Prediction of shrinkage of individual parameters using the bayesian information matrix in non-linear mixed effect models with evaluation in pharmacokinetics

The Use of Microdosing for In vivo Phenotyping of Cytochrome P450 Enzymes: Where Do We Stand? A Narrative Review

Cytochrome P450 (CYP) enzymes play a central role in the elimination of approximately 80% of all clinically used drugs. Differences in CYP enzyme activity between individuals can contribute to interindividual variability in exposure and, therefore, treatment outcome. In vivo CYP enzyme activity could be determined with phenotyping. Currently, (sub)therapeutic doses are used for in vivo phenotyping, which can lead to side effects. The use of microdoses (100 µg) for in vivo phenotyping for CYP enzymes could overcome the limitations associated with the use of (sub)therapeutic doses of substrates. The aim of this review is to provide a critical overview of the application of microdosing for in vivo phenotyping of CYP enzymes. A literature search was performed to find drug-drug interaction studies of CYP enzyme substrates that used microdoses of the respective substrates. A substrate was deemed sensitive to changes in CYP enzyme activity when the pharmacokinetics of the substrate significantly changed during inhibition and induction of the enzyme. On the basis of the currently available evidence, the use of microdosing for in vivo phenotyping for subtypes CYP1A2, CYP2C9, CYP2D6, and CYP2E1 is not recommended. Microdosing can be used for the in vivo phenotyping of CYP2C19 and CYP3A. The recommended microdose phenotyping test for CYP2C19 is measuring the omeprazole area-under-the-concentration-time curve over 24 h (AUC0-24) after administration of a single 100 µg dose. CYP3A activity could be best determined with a 0.1-75 µg dose of midazolam, and subsequently measuring AUC extrapolated to infinity (AUC∞) or clearance. Moreover, there are two metrics available for midazolam using a limited sampling strategy: AUC over 10 h (AUC0-10) and AUC from 2 to 4 h (AUC2-4).

Establishment of a pharmacokinetics and pharmacodynamics model of Schisandra lignans against hippocampal neurotransmitters in AD rats based on microdi-alysis liquid chromatography-mass spectrometry

Objective: Our previous studies substantiated that the biological activity of Schisandra chinensis lignans during the treatment of Alzheimer's disease (AD) was mediated by neurotransmitter levels, and 15 of its active components were identified. However, the pharmacokinetic and pharmacodynamic relationship of Schisandra chinensis lignans has been less studied. The objective of this study was to investigate the relationship between the pharmacokinetics and pharmacodynamics of Schisandra chinensis lignans in the treatment of AD, and to establish a pharmacokinetic-pharmacodynamic (PK-PD) model. Methods and Results: Herein, we established a microdialysis-ultra performance liquid chromatography-triple quadruple mass spectrometry (MD-LC-TQ-MS) technique that could simultaneously and continuously collect and quantitatively analyze the active compounds and neurotransmitters related to the therapeutic effects of Schisandra chinensis in awake AD rats. Eight lignans were detected in the hippocampus, and a PK-PD model was established. The fitted curves highlighted a temporal lag between the maximum drug concentration and the peak drug effect. Following treatment, the levels of four neurotransmitters tended to converge with those observed in the sham operation group. Conclusion: By establishing a comprehensive concentration-time-effect relationship for Schisandra chinensis lignans in AD treatment, our study provides novel insights into the in vivo effects of these lignans in AD rats.

Conjunction of semi-mechanistic in vitro-in vivo modeling and population pharmacokinetics as a tool for virtual bioequivalence analysis - a case study for a BCS class II drug

Virtual bioequivalence trial (VBE) simulations based on (semi)mechanistic in vitro-in vivo (IVIV) modeling have gained a huge interest in the pharmaceutical industry. Sophisticated commercially available software allows modeling variable drug fates in the gastrointestinal tract (GIT). Surprisingly, the between-subject and inter-occasion variability (IOV) of the distribution volumes and clearances are ignored or simplified, despite substantially contributing to varied plasma drug concentrations. The paper describes a novel approach for IVIV-based VBE by using population pharmacokinetics (popPK). The data from two bioequivalence trials with a poorly soluble BCS class II drug were analyzed retrospectively. In the first trial, the test drug product (biobatch 1) did not meet the bioequivalence criteria, but after a reformulation, the second trial succeeded (biobatch 2). The popPK model was developed in the Monolix software (Lixoft SAS, Simulation Plus) based on the originator's plasma concentrations. The modified Noyes-Whitney model was fitted to the results of discriminative biorelevant dissolution tests of the two biobatches and seven other reformulations. Then, the IVIV model was constructed by joining the popPK model with fixed drug disposition parameters, the drug dissolution model, and mechanistic approximation of the GIT transit. It was used to simulate the drug concentrations at different IOV levels of the primary pharmacokinetic parameters and perform the VBE. Estimated VBE success rates for both biobatches well reflected the outcomes of the bioequivalence trials. The predicted 90% confidence intervals for the area under the time-concentration curves were comparable with the observed values, and the 10% IOV allowed the closest approximation to the clinical results. Simulations confirmed that a significantly lower maximum drug concentration for biobatch 1 was responsible for the first clinical trial's failure. In conclusion, the proposed workflow might aid formulation screening in generic drug development.

