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The Reference-Corrected visual predictive check: A More Intuitive Diagnostic for Non-Linear Mixed Effects Models

AAPS Journal 2025年第4期27卷 1-13页

作者： Ibrahim, Moustafa M. A. Jonsson, E. Niclas Bergstrand, Martin Pharmetheus AB Uppsala Sweden

The prediction-corrected visual predictive check (pcVPC) is an informative model diagnostic that can offer advantages over the standard visual predictive check (VPC) when heterogenous study designs and adaptive dosing are used. However, a drawback with these plots is that prediction correction often results in y-axis values and trends that are unintuitive, difficult to explain, and challenging to communicate even among experts. The reference-corrected visual predictive check (rcVPC) offers a solution to these problems by leveraging a user-defined set of independent variables, for a more intuitive model diagnostic and an efficient communication of results to a wider audience. The rcVPC methodology is based on the definition of a reference dataset. Simulations are conducted with this reference dataset and the observed dataset, and then the simulated and the observed dependent variables are normalized by the population prediction for the user-defined independent variables in the reference dataset. The opportunity to manipulate time in the reference dataset is a unique feature that gives rcVPC the ability to visually characterize exposure–response relationships with delayed effect onset. The rcVPC approach was compared to pcVPCs and traditional VPCs for a range of examples inspired by real data. The rcVPC methodology was demonstrated to offer a more intuitive interpretation and more effective guidance to model development in a way that is not possible for VPC or pcVPC plots. © The Author(s) 2025.

关键词： Model diagnostics NONMEM PcVPC Population pharmacokinetic exposure–response Prediction-corrected visual predictive check PvcVPC RcVPC Reference-corrected visual predictive check RVPC visual predictive check VPC

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visual predictive check in Models with Time-Varying Input Function

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AAPS JOURNAL 2015年第6期17卷 1455-1463页

作者： Largajolli, Anna Bertoldo, Alessandra Campioni, Marco Cobelli, Claudio Univ Padua Dept Informat Engn I-35131 Padua Italy Merck KGaA Exploratory Med Darmstadt Germany

The nonlinear mixed effects models are commonly used modeling techniques in the pharmaceutical research as they enable the characterization of the individual profiles together with the population to which the individuals belong. To ensure a correct use of them is fundamental to provide powerful diagnostic tools that are able to evaluate the predictive performance of the models. The visual predictive check (VPC) is a commonly used tool that helps the user to check by visual inspection if the model is able to reproduce the variability and the main trend of the observed data. However, the simulation from the model is not always trivial, for example, when using models with time-varying input function (IF). In this class of models, there is a potential mismatch between each set of simulated parameters and the associated individual IF which can cause an incorrect profile simulation. We introduce a refinement of the VPC by taking in consideration a correlation term (the Mahalanobis or normalized Euclidean distance) that helps the association of the correct IF with the individual set of simulated parameters. We investigate and compare its performance with the standard VPC in models of the glucose and insulin system applied on real and simulated data and in a simulated pharmacokinetic/pharmacodynamic (PK/PD) example. The newly proposed VPC performance appears to be better with respect to the standard VPC especially for the models with big variability in the IF where the probability of simulating incorrect profiles is higher.

关键词： mixed-effect modeling model diagnostic models using input function visual predictive check

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Application of a hazard-based visual predictive check to evaluate parametric hazard models

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JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS 2016年第1期43卷 57-71页

作者： Huh, Yeamin Hutmacher, Matthew M. Ann Arbor Pharmacometr Grp Inc 301 N Main StSuite 102 Ann Arbor MI 48104 USA

Parametric models used in time to event analyses are evaluated typically by survival-based visual predictive checks (VPC). Kaplan Meier survival curves for the observed data are compared with those estimated using model-simulated data. Because the derivative of the log of the survival curve is related to the hazard the typical quantity modeled in parametric analysis isolation, interpretation and correction of deficiencies in the hazard model determined by inspection of survival-based VPC's is indirect and thus more difficult. The purpose of this study is to assess the performance of nonparametric hazard estimators of hazard functions to evaluate their viability as VPC diagnostics. Histogram-based and kernel -smoothing estimators were evaluated in terms of bias of estimating the hazard for Weibull and bathtub-shape hazard scenarios. After the evaluation of bias, these nonparametric estimators were assessed as a method for VPC evaluation of the hazard model. The results showed that nonparametric hazard estimators performed reasonably at the sample sizes studied with greater bias near the boundaries (time equal to 0 and last observation) as expected. Flexible bandwidth and boundary correction methods reduced these biases. All the nonparametric estimators indicated a misfit of the Weibull model when the true hazard was a bathtub shape. Overall, hazard -based VPC plots enabled more direct interpretation of the VPC results compared to survival -based VPC plots.

