a population pharmacokinetic (PK) model for D2 and 25OHD2 and the use of a previously developed D3-25OHD3 PK model [1] for comparing D3 and D2-related exposures. Public-source D2 and 25OHD2 PK data in healthy or osteoporotic populations, including 17 studies representing 278 individuals (15 individual-level and 18 arm-level units), were selected using search criteria in PUBMED. Data included oral, single and multiple D2 doses (400-100,000 IU/d). Nonlinear mixed effects models were developed simultaneously for D2 and 25OHD2 PK (NONMEM v7.2) by considering 1- and 2-compartment models with linear or nonlinear clearance. Unit-level random effects and residual errors were weighted by arm sample size. Model simulations compared 25OHD exposures, following repeated D2 and D3 oral administration across typical dosing and baseline ranges. D2 parent and metabolite were each described by 2-compartment models with numerous parameter estimates shared with the D3-25OHD3 model [1]. Notably, parent D2 was eliminated (converted to 25OHD) through a first-order clearance whereas the previously published D3 model [1] included a saturable non-linear clearance. Similar to 25OHD3 PK model results [1], 25OHD2 was eliminated by a first-order clearance, which was almost twice as fast as the former. Simulations at lower baselines, following lower equivalent doses, indicated that D3 was more effective than D2 at raising 25OHD concentrations. Due to saturation of D3 clearance, however, at higher doses or baselines, the probability of D2 surpassing D3's ability to raise 25OHD concentrations increased substantially. Since 25OHD concentrations generally surpassed 75 nmol/L at these higher baselines by 3 months, there would be no expected clinical difference in the two forms.

Model-based meta-analysis for development of a population-pharmacokinetic (PPK) model for Vitamin D3 and its 25OHD3 metabolite using both individual and arm-level data.

Clinical studies investigating relationships between D3 and 25OHD3 vary in dosing regimen, assays, demographics, and control of exogenous D3. This leads to uncertain and conflicting exposure-related associations with D3 and 25OHD3. To elucidate this parent-metabolite system, a PPK model was developed to predict mean D3 and 25OHD3 exposure from varied doses and administration routes. Sources of exposure variability related to metabolite baseline, weight, and assay type were explored. Specific search criteria were used in PUBMED to identify public source PK data pertaining to D3 and 25OHD3 in healthy or osteoporotic populations. Overall 57 studies representing 5395 individuals were selected, including 25 individual-level profiles and treatment-arm data. IV, oral, single and multiple dose data were used, with D3 and 25OHD3 dosing. A nonlinear mixed effects model was developed to simultaneously model PK dispositions of D3 and 25OHD3 (NONMEM v7.2), which were described by 2-compartment models with nonlinear and linear clearances, respectively. Proportional and additive assay variances were included on the 25OHD3 prediction. Unit-level random effects were weighted by treatment-arm size. D3 model estimates, relative to bioavailability were: maximum rate of metabolism ([Formula: see text], 1.62 nmol/h), Michaelis-Menten constant ([Formula: see text], 6.39 nmol/L), central volume of distribution ([Formula: see text], 15.5 L), intercompartmental clearance ([Formula: see text], 0.185 L/h), peripheral volume of distribution ([Formula: see text], 2333 L/h), and baseline concentration ([Formula: see text], 3.75 nmol/L). For 25OHD3 ([Formula: see text] = metabolite): [Formula: see text] = 0.0153 L/h, [Formula: see text] = 4.35 L, [Formula: see text] = 6.87 L, [Formula: see text] = 0.0507 L/h. Simulations of 25OHD3 concentration indicated an inverse relationship between 25OHD3 baseline and response, as well as a less than proportional 25OHD3 response. Estimation of assay bias parameters suggested that HPLC-MS and RIA produced similar measurement results, whereas CPBA and CHEMI are over-predictive of 25OHD3 concentration, relative to HPLC-MS.

A Priori Identifiability of Target-Mediated Drug Disposition Models and Approximations.