"De-Shrinking" EBEs: The Solution for Bayesian Therapeutic Drug Monitoring

BACKGROUND

Therapeutic drug monitoring (TDM) aims at individualising a dosage regimen and is increasingly being performed by estimating individual pharmacokinetic parameters via empirical Bayes estimates (EBEs). However, EBEs suffer from shrinkage that makes them biased. This bias is a weakness for TDM and probably a barrier to the acceptance of drug dosage adjustments by prescribers.

OBJECTIVE

The aim of this article is to propose a methodology that allows a correction of EBE shrinkage and an improvement in their precision.

METHODS

As EBEs are defined, they can be seen as a special case of ridge estimators depending on a parameter usually denoted λ. After a bias correction depending on λ, we chose λ so that the individual pharmacokinetic estimations have minimal imprecision. Our estimate is by construction always better than EBE with respect to bias (i.e. shrinkage) and precision.

RESULTS

We illustrate the performance of this approach with two different drugs: iohexol and isavuconazole. Depending on the patient's actual pharmacokinetic parameter values, the improvement given by our approach ranged from 0 to 100%.

CONCLUSION

This innovative methodology is promising since, to the best of our knowledge, no other individual shrinkage correction has been proposed.

Tutorial for $DESIGN in NONMEM: Clinical trial evaluation and optimization

This NONMEM tutorial shows how to evaluate and optimize clinical trial designs, using algorithms developed in design software, such as PopED and PFIM 4.0. Parameter precision and model parameter estimability is obtained by assessing the Fisher Information Matrix (FIM), providing expected model parameter uncertainty. Model parameter identifiability may be uncovered by very large standard errors or inability to invert an FIM. Because evaluation of FIM is more efficient than clinical trial simulation, more designs can be investigated, and the design of a clinical trial can be optimized. This tutorial provides simple and complex pharmacokinetic/pharmacodynamic examples on obtaining optimal sample times, doses, or best division of subjects among design groups. Robust design techniques accounting for likely variability among subjects are also shown. A design evaluator and optimizer within NONMEM allows any control stream first developed for trial design exploration to be subsequently used for estimation of parameters of simulated or clinical data, without transferring the model to another software. Conversely, a model developed in NONMEM could be used for design optimization. In addition, the $DESIGN feature can be used on any model file and dataset combination to retrospectively evaluate the model parameter uncertainty one would expect given that the model generated the data, particularly if outliers of the actual data prevent a reasonable assessment of the variance‐covariance. The NONMEM trial design feature is suitable for standard continuous data, whereas more elaborate trial designs or with noncontinuous data‐types can still be accomplished in optimal design dedicated software like PopED and PFIM.

An Integrated Population Pharmacokinetic Model Versus Individual Models of Depatuxizumab Mafodotin, an Anti-EGFR Antibody Drug Conjugate, in Patients With Solid Tumors Likely to Overexpress EGFR

Depatuxizumab mafodotin (depatux-m) is an antibody-drug conjugate (ADC) designed for the treatment of tumors expressing epidermal growth factor receptor (EGFR), consisting of a veneered "humanized" recombinant IgG1κ antibody that has binding properties specific to a unique epitope of human EGFR with noncleavable maleimido-caproyl linkers each attached to a potent antimitotic cytotoxin, monomethyl auristatin F. We aimed to describe the development and comparison of 2 population pharmacokinetic modeling approaches. Data from 2 phase 1 studies enrolling patients with glioblastoma multiforme or advanced solid tumors were included in the analysis. Patients in these studies received doses of depatux-m ranging from 0.5 to 4.0 mg/kg as monotherapy, in combination with temozolomide, or radiation plus temozolomide depending on the study and/or arm. First, an integrated ADC model to simultaneously describe the concentration-time data for ADC, total antibody, and cys-mafodotin was built using a 2-compartment model for ADC for each drug-to-antibody ratio. Then, 3 individual models were developed for ADC, total antibody, and cys-mafodotin separately using 2-compartment models for ADC and total antibody and a 1-compartment model for cys-mafodotin. Visual predictive checks suggested accurate model fitting across a range of concentrations. The analysis showed that both an integrated complex ADC model and the individual models that have shorter computational time would result in similar outcomes.

PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models

BACKGROUND AND OBJECTIVE

Nonlinear mixed-effect models (NLMEMs) are increasingly used for the analysis of longitudinal studies during drug development. When designing these studies, the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. The function PFIM is the first tool for design evaluation and optimization that has been developed in R. In this article, we present an extended version, PFIM 4.0, which includes several new features.

METHODS

Compared with version 3.0, PFIM 4.0 includes a more complete pharmacokinetic/pharmacodynamic library of models and accommodates models including additional random effects for inter-occasion variability as well as discrete covariates. A new input method has been added to specify user-defined models through an R function. Optimization can be performed assuming some fixed parameters or some fixed sampling times. New outputs have been added regarding the FIM such as eigenvalues, conditional numbers, and the option of saving the matrix obtained after evaluation or optimization. Previously obtained results, which are summarized in a FIM, can be taken into account in evaluation or optimization of one-group protocols. This feature enables the use of PFIM for adaptive designs. The Bayesian individual FIM has been implemented, taking into account a priori distribution of random effects. Designs for maximum a posteriori Bayesian estimation of individual parameters can now be evaluated or optimized and the predicted shrinkage is also reported. It is also possible to visualize the graphs of the model and the sensitivity functions without performing evaluation or optimization.

RESULTS

The usefulness of these approaches and the simplicity of use of PFIM 4.0 are illustrated by two examples: (i) an example of designing a population pharmacokinetic study accounting for previous results, which highlights the advantage of adaptive designs; (ii) an example of Bayesian individual design optimization for a pharmacodynamic study, showing that the Bayesian individual FIM can be a useful tool in therapeutic drug monitoring, allowing efficient prediction of estimation precision and shrinkage for individual parameters.

CONCLUSION

PFIM 4.0 is a useful tool for design evaluation and optimization of longitudinal studies in pharmacometrics and is freely available at http://www.pfim.biostat.fr.

Model-Based Approach to Predict Adherence to Protocol During Antiobesity Trials

Development of antiobesity drugs is continuously challenged by high dropout rates during clinical trials. The objective was to develop a population pharmacodynamic model that describes the temporal changes in body weight, considering disease progression, lifestyle intervention, and drug effects. Markov modeling (MM) was applied for quantification and characterization of responder and nonresponder as key drivers of dropout rates, to ultimately support the clinical trial simulations and the outcome in terms of trial adherence. Subjects (n = 4591) from 6 Contrave^® trials were included in this analysis. An indirect‐response model developed by van Wart et al was used as a starting point. Inclusion of drug effect was dose driven using a population dose‐ and time‐dependent pharmacodynamic (DTPD) model. Additionally, a population‐pharmacokinetic parameter‐ and data (PPPD)‐driven model was developed using the final DTPD model structure and final parameter estimates from a previously developed population pharmacokinetic model based on available Contrave^® pharmacokinetic concentrations. Last, MM was developed to predict transition rate probabilities among responder, nonresponder, and dropout states driven by the pharmacodynamic effect resulting from the DTPD or PPPD model. Covariates included in the models and parameters were diabetes mellitus and race. The linked DTPD‐MM and PPPD‐MM was able to predict transition rates among responder, nonresponder, and dropout states well. The analysis concluded that body‐weight change is an important factor influencing dropout rates, and the MM depicted that overall a DTPD model‐driven approach provides a reasonable prediction of clinical trial outcome probabilities similar to a pharmacokinetic‐driven approach.

Combined Analysis of Phase I and Phase II Data to Enhance the Power of Pharmacogenetic Tests

We show through a simulation study how the joint analysis of data from phase I and phase II studies enhances the power of pharmacogenetic tests in pharmacokinetic (PK) studies. PK profiles were simulated under different designs along with 176 genetic markers. The null scenarios assumed no genetic effect, while under the alternative scenarios, drug clearance was associated with six genetic markers randomly sampled in each simulated dataset. We compared penalized regression Lasso and stepwise procedures to detect the associations between empirical Bayes estimates of clearance, estimated by nonlinear mixed effects models, and genetic variants. Combining data from phase I and phase II studies, even if sparse, increases the power to identify the associations between genetics and PK due to the larger sample size. Design optimization brings a further improvement, and we highlight a direct relationship between η‐shrinkage and loss of genetic signal.

