Navigating the landscape of parameter identifiability methods: A workflow recommendation for model development.

In pharmacometric modeling, it is often important to know whether the data is sufficiently rich to identify the parameters of a proposed model. While it may be possible to assess this based on the results of a model fit, it is often difficult to disentangle identifiability issues from other model fitting and numerical problems. Furthermore, it can be of value to ascertain identifiability beforehand. This paper compares four methods for parameter identifiability, namely Differential Algebra for Identifiability of SYstems (DAISY), the sensitivity matrix method (SMM), Aliasing, and the Fisher information matrix method (FIMM). We discuss the characteristics of the methods and apply them to a set of applications, consisting of frequently used PK model structures, with suitable dosing regimens and sampling times. These applications were selected to validate the methods and demonstrate their usefulness. While traditional identifiability analysis provides a categorical result [PLoS One, 6, 2011, e27755; CPT Pharmacometrics Syst Pharmacol, 8, 2019, 259; Bioinformatics, 30, 2014, 1440], we argue that in practice a continuous scale better reflects the limitations on the data and is more informative. The methods were generally consistent in their evaluation of the applications. The Fisher information matrix method seemed to provide the most consistent answers. All methods provided information on the parameters that were unidentifiable. Some of the results were unexpected, indicating identifiability issues where none were foreseen, but could be explained upon further analysis. This illustrated the usefulness of identifiability assessment.

Building an adaptive dose simulation framework to aid dose and schedule selection.

Establishing a dosing regimen that maximizes clinical benefit and minimizes adverse effects for novel therapeutics is a key objective for drug developers. Finding an optimal dose and schedule can be particularly challenging for compounds with a narrow therapeutic window such as in oncology. Modeling and simulation tools can be valuable to conduct in silico evaluations of various dosing scenarios with the goal to identify those that could minimize toxicities, avoid unscheduled dose interruptions, or minimize premature discontinuations, which all could limit the potential for therapeutic benefit. In this tutorial, we present a stepwise development of an adaptive dose simulation framework that can be used for dose optimization simulations. The tutorial first describes the general workflow, followed by a technical description with basic to advanced practical examples of its implementation in mrgsolve and is concluded with examples on how to use this in decision-making around dose and schedule optimization. The adaptive simulation framework is built with pharmacokinetic, pharmacodynamic (i.e., biomarkers, activity markers, target engagement markers, efficacy markers), and safety models that include evaluations of unexplained interindividual and intraindividual variability and covariate impact, which can be replaced and expanded (e.g., combination setting, comparator setting) with user-defined models. Subsequent adaptive simulations allow investigation of the impact of starting dose, dosing intervals, and event-driven (exposure or effect) dose modifications on any end point. The resulting simulation-derived insights can be used in quantitatively proposing dose and regimens that better balance benefit and adverse effects for further evaluation, aiding dose selection discussions, and designing dose modification recommendations, among others.

PK/PD modeling of FXI antisense oligonucleotides to bridge the dose-FXI activity relation from healthy volunteers to end-stage renal disease patients.

IONIS-FXIRX (BAY2306001) is an antisense oligonucleotide that inhibits the synthesis of coagulation factor XI (FXI) and has been investigated in healthy volunteers and patients with end-stage renal disease (ESRD). FXI-LICA (BAY2976217) shares the same RNA sequence as IONIS-FXIRX but contains a GalNAc-conjugation that facilitates asialoglycoprotein receptor (ASGPR)-mediated uptake into hepatocytes. FXI-LICA has been studied in healthy volunteers and is currently investigated in patients with ESRD on hemodialysis. We present a model-informed bridging approach that facilitates the extrapolation of the dose-exposure-FXI relationship from IONIS-FXIRX to FXI-LICA in patients with ESRD and, thus, supports the selection of FX-LICA doses being investigated in patients with ESRD. A two-compartment pharmacokinetic (PK) model, with mixed first- and zero-order subcutaneous absorption and first-order elimination, was combined with an indirect response model for the inhibitory effect on the FXI synthesis rate via an effect compartment. This PK/pharmacodynamic model adequately described the median trends, as well as the interindividual variabilities for plasma drug concentration and FXI activity in healthy volunteers of IONIS-FXIRX and FXI-LICA, and in patients with ESRD of IONIS-FXIRX . The model was then used to predict dose-dependent steady-state FXI activity following repeat once-monthly doses of FXI-LICA in a virtual ESRD patient population. Under the assumption of similar ASGPR expression in patients with ESRD and healthy volunteers, doses of 40 mg, 80 mg, and 120 mg FXI-LICA are expected to cover the target range of clinical interest for steady-state FXI activity in the phase IIb study of FXI-LICA in patients with ESRD undergoing hemodialysis.