A priori identifiability of mathematical models assures that for a given input/output experiment, the parameter set has one unique solution within a defined space, independent of the experimental design. Many biologic therapeutics exhibit target-mediated drug disposition (TMDD), and use of the full compartmental model describing this system is well documented. In practice, estimation of the full parameter set for TMDD models, given real-world clinical data, is characterized by convergence difficulties and unstable solutions. Still, the formal assessment of the a priori identifiability of these systems has yet to be reported. The exact arithmetic rank (EAR) approach was used to test the a priori identifiability of a TMDD model as well as model approximations. The full TMDD and quasi-equilibrium/rapid binding (QE/RB), quasi-steady state (QSS), and Michaelis-Menten (MM) approximations were fully identifiable, a priori, regardless of whether observations were taken from a single or multiple compartments. The results of these identifiability analyses indicated that the difficulty with TMDD model convergence, a posteriori, lies in the experimental design, not in the mathematical identifiability in the lack of samples from several compartments. Experiments can be tailored to resolve these structurally non-identifiable parameters, notwithstanding practical implementation challenges. This work highlights the importance of identifiability analyses, specifically how they can influence experimental design and selection of the appropriate model structure to describe a dynamic biological system.

Exposure-response modelling for empagliflozin, a sodium glucose cotransporter 2 (SGLT2) inhibitor, in patients with type 2 diabetes.

AIMS: To provide model-based clinical development decision support including dose selection guidance for empagliflozin, an orally administered sodium glucose cotransporter 2 inhibitor, through developed exposure-response (E-R) models for efficacy and tolerability in patients with type 2 diabetes mellitus (T2DM). METHODS: Five randomized, placebo-controlled, multiple oral dose studies of empagliflozin in patients with T2DM (n = 974; 1-100 mg once daily, duration ≤12 weeks) were used to develop E-R models for efficacy (glycosylated haemoglobin [HbA1c ], fasting plasma glucose [FPG] and urinary glucose excretion). Two studies (n = 748, 12 weeks) were used to evaluate tolerability E-R. RESULTS: The efficacy model predicted maximal decreases in FPG and HbA1c of 16% and 0.6%, respectively, assuming a baseline FPG concentration of 8 mm (144 mg dl(-1) ) and 10-25 mg every day empagliflozin targeted 80-90% of these maximums. Increases in exposure had no effect on incidence rates of hypoglycaemia (n = 4), urinary tract infection (n = 17) or genital/vulvovaginal-related (n = 16) events, although low prevalence rates may have precluded more accurate evaluation. CONCLUSIONS: E-R analyses indicated that 10 and 25 mg once daily empagliflozin doses achieved near maximal glucose lowering efficacy.

Population pharmacokinetics of empagliflozin, a sodium glucose cotransporter 2 inhibitor, in patients with type 2 diabetes.

Data from five randomized, placebo-controlled, multiple oral dose studies of empagliflozin in patients with type 2 diabetes mellitus (T2DM; N = 974; 1-100 mg q.d.; ≤12 weeks) were used to develop a population pharmacokinetic (PK) model for empagliflozin. The model consisted of two-compartmental disposition, lagged first-order absorption and first-order elimination, and incorporated appropriate covariates. Population estimates (interindividual variance, CV%) of oral apparent clearance, central and peripheral volumes of distribution, and inter-compartmental clearance were 9.87 L/h (26.9%), 3.02 L, 60.4 L (30.8%), and 5.16 L/h, respectively. An imposed allometric weight effect was the most influential PK covariate effect, with a maximum effect on exposure of ±30%, using 2.5th and 97.5th percentiles of observed weights, relative to the median observed weight. Sex and race did not lend additional description to PK variability beyond allometric weight effects, other than ∼25% greater oral absorption rate constant for Asian patients. Age, total protein, and smoking/alcohol history did not affect PK parameters. Predictive check plots were consistent with observed data, implying an adequate description of empagliflozin PKs following multiple dosing in patients with T2DM. The lack of marked covariate effects, including weight, suggests that no exposure-based dose adjustments were required within the study population and dose range.

Facilitating pharmacometric workflow with the metrumrg package for R.

metrumrg is an R package that facilitates workflow for the discipline of pharmacometrics. Support is provided for data preparation, modeling, simulation, diagnostics, and reporting. Existing tools and techniques are emphasized where available; original solutions are provided for otherwise unmet needs. In particular, metrumrg implements an R interface for the NONMEM(®) modeling software, optionally run in a distributed computing environment. The paradigm allows start-to-finish analyses in a single scripting language. Emphasis on text-based formats promotes traceability of results.

