Celine M. Laffont

Metrics for external model evaluation with an application to the population pharmacokinetics of gliclazide.

PurposeThe aim of this study is to define and illustrate metrics for the external evaluation of a population model.Materials and MethodsIn this paper, several types of metrics are defined: based on observations (standardized prediction error with or without simulation and normalized prediction distribution error); based on hyperparameters (with or without simulation); based on the likelihood of the model. All the metrics described above are applied to evaluate a model built from two phase II studies of gliclazide. A real phase I dataset and two datasets simulated with the real dataset design are used as external validation datasets to show and compare how metrics are able to detect and explain potential adequacies or inadequacies of the model.ResultsNormalized prediction errors calculated without any approximation, and metrics based on hyperparameters or on objective function have good theoretical properties to be used for external model evaluation and showed satisfactory behaviour in the simulation study.ConclusionsFor external model evaluation, prediction distribution errors are recommended when the aim is to use the model to simulate data. Metrics through hyperparameters should be preferred when the aim is to compare two populations and metrics based on the objective function are useful during the model building process.

Similarity of bisphenol A pharmacokinetics in rhesus monkeys and mice: Relevance for human exposure

Objective Daily adult human exposure to bisphenol A (BPA) has been estimated at < 1 μg/kg, with virtually complete first-pass conjugation in the liver in primates but not in mice. We measured unconjugated and conjugated BPA levels in serum from adult female rhesus monkeys and adult female mice after oral administration of BPA and compared findings in mice and monkeys with prior published data in women. Methods Eleven adult female rhesus macaques were fed 400 μg/kg deuterated BPA (dBPA) daily for 7 days. Levels of serum dBPA were analyzed by isotope-dilution liquid chromatography–mass spectrometry (0.2 ng/mL limit of quantitation) over 24 hr on day 1 and on day 7. The same dose of BPA was fed to adult female CD-1 mice; other female mice were administered 3H-BPA at doses ranging from 2 to 100,000 μg/kg. Results In monkeys, the maximum unconjugated serum dBPA concentration of 4 ng/mL was reached 1 hr after feeding and declined to low levels by 24 hr, with no significant bioaccumulation after seven daily doses. Mice and monkeys cleared unconjugated serum BPA at virtually identical rates. We observed a linear (proportional) relationship between administered dose and serum BPA in mice. Conclusions BPA pharmacokinetics in women, female monkeys, and mice is very similar. By comparison with approximately 2 ng/mL unconjugated serum BPA reported in multiple human studies, the average 24-hr unconjugated serum BPA concentration of 0.5 ng/mL in both monkeys and mice after a 400 μg/kg oral dose suggests that total daily human exposure is via multiple routes and is much higher than previously assumed.

Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004.

Model evaluation is an important issue in population analyses. We aimed to perform a systematic review of all population pharmacokinetic and/or pharmacodynamic analyses published between 2002 and 2004 to survey the current methods used to evaluate models and to assess whether those models were adequately evaluated.We selected 324 articles in MEDLINE using defined key words and built a data abstraction form composed of a checklist of items to extract the relevant information from these articles with respect to model evaluation. In the data abstraction form, evaluation methods were divided into three subsections: basic internal methods (goodness-of-fit [GOF] plots, uncertainty in parameter estimates and model sensitivity), advanced internal methods (data splitting, resampling techniques and Monte Carlo simulations) and external model evaluation.Basic internal evaluation was the most frequently described method in the reports: 65% of the models involved GOF evaluation. Standard errors or confidence intervals were reported for 50% of fixed effects but only for 22% of random effects. Advanced internal methods were used in approximately 25% of models: data splitting was more often used than bootstrap and cross-validation; simulations were used in 6% of models to evaluate models by a visual predictive check or by a posterior predictive check. External evaluation was performed in only 7% of models.Using the subjective synthesis of model evaluation for each article, we judged the models to be adequately evaluated in 28% of pharmacokinetic models and 26% of pharmacodynamic models. Basic internal evaluation was preferred to more advanced methods, probably because the former is performed easily with most software. We also noticed that when the aim of modelling was predictive, advanced internal methods or more stringent methods were more often used.