Inter occasion variability in individual optimal design

Inter occasion variability (IOV) is of importance to consider in the development of a design where individual pharmacokinetic or pharmacodynamic parameters are of interest. IOV may adversely affect the precision of maximum a posteriori (MAP) estimated individual parameters, yet the influence of inclusion of IOV in optimal design for estimation of individual parameters has not been investigated. In this work two methods of including IOV in the maximum a posteriori Fisher information matrix (FIM_MAP) are evaluated: (i) MAP_occ—the IOV is included as a fixed effect deviation per occasion and individual, and (ii) POP_occ—the IOV is included as an occasion random effect. Sparse sampling schedules were designed for two test models and compared to a scenario where IOV is ignored, either by omitting known IOV (Omit) or by mimicking a situation where unknown IOV has inflated the IIV (Inflate). Accounting for IOV in the FIM_MAP markedly affected the designs compared to ignoring IOV and, as evaluated by stochastic simulation and estimation, resulted in superior precision in the individual parameters. In addition MAP_occ and POP_occ accurately predicted precision and shrinkage. For the investigated designs, the MAP_occ method was on average slightly superior to POP_occ and was less computationally intensive.

MatVPC: A User-Friendly MATLAB-Based Tool for the Simulation and Evaluation of Systems Pharmacology Models

Quantitative systems pharmacology (QSP) models are progressively entering the arena of contemporary pharmacology. The efficient implementation and evaluation of complex QSP models necessitates the development of flexible computational tools that are built into QSP mainstream software. To this end, we present MatVPC, a versatile MATLAB-based tool that accommodates QSP models of any complexity level. MatVPC executes Monte Carlo simulations as well as automatic construction of visual predictive checks (VPCs) and quantified VPCs (QVPCs).

Powers of the likelihood ratio test and the correlation test using empirical bayes estimates for various shrinkages in population pharmacokinetics

We compared the powers of the likelihood ratio test (LRT) and the Pearson correlation test (CT) from empirical Bayes estimates (EBEs) for various designs and shrinkages in the context of nonlinear mixed-effect modeling. Clinical trial simulation was performed with a simple pharmacokinetic model with various weight (WT) effects on volume (V). Data sets were analyzed with NONMEM 7.2 using first-order conditional estimation with interaction and stochastic approximation expectation maximization algorithms. The powers of LRT and CT in detecting the link between individual WT and V or clearance were computed to explore hidden or induced correlations, respectively. Although the different designs and variabilities could be related to the large shrinkage of the EBEs, type 1 errors and powers were similar in LRT and CT in all cases. Power was mostly influenced by covariate effect size and, to a lesser extent, by the informativeness of the design. Further studies with more models are needed.

Largazole pharmacokinetics in rats by LC-MS/MS

A highly sensitive and specific LC-MS/MS method for the quantitation of largazole thiol, the active species of the marine-derived preclinical histone deacetylase inhibitor, largazole (prodrug), was developed and validated. Largazole thiol was extracted with ethyl acetate from human or rat plasma along with the internal standard, harmine. Samples were separated on an Onyx Monolithic C18 column by a stepwise gradient elution with 0.1% formic acid in methanol and 0.1% aqueous formic acid employing multiple reaction monitoring (MRM) detection. Linear calibration curves were obtained in the range of 12.5-400 ng/mL with 200 µL of human plasma. The overall intra-day precision was from 3.87% to 12.6%, and the inter-day precision was from 7.12% to 9.8%. The accuracy at low, medium and high concentrations ranged from 101.55% to 105.84%. Plasma protein bindings of largazole thiol in human and rat plasma as determined by an ultrafiltration method were 90.13% and 77.14%, respectively. Plasma drug concentrations were measured by this LC-MS/MS method. The pharmacokinetics of largazole thiol in rats was studied following i.v. administration at 10 mg/kg and found to follow a two-compartment model. Largazole thiol was rapidly eliminated from systemic circulation within 2 h. The established LC-MS/MS method is suitable for the analysis of largazole thiol in human plasma, as well.

Influence of a priori Information, Designs, and Undetectable Data on Individual Parameters Estimation and Prediction of Hepatitis C Treatment Outcome

Hepatitis C viral kinetic analysis based on nonlinear mixed effect models can be used to individualize treatment. For that purpose, it is necessary to obtain precise estimation of individual parameters. Here, we evaluated by simulation the influence on Bayesian individual parameter estimation and outcome prediction of a priori information on population parameters, viral load sampling designs, and methods for handling data below detection limit (BDL). We found that a precise estimation of both individual parameters and treatment outcome could be obtained using as few as six measurements in the first month of therapy. This result remained valid even when incorrect a priori information on population parameters was set as long as the parameters were identifiable and BDL data were properly handled. However, setting wrong values for a priori population parameters could lead to severe estimation/prediction errors if BDL data were ignored and not properly accounted in the likelihood function.