Incorporation of stochastic variability in mechanistic population pharmacokinetic models: handling the physiological constraints using normal transformations

Employing zero-inflated beta distribution in an exposure-response analysis of TYK2/JAK1 inhibitor brepocitinib in patients with plaque psoriasis

Brepocitinib is an oral selective dual TYK2/JAK1 inhibitor and based on its cytokine inhibition profile is expected to provide therapeutic benefit in the treatment of plaque psoriasis. Efficacy data from a completed Phase 2a study in patients with moderate-to-severe plaque psoriasis were utilized to develop a population exposure-response model that can be employed to inform dose selection decisions for further clinical development. A modeling approach that employs the zero-inflated beta distribution was used to account for the bounded nature and distributional characteristics of the Psoriasis Area and Severity Index (PASI) score data. The developed exposure-response model provided an adequate description of the observed PASI scores across all the treatment arms tested and across both the induction and maintenance dosing periods of the study. In addition, the developed model exhibited a good predictive capacity with regard to the derived responder metrics (e.g., 75%/90%/100% improvement in PASI score [PASI75/90/100]). Clinical trial simulations indicated that the induction/maintenance dosing paradigm explored in this study does not offer any advantages from an efficacy perspective and that doses of 10, 30, and 60 mg once-daily may be suitable candidates for clinical evaluation in subsequent Phase 2b studies.

Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis

The aim of the study is to develop a population pharmacokinetic (PPK) model, of Octreotide long acting repeatable (LAR) formulation in healthy volunteers, which describes the highly variable, multiple peak absorption pattern of the pharmacokinetics of the drug, in individual and population levels. An empirical absorption model, coupled with a one-compartment distribution model with linear elimination was found to describe the data well. Absorption was modelled as a weighted sum of a first order and three transit compartment absorption processes, with delays and appropriately constrained model parameters. Identifiability analysis verified that all twelve parameters of the structural model are identifiable. A machine learning method, i.e., cluster analysis, was performed as pre-processing of the PK profiles, to define subpopulations, before PPK modelling. It revealed that 13% of the patients deviated considerably from the typical absorption pattern and allowed better characterization of the observed heterogeneity and variability of the study, while the approach may have wider applicability in building PPK models. The final model was evaluated by goodness of fit plots, Visual Predictive Check plots and bootstrap. The present model is the first to describe the multiple-peak absorption pattern observed after octreotide LAR administration and may be useful to provide insights and validate hypotheses regarding release from PLGA-based formulations.

A latent variable approach to account for correlated inputs in global sensitivity analysis

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.

Global Sensitivity Analysis of the Rodgers and Rowland Model for Prediction of Tissue: Plasma Partitioning Coefficients: Assessment of the Key Physiological and Physicochemical Factors That Determine Small-Molecule Tissue Distribution

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fu_p) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.

Accounting for inter-correlation between enzyme abundance: a simulation study to assess implications on global sensitivity analysis within physiologically-based pharmacokinetics

Physiologically based pharmacokinetic (PBPK) models often include several sets of correlated parameters, such as organ volumes and blood flows. Because of recent advances in proteomics, it has been demonstrated that correlations are also present between abundances of drug-metabolising enzymes in the liver. As the focus of population PBPK has shifted the emphasis from the average individual to theoretically conceivable extremes, reliable estimation of the extreme cases has become paramount. We performed a simulation study to assess the impact of the correlation between the abundances of two enzymes on the pharmacokinetics of drugs that are substrate of both, under assumptions of presence or lack of such correlations. We considered three semi-physiological models representing the cases of: (1) intravenously administered drugs metabolised by two enzymes expressed in the liver; (2) orally administered drugs metabolised by CYP3A4 expressed in the liver and gut wall; (3) intravenously administered drugs that are substrates of CYP3A4 and OATP1B1 in the liver. Finally, the impact of considering or ignoring correlation between enzymatic abundances on global sensitivity analysis (GSA) was investigated using variance based GSA on a reduced PBPK model for repaglinide, substrate of CYP3A4 and CYP2C8. Implementing such correlations can increase the confidence interval for population pharmacokinetic parameters (e.g., AUC, bioavailability) and impact the GSA results. Ignoring these correlations could lead to the generation of implausible parameters combinations and to an incorrect estimation of pharmacokinetic related parameters. Thus, known correlations should always be considered in building population PBPK models.