关键词： Time to event analysis visual predictive check Hazard Survival analysis

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Extensions to the visual predictive check to facilitate model performance evaluation

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JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS 2008年第2期35卷 185-202页

作者： Post, Teun M. Freijer, Jan I. Ploeger, Bart A. Danhof, Meindert Leiden Univ Leiden Amsterdam Ctr Drug Res Div Pharmacol NL-2300 RA Leiden Netherlands NV Organon NL-5340 BH Oss Netherlands Leiden Experts Adv Pharmacokinet & Pharmacodynam Leiden Netherlands Astellas Pharma Leiderdorp Netherlands

The visual predictive check (VPC) is a valuable and supportive instrument for evaluating model performance. However in its most commonly applied form, the method largely depends on a subjective comparison of the distribution of the simulated data with the observed data, without explicitly quantifying and relating the information in both. In recent adaptations to the VPC this drawback is taken into consideration by presenting the observed and predicted data as percentiles. In addition, in some of these adaptations the uncertainty in the predictions is represented visually. However, it is not assessed whether the expected random distribution of the observations around the predicted median trend is realised in relation to the number of observations. Moreover the influence of and the information residing in missing data at each time point is not taken into consideration. Therefore, in this investigation the VPC is extended with two methods to support a less subjective and thereby more adequate evaluation of model performance: (i) the Quantified visual predictive check (QVPC) and (ii) the Bootstrap visual predictive check (BVPC). The QVPC presents the distribution of the observations as a percentage, thus regardless the density of the data, above and below the predicted median at each time point, while also visualising the percentage of unavailable data. The BVPC weighs the predicted median against the 5th, 50th and 95th percentiles resulting from a bootstrap of the observed data median at each time point, while accounting for the number and the theoretical position of unavailable data. The proposed extensions to the VPC are illustrated by a pharmacokinetic simulation example and applied to a pharmacodynamic disease progression example.

关键词： visual predictive check pharmacokinetics pharmacodynamics disease progression evaluation validation qualification model performance

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Standardized visual predictive check Versus visual predictive check for Model Evaluation

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JOURNAL OF CLINICAL PHARMACOLOGY 2012年第1期52卷 39-54页

作者： Wang, Diane D. Zhang, Shuzhong Pfizer Oncol San Diego CA 92121 USA

The visual predictive check (VPC) is a commonly used approach in model evaluation. However, it may not be feasible to conduct a VPC, or the results of a VPC could be misleading in certain situations. The objectives of the present study were to (1) examine the performance and applicability of the VPC and (2) propose the standardized visual predictive check (SVPC) as an alternative/complementary approach to the VPC. The difference between the SVPC and normalized prediction distribution error (npde) as visual tools for model evaluation is also discussed. The results of the simulation studies demonstrate that the VPC is not appropriate when stratification of covariate(s) in a model is difficult or arbitrary and may not be feasible when study design varies during a study/among participants. The SVPC addresses these issues by displaying the percentiles (P(i,j)) of each participant's observations in the marginal distribution of the corresponding model-simulated endpoints as a function of time (or any covariate of interest) based on that participant's own design template. Since the calculation of P(i),(j) factors out subject-specific design features, the difference between observation and simulated values is only caused by misspecification of the structure model and/or inadequate estimation of random effect. Thus, the SVPC can be used in any situation.