Pharmacokinetic and Pharmacodynamic Modelling to Characterize the Tolerability of Alternative Up-Titration Regimens of Roflumilast in Patients with Chronic Obstructive Pulmonary Disease.

BACKGROUND: In the OPTIMIZE study, 4 weeks of roflumilast 250 µg once daily before escalation to the approved 500 µg once daily maintenance dose reduced treatment discontinuations and improved tolerability to roflumilast among patients with chronic obstructive pulmonary disease (COPD). In this study, we present the pharmacokinetic (PK) results and PK/pharmacodynamic (PD) modelling data from OPTIMIZE. METHODS: OPTIMIZE was a multicentre, double-blind, phase III study in which patients with severe COPD were randomized 1:1:1 to receive oral roflumilast 250 µg once daily, 500 µg every other day, or 500 µg once daily for 4 weeks, followed by 500 µg once daily for 8 weeks. A population PK (popPK) model characterized roflumilast exposure levels (total phosphodiesterase-4 inhibition [tPDE4i]). Furthermore, models characterized the percentage of patients with adverse events (AEs) of interest (PK/AE model), and time to discontinuation due to such AEs (PK/time-to-event model). RESULTS: The popPK model adequately described average plasma concentrations and variability from 1238 patients. The percentage of patients with AEs of interest increased with predicted tPDE4i exposure (logit scale slope 0.484; confidence interval 0.262-0.706; p = 2 × 10-5). PK/time-to-event model analysis predicted that patients receiving the 250 µg up-titration regimen had significantly lower discontinuation rates and longer time to discontinuation compared with roflumilast 500 µg every other day or 500 µg once daily (p = 0.0014). CONCLUSIONS: In this PK/PD model, a 4-week up-titration regimen with roflumilast 250 µg once daily was found to reduce discontinuations and improve tolerability, confirming the main clinical findings of the OPTIMIZE study. However, use of this lower dose as long-term maintenance therapy may not induce sufficient phosphodiesterase-4 inhibition to exert clinical efficacy, supporting the approval of 500 µg as maintenance dose. TRIAL REGISTRATION: OPTIMIZE: NCT02165826; REACT: NCT01329029.

Pharmacokinetic analysis of modified-release metoprolol formulations: An interspecies comparison.

In the current study, we investigated the metoprolol absorption kinetics of an in-house produced oral sustained-release formulation, matrices manufactured via prilling, and two commercially available formulations, ZOK-ZID® (reservoir) and Slow-Lopresor® (matrix) in both New Zealand White rabbits and Beagle dogs, using a population pharmacokinetic analysis approach. The aim of this study was to compare the in vivo pharmacokinetic (PK) profiles of different formulations based on metoprolol, a selective adrenergic ß1-receptor antagonist, in dogs and rabbits and to contrast the observed differences. To that end, metoprolol (50 to 200mg) was administered to 6 Beagle dogs and 6 New Zealand White rabbits as a single intravenous (IV) bolus injection and to 8 dogs and 6 rabbits as an oral modified release formulation. To derive pharmacokinetic parameters from the data, a non-linear mixed-effects model was developed using NONMEM® where the contribution of observations below the limit of detection (BDL, below detection limit) to the parameter estimates was taken into account in the parameter estimation procedure. In both species and for the three modified release formulations, different absorption models were tested to describe the PK of metoprolol following oral dosing. In Beagle dogs, plasma concentration-time profiles were best described using a sequential zero- and first-order absorption model. In rabbits though, the absorption phase was best described using a first-order process only. In both species, the reservoir formulation ZOK-ZID® was behaving quite similarly. In contrast, the absorption properties of both matrix formulations were rather different between species. This study indicates that the PK of the reservoir formulation is similar in both species, even after accounting for the almost completely missed absorption phase in rabbits. The insights gained further illustrate that rabbits are not very well suited to study the PK of the current matrix formulations in view of their less optimal prolonged release characteristics and the resulting fast decline in metoprolol plasma levels.

PK/PD Modelling of the QT Interval: a Step Towards Defining the Translational Relationship Between In Vitro, Awake Beagle Dogs, and Humans.

Inhibiting the human ether-a-go-go-related gene (hERG)-encoded potassium ion channel is positively correlated with QT-interval prolongation in vivo, which is considered a risk factor for the occurrence of Torsades de Pointes (TdP). A pharmacokinetic/pharmacodynamic model was developed for four compounds that reached the clinic, to relate drug-induced QT-interval change in awake dogs and humans and to derive a translational scaling factor a 1. Overall, dogs were more sensitive than humans to QT-interval change, an a 1 of 1.5 was found, and a 10% current inhibition in vitro produced a higher percent QT-interval change in dogs as compared to humans. The QT-interval changes in dogs were predictive for humans. In vitro and in vivo information could reliably describe the effects in humans. Robust translational knowledge is likely to reduce the need for expensive thorough QT studies; therefore, expanding this work to more compounds is recommended.