Evaluation of different tests based on observations for external model evaluation of population analyses

To evaluate by simulation the statistical properties of normalized prediction distribution errors (NPDE), prediction discrepancies (pd), standardized prediction errors (SPE), numerical predictive check (NPC) and decorrelated NPC (NPCdec) for the external evaluation of a population pharmacokinetic analysis, and to illustrate the use of NPDE for the evaluation of covariate models. We assume that a model MB has been built using a building dataset B, and that a separate validation dataset, V is available. Our null hypothesis H0 is that the data in V can be described by MB. We use several methods to test this hypothesis: NPDE, pd, SPE, NPC and NPCdec. First, we evaluated by simulation the type I error under H0 of different tests applied to the four methods. We also propose and evaluate a single global test combining normality, mean and variance tests applied to NPDE, pd and SPE. We perform tests on NPC and NPCdec, after a decorrelation. MB was a one compartment model with first order absorption (without covariate), previously developed from two phase II and one phase III studies of the antidiabetic drug, gliclazide. We simulated 500 external datasets according to the design of a phase III study. Second, we investigated the application of NPDE to covariate models. We propose two approaches: the first approach uses correlation tests or mean comparisons to test the relationship between NPDE and covariates; the second evaluates NPDE split by category for discrete covariates or quantiles for continuous covariates. We generated several validation datasets under H0 and under alternative assumptions with a model without covariate, with one continuous covariate (weight), or one categorical covariate (sex). We calculated the powers of the different tests using simulations, where the covariates of the phase III study were used. The simulations under H0 show a high type I error for the different tests applied to SPE and an increased type I error for pd. The different tests present a type I error close to 5% for the global test appied to NPDE. We find a type I error higher than 5% for the test applied to classical NPC but this test becomes close to 5% for NPCdec. For covariate models, when model and validation dataset are consistent, type I error of the tests are close to 5% for both effects. When validation datasets and models are not consistent, the tests detect the correlation between NPDE and the covariate. We recommend to use NPDE over SPE for external model evaluation, since they do not depend on an approximation of the model and have good statistical properties. NPDE represent a better approach than NPC, since in order to perform tests on NPC, a decorrelation step must be applied before. NPDE, in this illustration, is also a good tool to evaluate model with or without covariates.

Population pharmacokinetic modeling and simulation to guide dose selection for RBP‐7000, a new sustained‐release formulation of risperidone

RBP‐7000 is a long‐acting formulation of risperidone designed for once‐monthly subcutaneous injection for the treatment of schizophrenia. The objective was to estimate clinically effective doses of RBP‐7000 based on model simulations and on the comparison with other long‐acting injectable antipsychotics. A population pharmacokinetic model of RBP‐7000 was developed in 90 clinically stable schizophrenic patients having received single/repeated doses of 60, 90, or 120 mg. Model simulations were conducted to compare active moiety plasma exposure after repeated RBP‐7000 administrations to the published data of long‐acting risperidone injection (Risperdal® Consta®) at 25 and 50 mg, and of paliperidone palmitate (Invega® Sustenna®) at 50 and 100 mg equivalent paliperidone. Predictions of dopamine D2 receptor occupancy were derived from the simulated active moiety concentrations. Simulations showed similar active moiety plasma exposure at steady‐state for 90 mg of RBP‐7000 and 25 mg of long‐acting risperidone. In comparison to risperidone, RBP‐7000 reached effective concentrations immediately after the first administration. RBP‐7000 at the doses of 60 and 90 mg provided similar active moiety plasma concentrations at steady‐state compared to 50 and 100 mg equivalent paliperidone, respectively. These findings provide guidance for dose selection in Phase III clinical trials and suggest potential benefits for RBP‐7000 over competitors.

A whole-body physiologically based pharmacokinetic (WB-PBPK) model of ciprofloxacin : a step towards predicting bacterial killing at sites of infection.