关键词： pharmacokinetics pharmacodynamics model evaluation visual predictive check standardized visual predictive check prediction discrepancy normalized prediction distribution error

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Inverse probability of censoring weighting for visual predictive checks of time-to-event models with time-varying covariates

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PHARMACEUTICAL STATISTICS 2021年第6期20卷 1051-1060页

作者： Bartels, Christian Dumortier, Thomas Novartis Pharma AG Basel Switzerland

When constructing models to summarize clinical data to be used for simulations, it is good practice to evaluate the models for their capacity to reproduce the data. This can be done by means of visual predictive checks (VPC), which consist of several reproductions of the original study by simulation from the model under evaluation, calculating estimates of interest for each simulated study and comparing the distribution of those estimates with the estimate from the original study. This procedure is a generic method that is straightforward to apply, in general. Here we consider the application of the method to time-to-event data and consider the special case when a time-varying covariate is not known or cannot be approximated after event time. In this case, simulations cannot be conducted beyond the end of the follow-up time (event or censoring time) in the original study. Thus, the simulations must be censored at the end of the follow-up time. Since this censoring is not random, the standard KM estimates from the simulated studies and the resulting VPC will be biased. We propose to use inverse probability of censoring weighting (IPoC) method to correct the KM estimator for the simulated studies and obtain unbiased VPCs. For analyzing the Cantos study, the IPoC weighting as described here proved valuable and enabled the generation of VPCs to qualify PKPD models for simulations. Here, we use a generated data set, which allows illustration of the different situations and evaluation against the known truth.

关键词： inverse probability weighting model diagnostics time‐ to‐ event models time‐ varying covariates visual predictive check

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Population Pharmacokinetics of Cladribine in Patients with Multiple Sclerosis

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CLINICAL PHARMACOKINETICS 2017年第10期56卷 1245-1253页

作者： Savic, Radojka M. Novakovic, Ana M. Ekblom, Marianne Munafo, Alain Karlsson, Mats O. Univ Calif San Francisco Dept Bioengn & Therapeut Sci San Francisco CA 94143 USA Uppsala Univ Dept Pharmaceut Biosci Box 591 S-75124 Uppsala Sweden Persson Ekblom Sarl St Prex Switzerland Merck Inst Pharmacometr Lausanne Switzerland

The aims of this study were to characterize the concentration-time course of cladribine (CdA) and its main metabolite 2-chloroadenine (CAde), estimate interindividual variability in pharmacokinetics (PK), and identify covariates explaining variability in the PK of CdA. This population PK analysis was based on the combined dataset from four clinical studies in patients with multiple sclerosis (MS): three phase I studies, including one food and one drug-drug interaction study, and one phase III clinical study. Plasma and urine concentration data of CdA and CAde were modeled simultaneously. The analysis comprised a total of 2619 CdA and CAde plasma and urine concentration observations from 173 patients with MS who received an intravenous infusion or oral tablet doses of CdA as a single agent or in combination with interferon (IFN) beta-1a. CdA PK data were best described by a three-compartment model, while a one-compartment model best described the PK of CAde. CdA renal clearance (CLR) was correlated with creatinine clearance (CLCR), predicting a decrease in the total clearance of 19%, 30% and 40% for patients with mild (CLCR = 65 ml/min), moderate (CLCR = 40 ml/min) and severe (CLCR = 20 ml/min) renal impairment, respectively. Food decreased the extent of CdA absorption by 11.2% and caused an absorption delay. Coadministration with IFN beta-1a was found to increase non-CLR (CLNR) by 21%, resulting in an increase of 11% in total clearance. Both CdA and CAde displayed linear PK after intravenous and oral administration of CdA, with CdA renal function depending on CLCR. Trial registration number for study 25643: NCT00213135.

关键词： Absorption Delay Cladribine Multiple Sclerosis Oral Tablet visual predictive check

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Informative dropout modeling of longitudinal ordered categorical data and model validation: application to exposure-response modeling of physician's global assessment score for ustekinumab in patients with psoriasis

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JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS 2011年第2期38卷 237-260页

作者： Hu, Chuanpu Szapary, Philippe O. Yeilding, Newman Zhou, Honghui Centocor Res & Dev Inc Pharmacokinet & Pharmacometr Biol Clin Pharmacol Malvern PA 19355 USA Centocor Res & Dev Inc Clin Immunol Malvern PA 19355 USA