Modelling of drug-induced QT-interval prolongation: estimation approaches and translational opportunities.

Safety pharmacology studies are performed to assess whether compounds may provoke severe arrhythmias (e.g. Torsades de Pointes, TdP) and sudden death in man. Although there is strong evidence that drugs inducing TdP in man prolong the QT interval in vivo and block the human ether-a-go-go-related gene (hERG) ion channel in vitro, not all drugs affecting the QT interval or the hERG will induce TdP. Nevertheless, QT-interval prolongation and hERG blockade currently represent the most accepted early risk biomarkers to deselect drugs. An extensive pharmacokinetic/pharmacodynamic (PK/PD) analysis is developed to understand moxifloxacin's-induced effects on the QT interval by comparing the relationship between results of an in vitro patch-clamp model to in vivo models. The frequentist and the fully Bayesian estimation procedures were compared and provided similar performances when the best model selected in NONMEM is subsequently implemented in WinBUGS, which guarantees a straightforward calculation of the probability of QT-interval prolongation greater than 2.5 % (10 ms). The use of the percent threshold to account for the intrinsic differences between species and a new calculation of the probability curve are introduced. The concentration providing the 50 % probability indicates that dogs are more sensitive than humans to QT-interval prolongation. However, based on the drug effect, a clear distinction between species cannot be made. An operational PK/PD model of agonism was used to investigate the relationship between effects on the hERG and QT-interval prolongation in dogs. The proposed analysis contributes to establish a translational relationship that could potentially reduce the need for thorough QT studies.

Population modelling of patient responses in antidepressant studies: a stochastic approach.

This paper addresses the problem of modelling longitudinal data describing patients' responses in clinical trials. In particular, a systematic approach relying on a system theoretic paradigm is proposed to deal with contexts where limited physiopathological knowledge is available on disease, drug response, and patients' characteristics. The model relies on the notion of patient's health state which summarizes the patient's condition. In order to cope with the limited number of clinical data usually available, the paper considers a very parsimonious realization where the two state variables are the clinical endpoint and its derivative. Within a population framework, the individual response is modelled as the sum of an individual shift and the average response of subjects belonging to the same study, both described as Markovian processes and identified by empirical Bayes techniques. The proposed approach is validated with experimental data from a Phase II, flexible-dose, depression trial. The dose changes due to the flexible-dose scheme are handled as perturbations on the state. The connection between inter-individual variability and model stability is evaluated showing that the introduction of stable poles helps to describe populations whose range of individual responses does not diverge with time. In this way, good individual fittings and visual predictive checks were obtained for the clinical data. The proposed analysis provides a systematic approach to semi-mechanistic modelling when a precise knowledge of the physiological mechanisms of the disease is incomplete or missing.

Population pharmacokinetic model of ibrutinib, a Bruton tyrosine kinase inhibitor, in patients with B cell malignancies.

PURPOSE: Ibrutinib is an oral Bruton's tyrosine kinase inhibitor, recently approved for the treatment of mantle cell lymphoma (MCL) and chronic lymphocytic leukemia (CLL) patients with at least one prior therapy. We developed a population pharmacokinetic (PK) model for ibrutinib in patients. METHODS: Ibrutinib PK data (3,477 observations/245 patients) were available from the following clinical studies: (1) A phase I dose-escalation study in recurrent B cell malignancies (dose levels of 1.25-12.5 mg/kg/day and fixed dose of 560 mg/day); (2) a phase II study in MCL (fixed dose level of 560 mg/day); (3) a phase Ib/II dose-finding study in CLL (fixed dose levels of 420 and 840 mg/day). Different compartmental PK models were explored using nonlinear mixed effects modeling. RESULTS: A two-compartment PK model with sequential zero-first-order absorption and first-order elimination was able to characterize the PK of ibrutinib. The compound was rapidly absorbed, had a high oral plasma clearance (approximately 1,000 L/h) and a high apparent volume of distribution at steady state (approximately 10,000 L). PK parameters were not dependent on dose, study, or clinical indication. The fasting state was characterized by a 67 % relative bioavailability compared with the meal conditions used in the trials and administration after a high-fat meal. Body weight and coadministration of antacids marginally increased volume of distribution and duration of absorption, respectively. CONCLUSIONS: The proposed population PK model was able to describe the plasma concentration-time profiles of ibrutinib across various trials. The linear model indicated that the compound's PK was dose independent and time independent.

Continuous-time Markov modelling of flexible-dose depression trials.