The purpose of this study was to develop a whole-body physiologically based pharmacokinetic (WB-PBPK) model for ciprofloxacin for ICU patients, based on only plasma concentration data. In a next step, tissue and organ concentration time profiles in patients were predicted using the developed model. The WB-PBPK model was built using a non-linear mixed effects approach based on data from 102 adult intensive care unit patients. Tissue to plasma distribution coefficients (Kp) were available from the literature and used as informative priors. The developed WB-PBPK model successfully characterized both the typical trends and variability of the available ciprofloxacin plasma concentration data. The WB-PBPK model was thereafter combined with a pharmacokinetic–pharmacodynamic (PKPD) model, developed based on in vitro time-kill data of ciprofloxacin and Escherichia coli to illustrate the potential of this type of approach to predict the time-course of bacterial killing at different sites of infection. The predicted unbound concentration–time profile in extracellular tissue was driving the bacterial killing in the PKPD model and the rate and extent of take-over of mutant bacteria in different tissues were explored. The bacterial killing was predicted to be most efficient in lung and kidney, which correspond well to ciprofloxacin’s indications pneumonia and urinary tract infections. Furthermore, a function based on available information on bacterial killing by the immune system in vivo was incorporated. This work demonstrates the development and application of a WB-PBPK–PD model to compare killing of bacteria with different antibiotic susceptibility, of value for drug development and the optimal use of antibiotics .

Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis

Our objective was to evaluate the efficacy of robenacoxib in osteoarthritic dogs using four ordinal responses measured repeatedly over time. We propose a multivariate probit mixed effects model to describe the joint evolution of endpoints and to evidence the intrinsic correlations between responses that are not due to treatment effect. Maximum likelihood computation is intractable within reasonable time frames. We therefore use a pairwise modeling approach in combination with a stochastic EM algorithm. Multidimensional ordinal responses with longitudinal measurements are a common feature in clinical trials. However, the standard methods for data analysis use unidimensional models, resulting in a loss of information. Our methodology provides substantially greater insight than these methods for the evaluation of treatment effects and shows a good performance at low computational cost. We thus believe that it could be used in routine practice to optimize the evaluation of treatment efficacy.

Population Pharmacokinetic Modeling After Repeated Administrations of RBP‐6000, a New, Subcutaneously Injectable, Long‐Acting, Sustained‐Release Formulation of Buprenorphine, for the Treatment of Opioid Use Disorder

RBP‐6000 is a novel sustained‐release formulation of buprenorphine for the treatment of opioid use disorder, which has been designed for once‐monthly (28 days) subcutaneous (SC) injections. A population pharmacokinetic (PK) model was developed to describe the time course of buprenorphine plasma concentrations after repeated SC injections of RBP‐6000 at 50 mg, 100 mg, 200 mg, or 300 mg in treatment‐seeking opioid‐dependent subjects previously on sublingual buprenorphine (Subutex®) treatment. The μ‐opioid receptor occupancy was predicted using a previously developed PK/PD Emax model. The results of the population PK analysis jointly with the predicted level of μ‐opioid receptor occupancy provided quantitative criteria for clinical dose selection for RBP‐6000: the dose of 300 mg every 28 days seems appropriate for immediately achieving an effective exposure after the first SC injection and to maintain effective levels of exposure during chronic treatment. Furthermore, simulations conducted to evaluate the potential impact of a holiday in drug intake indicated that in the unexpected event of a 2‐week holiday, levels of μ‐opioid receptor occupancy remained consistently above 70% with no significant loss of drug efficacy. This analysis indicated that RBP‐6000 has the potential for becoming an effective treatment for opioid‐dependent subjects by addressing compliance issues associated with the current once‐a‐day treatments.

A New Exact Test for the Evaluation of Population Pharmacokinetic and/or Pharmacodynamic Models Using Random Projections

ABSTRACTPurposeWithin-subject dependency of observations has a strong impact on the evaluation of population pharmacokinetic (PK) and/or pharmacodynamic (PD) models. To our knowledge, none of the current model evaluation tools correctly address this issue. We present a new method with a global test and easy diagnostic plot which relies on the use of a random projection technique that allows the analysis of dependent data.MethodsFor each subject, the vector of standardised residuals is calculated and projected onto many random directions drawn uniformly from the unit sphere. Our test compares the empirical distribution of projections with their distribution under the model. Simulation studies assess the level of the test and compare its performance with common metrics including normalised prediction distribution errors and different types of weighted residuals. An application to real data is performed.ResultsIn contrast to other evaluated methods, our test shows adequate level for all models and designs investigated, which confirms its good theoretical properties. The weakness of other methods is demonstrated and discussed.ConclusionsThis new test appears promising and could be used in combination with other tools to drive model evaluation in population PK/PD analyses.