Multiscale physiology-based modeling of mineral bone disorder in patients with impaired kidney function.

A physiologically based, multiscale model of calcium homeostasis and bone remodeling was used to describe the impact of progressive loss of kidney function over a typical 10-year course of chronic kidney disease (CKD), including the evolution of secondary hyperparathyroidism (HPT) caused by diminished renal phosphate clearance and increased plasma phosphate. An important sequela of HPT is marked elevations in bone resorption and loss of bone mineral density (BMD). Clinically, this CKD-related disease state is described as mineral bone disorder, or CKD-MBD. A multiscale physiologic model previously had been shown to describe CKD-MBD-related clinical changes in phosphate, parathyroid hormone (PTH), and calcitriol. The authors have extended the model to link bone remodeling markers with BMD elimination (0.000145 h(-1)) and formation rates. The composite model predicted lumbar spine BMD losses, relative to baseline, at months 28 (glomerular filtration rate = 58 mL/min), 50 (39 mL/min), and 120 (16 mL/min) of approximately -0.98%, -3.0%, and -6.5%, respectively, compared to the observed BMD values in corresponding renal function groups, scaled to a 100-mL/min baseline, of -0.5%, -4.0%, and -8.1%, respectively. In addition, simulated interventions with a hypothetical calcimimetic agent and calcitriol are provided to show the utility of this model as a platform for evaluating therapeutics.

Population pharmacokinetics and exposure-response of albinterferon alfa-2b.

Albinterferon alfa-2b (albIFN) has been studied for treatment of chronic hepatitis C virus (HCV). A population pharmacokinetics model was developed using nonlinear mixed-effects modeling. Efficacy/safety exposure-response relationships were assessed for subcutaneous albIFN doses (900-1800 µg once every 2 or 4 weeks) administered for either 24 weeks (HCV genotypes 2/3) or 48 weeks (genotype 1), plus daily oral ribavirin. Sustained virologic response (SVR) exposure-response was modeled using logistic regression. Adverse event incidence was tabulated versus exposure quartiles. First-order absorption rate constant (0.0148 h(-1)), apparent clearance (38.9 mL/h), and apparent volume of distribution (11.6 L) had interindividual variances (coefficient of variation) of 21%, 34%, and 24%, respectively. Residual variance estimates were 27% (coefficient of variation) and 1.51 ng/mL (standard deviation). For the only explanatory covariate-body weight-exposure decreased as weight increased. Important SVR predictors included baseline HCV RNA, fibrosis score, and black race (genotype 1); SVR was minimally related to exposure. Most adverse events had similar incidence rates across exposure quartiles. Some adverse events had a higher incidence in the upper exposure quartile without evidence of exposure-response across the lower quartiles. Given the lack of consistent efficacy/safety exposure-response relationships, further investigation is necessary to optimize albIFN dosing.

A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling.

Bone biology is physiologically complex and intimately linked to calcium homeostasis. The literature provides a wealth of qualitative and/or quantitative descriptions of cellular mechanisms, bone dynamics, associated organ dynamics, related disease sequela, and results of therapeutic interventions. We present a physiologically based mathematical model of integrated calcium homeostasis and bone biology constructed from literature data. The model includes relevant cellular aspects with major controlling mechanisms for bone remodeling and calcium homeostasis and appropriately describes a broad range of clinical and therapeutic conditions. These include changes in plasma parathyroid hormone (PTH), calcitriol, calcium and phosphate (PO4), and bone-remodeling markers as manifested by hypoparathyroidism and hyperparathyroidism, renal insufficiency, daily PTH 1-34 administration, and receptor activator of NF-kappaB ligand (RANKL) inhibition. This model highlights the utility of systems approaches to physiologic modeling in the bone field. The presented bone and calcium homeostasis model provides an integrated mathematical construct to conduct hypothesis testing of influential system aspects, to visualize elements of this complex endocrine system, and to continue to build upon iteratively with the results of ongoing scientific research.