The aim of this paper is to provide a systematic methodology for modelling longitudinal data to be used in contexts of limited or even absent knowledge of the physiological mechanism underlying the disease time course. Adopting a system-theoretic paradigm, a population response model is developed where the clinical endpoint is described as a function of the patient's health state. In particular, a continuous-time stochastic approach is proposed where the clinical score and its time-derivative summarize the patient's health state affected by a random term accounting for exogenous unpredictable factors. The proposed approach is validated on experimental data from the placebo and drug arms of a Phase II depression trial. Since some subjects in the trial may undergo changes in their treatment dose due to the flexible dosing scheme, dose escalations are modelled as instantaneous perturbations on the state. In its simplest form--an integrated Wiener process--was able to correctly capture the individual responses in both treatment arms. However, a better description of inter-individual variability was obtained by means of a stable Markovian model. Parameter estimation has been carried out according to the empirical Bayes method.

Population model of longitudinal FEV1 data in asthmatics: meta-analysis and predictability of placebo response.

Asthma is an obstructive lung disease where the mechanism of disease progression is not fully understood hence motivating the use of empirical models to describe the evolution of the patient's health state. With reference to placebo response, measured in terms of FEV1 (Forced Expiratory Volume in 1 s), a range of empirical models taken from the literature were compared at a single trial level. In particular, eleven GSK trials lasting 12 weeks in mild-to-moderate asthma were used for the modelling of longitudinal placebo responses. Then, the chosen exponential model was used to carry out an individual participant data meta-analysis on eleven trials. A covariate analysis was also performed to find relevant covariates in asthma to be accounted for in the meta-analysis model. Age, gender, and height were found statistically significant (e.g. the taller the patients the higher the FEV1, the older the patients the lower the FEV1, and females have lower FEV1). By truncating each trial at week 4, the predictive properties of the meta-analysis model were also investigated, showing its ability to predict long-term FEV1 response from truncated trials. Summarizing, the study suggests that: (i) the exponential model effectively describes the placebo response; (ii) the meta-analysis approach may prove helpful to simulate new trials as well as to reduce trial duration in view of its predictive properties; (iii) the inclusion of available covariates within the meta-analysis model provides a reduction of the inter-individual variability.

A PCA approach to population analysis: with application to a Phase II depression trial.

For psychiatric diseases, established mechanistic models are lacking and alternative empirical mathematical structures are usually explored by a trial-and-error procedure. To address this problem, one of the most promising approaches is an automated model-free technique that extracts the model structure directly from the statistical properties of the data. In this paper, a linear-in-parameter modelling approach is developed based on principal component analysis (PCA). The model complexity, i.e. the number of components entering the PCA-based model, is selected by either cross-validation or Mallows' Cp criterion. This new approach has been validated on both simulated and clinical data taken from a Phase II depression trial. Simulated datasets are generated through three parametric models: Weibull, Inverse Bateman and Weibull-and-Linear. In particular, concerning simulated datasets, it is found that the PCA approach compares very favourably with some of the popular parametric models used for analyzing data collected during psychiatric trials. Furthermore, the proposed method performs well on the experimental data. This approach can be useful whenever a mechanistic modelling procedure cannot be pursued. Moreover, it could support subsequent semi-mechanistic model building.

Deconvolution-based assessment of pituitary GH secretion stimulated with GHRH+arginine in Prader-Willi adults and obese controls.

OBJECTIVE: The assessment of GH deficiency in adult patients with Prader-Willi syndrome (PWS) has been previously assessed through the evaluation of quantitative parameters, such as the peak value of GH response to exogenous stimuli. A comprehensive description of the pattern of secretory response obtainable by deconvolution analysis is still lacking. The aim of our study was to characterize the time evolution of responses of PWS subjects compared with obese controls. DESIGN AND SUBJECTS: GH responsiveness was measured following the combined administration of GHRH+arginine to 65 PWS adults (24 males, 41 females) aged 18-41·2 years, and 17 age-, gender- and body mass index-matched obese controls. PWS subjects were analysed considering the stratification on different genotypes. MEASUREMENTS: GH response to GHRH+arginine was analysed in terms of peak values, standard area under the curves (AUCs), AUCs due to the stimulus, AUCs of the Instantaneous Secretion Rate signal and Secretion Response Analysis. RESULTS: In terms of both peak values and AUC, GH responses were statistically different between PWS UPD15 and PWS DEL15 subjects as well as between PWS UPD15 and obese controls. PWS subjects showed a lower and a more delayed GH response compared with obese controls. Moreover, PWS UPD15 subjects had the most delayed GH response. CONCLUSIONS: Our findings demonstrate that impaired GH secretion in PWS subjects compared with obese controls regards not only amplitude parameters such as peak value and AUC, but also the shape of the secretory response, which is more delayed, especially for UPD15 subjects.