Implications of intercorrelation between hepatic CYP3A4-CYP2C8 enzymes for the evaluation of drug-drug interactions: a case study with repaglinide

AIMS

Statistically significant positive correlations are reported for the abundance of hepatic drug-metabolizing enzymes. We investigate, as an example, the impact of CYP3A4-CYP2C8 intercorrelation on the predicted interindividual variabilities of clearance and drug-drug interactions (DDIs) for repaglinide using physiologically based pharmacokinetic (PBPK) modelling.

METHODS

PBPK modelling and simulation were employed using Simcyp Simulator (v15.1). Virtual populations were generated assuming intercorrelations between hepatic CYP3A4-CYP2C8 abundances derived from observed values in 24 human livers. A repaglinide PBPK model was used to predict PK parameters in the presence and absence of gemfibrozil in virtual populations, and the results were compared with a clinical DDI study.

RESULTS

Coefficient of variation (CV) of oral clearance was 52.5% in the absence of intercorrelation between CYP3A4-CYP2C8 abundances, which increased to 54.2% when incorporating intercorrelation. In contrast, CV for predicted DDI (as measured by AUC ratio before and after inhibition) was reduced from 46.0% in the absence of intercorrelation between enzymes to 43.8% when incorporating intercorrelation: these CVs were associated with 5th/95th percentiles (2.48-11.29 vs. 2.49-9.69). The range of predicted DDI was larger in the absence of intercorrelation (1.55-77.06) than when incorporating intercorrelation (1.79-25.15), which was closer to clinical observations (2.6-12).

CONCLUSIONS

The present study demonstrates via a systematic investigation that population-based PBPK modelling incorporating intercorrelation led to more consistent estimation of extreme values than those observed in interindividual variabilities of clearance and DDI. As the intercorrelations more realistically reflect enzyme abundances, virtual population studies involving PBPK and DDI should avoid using Monte Carlo assignment of enzyme abundance.

Quantitative Assessment of Population Variability in Hepatic Drug Metabolism Using a Perfused Three-Dimensional Human Liver Microphysiological System

In this work, we first describe the population variability in hepatic drug metabolism using cryopreserved hepatocytes from five different donors cultured in a perfused three-dimensional human liver microphysiological system, and then show how the resulting data can be integrated with a modeling and simulation framework to accomplish in vitro–in vivo translation. For each donor, metabolic depletion profiles of six compounds (phenacetin, diclofenac, lidocaine, ibuprofen, propranolol, and prednisolone) were measured, along with metabolite formation, mRNA levels of 90 metabolism-related genes, and markers of functional viability [lactate dehydrogenase (LDH) release, albumin, and urea production]. Drug depletion data were analyzed with mixed-effects modeling. Substantial interdonor variability was observed with respect to gene expression levels, drug metabolism, and other measured hepatocyte functions. Specifically, interdonor variability in intrinsic metabolic clearance ranged from 24.1% for phenacetin to 66.8% for propranolol (expressed as coefficient of variation). Albumin, urea, LDH, and cytochrome P450 mRNA levels were identified as significant predictors of in vitro metabolic clearance. Predicted clearance values from the liver microphysiological system were correlated with the observed in vivo values. A population physiologically based pharmacokinetic model was developed for lidocaine to illustrate the translation of the in vitro output to the observed pharmacokinetic variability in vivo. Stochastic simulations with this model successfully predicted the observed clinical concentration-time profiles and the associated population variability. This is the first study of population variability in drug metabolism in the context of a microphysiological system and has important implications for the use of these systems during the drug development process.