The physician's global assessment (PGA) score is a 6-point measure of psoriasis severity that is widely used in clinical trials to assess response to psoriasis treatment. The objective of this study was to perform exposure-response modeling using the PGA score as a pharmacodynamic endpoint following treatment with ustekinumab in patients with moderate-to-severe psoriasis who participated in two Phase 3 studies (PHOENIX 1 and PHOENIX 2). Patients were randomly assigned to receive ustekinumab 45 or 90 mg or placebo, followed by active treatment or placebo crossover to ustekinumab, dose intensification or randomized withdrawal and long-term extension periods. A novel joint longitudinal-dropout model was developed from serum ustekinumab concentrations, PGA scores, and patient dropout information. The exposure-response component employed a semi-mechanistic drug model, integrated with disease progression and placebo effect under the mixed-effect logistic regression framework. This allowed potential tolerance to be investigated with a mechanistic approach. The dropout component of the joint model allowed the examination of its potential influence on the exposure-response relationship. The flexible Weibull dropout hazard function was used. visual predictive check of the joint longitudinal-dropout model required special handling, and a conditional approach was proposed. The conditional approach was extended to external model validation. Finally, appropriate interpretation of model validation is discussed. This longitudinal-dropout model can serve as a basis to support future alternative dosing regimens for ustekinumab in patients with moderate-to-severe plaque psoriasis.

关键词： Monoclonal antibody Informative censoring Nonlinear mixed effect modeling visual predictive check NONMEM

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Automatic data binning for improved visual diagnosis of pharmacometric models

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JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS 2011年第6期38卷 861-871页

作者： Lavielle, Marc Bleakley, Kevin INRIA Saclay Orsay France Univ Paris 11 Orsay France

visual predictive checks (VPC) are graphical tools to help decide whether a given model could have plausibly generated a given set of real data. Typically, time-course data is binned into time intervals, then statistics are calculated on the real data and data simulated from the model, and represented graphically for each interval. Poor selection of bins can easily lead to incorrect model diagnosis. We propose an automatic binning strategy that improves reliability of model diagnosis using VPC. It is implemented in version 4 of the MONOLIX software.

关键词： visual predictive check Model diagnostic Binning Dynamic programming Model selection

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Pharmacokinetics, hemodynamic and metabolic effects of epinephrine to prevent post-operative low cardiac output syndrome in children

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CRITICAL CARE 2014年第1期18卷 1-14页

作者： Oualha, Mehdi Urien, Saik Spreux-Varoquaux, Odile Bordessoule, Alice D'Agostino, Irene Pouard, Philippe Treluyer, Jean-Marc Univ Paris 05 Hop Necker Enfants Malad AP HP Paris France Univ Paris 05 CIC Cochin Necker Inserm 0109 Unite Rech ClinParis Ctr Descartes Necker Cochin Serv PharmacolHop ChochinAP HP Paris France Univ Paris 05 EA 3620 Paris France Univ Versailles St Quentin En Yvelines Ctr Hosp Versailles Le Chesnay France

Introduction: The response to exogenous epinephrine (Ep) is difficult to predict given the multitude of factors involved such as broad pharmacokinetic and pharmacodynamic between-subject variabilities, which may be more pronounced in children. We investigated the pharmacokinetics and pharmacodynamics of Ep, co-administered with milrinone, in children who underwent open heart surgical repair for congenital defects following cardiopulmonary bypass, including associated variability factors. Methods: Thirty-nine children with a high risk of low cardiac output syndrome were prospectively enrolled. Ep pharmacokinetics, hemodynamic and metabolic effects were analyzed using the non-linear mixed effects modeling software MONOLIX. According to the final model, an Ep dosing simulation was suggested. Results: Ep dosing infusions ranged from 0.01 to 0.23 ***(-1). min(-1) in children whose weight ranged from 2.5 to 58 kg. A one-compartment open model with linear elimination adequately described the Ep concentration-time courses. Bodyweight (BW) was the main covariate influencing clearance (CL) and endogenous Ep production rate (q0) via an allometric relationship: CL(BWi) = theta(CL) x (BWi)(3/4) and q0(BWi) = theta(q0) x (BWi)(3/4). The increase in heart rate (HR) and mean arterial pressure (MAP) as a function of Ep concentration were well described using an Emax model. The effect of age was significant on HR and MAP basal level parameters. Assuming that Ep stimulated the production rate of plasma glucose, the increases in plasma glucose and lactate levels were well described by turnover models without any significant effect of age, BW or exogenous glucose supply. Conclusions: According to this population analysis, the developmental effects of BW and age explained a part of the pharmacokinetic and pharmacodynamics between-subject variabilities of Ep administration in critically ill children. This approach ultimately leads to a valuable Ep dosing simulation which should help cli

关键词： Mean Arterial Pressure Milrinone Noonan Syndrome visual predictive check Plasma Lactate Level

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