Development of a Novel Simplified PBPK Absorption Model to Explain the Higher Relative Bioavailability of the OROS® Formulation of Oxybutynin

A new minimal Segmented Transit and Absorption model (mSAT) model has been recently proposed and combined with intrinsic intestinal effective permeability (P _eff,int ) to predict the regional gastrointestinal (GI) absorption (f _abs ) of several drugs. Herein, this model was extended and applied for the prediction of oral bioavailability and pharmacokinetics of oxybutynin and its enantiomers to provide a mechanistic explanation of the higher relative bioavailability observed for oxybutynin's modified-release OROS® formulation compared to its immediate-release (IR) counterpart. The expansion of the model involved the incorporation of mechanistic equations for the prediction of release, transit, dissolution, permeation and first-pass metabolism. The predicted pharmacokinetics of oxybutynin enantiomers after oral administration for both the IR and OROS® formulations were in close agreement with the observed data. The predicted absolute bioavailability for the IR formulation was within 5% of the observed value, and the model adequately predicted the higher relative bioavailability observed for the OROS® formulation vs. the IR counterpart. From the model predictions, it can be noticed that the higher bioavailability observed for the OROS® formulation was mainly attributable to differences in the intestinal availability (F _G ) rather than due to a higher colonic f _abs , thus confirming previous hypotheses. The predicted f _abs was almost 70% lower for the OROS® formulation compared to the IR formulation, whereas the F _G was almost eightfold higher than in the IR formulation. These results provide further support to the hypothesis of an increased F _G as the main factor responsible for the higher bioavailability of oxybutynin's OROS® formulation vs. the IR.

Reduction of a Whole-Body Physiologically Based Pharmacokinetic Model to Stabilise the Bayesian Analysis of Clinical Data

Whole-body physiologically based pharmacokinetic (PBPK) models are increasingly used in drug development for their ability to predict drug concentrations in clinically relevant tissues and to extrapolate across species, experimental conditions and sub-populations. A whole-body PBPK model can be fitted to clinical data using a Bayesian population approach. However, the analysis might be time consuming and numerically unstable if prior information on the model parameters is too vague given the complexity of the system. We suggest an approach where (i) a whole-body PBPK model is formally reduced using a Bayesian proper lumping method to retain the mechanistic interpretation of the system and account for parameter uncertainty, (ii) the simplified model is fitted to clinical data using Markov Chain Monte Carlo techniques and (iii) the optimised reduced PBPK model is used for extrapolation. A previously developed 16-compartment whole-body PBPK model for mavoglurant was reduced to 7 compartments while preserving plasma concentration-time profiles (median and variance) and giving emphasis to the brain (target site) and the liver (elimination site). The reduced model was numerically more stable than the whole-body model for the Bayesian analysis of mavoglurant pharmacokinetic data in healthy adult volunteers. Finally, the reduced yet mechanistic model could easily be scaled from adults to children and predict mavoglurant pharmacokinetics in children aged from 3 to 11 years with similar performance compared with the whole-body model. This study is a first example of the practicality of formal reduction of complex mechanistic models for Bayesian inference in drug development.

Application of a Bayesian approach to physiological modelling of mavoglurant population pharmacokinetics

Mavoglurant (MVG) is an antagonist at the metabotropic glutamate receptor-5 currently under clinical development at Novartis Pharma AG for the treatment of central nervous system diseases. The aim of this study was to develop and optimise a population whole-body physiologically-based pharmacokinetic (WBPBPK) model for MVG, to predict the impact of drug-drug interaction (DDI) and age on its pharmacokinetics. In a first step, the model was fitted to intravenous (IV) data from a clinical study in adults using a Bayesian approach. In a second step, the optimised model was used together with a mechanistic absorption model for exploratory Monte Carlo simulations. The ability of the model to predict MVG pharmacokinetics when orally co-administered with ketoconazole in adults or administered alone in 3-11 year-old children was evaluated using data from three other clinical studies. The population model provided a good description of both the median trend and variability in MVG plasma pharmacokinetics following IV administration in adults. The Bayesian approach offered a continuous flow of information from pre-clinical to clinical studies. Prediction of the DDI with ketoconazole was consistent with the results of a non-compartmental analysis of the clinical data (threefold increase in systemic exposure). Scaling of the WBPBPK model allowed reasonable extrapolation of MVG pharmacokinetics from adults to children. The model can be used to predict plasma and brain (target site) concentration-time profiles following oral administration of various immediate-release formulations of MVG alone or when co-administered with other drugs, in adults as well as in children.