Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Bazzoli, Caroline; Retout, Sylvie

doi:10.1002/sim.3573

Cited by 30 publications

(38 citation statements)

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“…, m γ ; γ 0 is an (m γ × 1)-vector of population means, and Ω is an (m γ × m γ ) variance--covariance matrix of i.i.d. random vectors γ i in (5) or ζ i in (6). The vector γ 0 and the matrix Ω are often referred to as population parameters.…”

Section: Modelmentioning

confidence: 99%

“…The model was parameterized via clearance CL, so that K e = CL/V . It was assumed that the individual response parameters γ i = (K ai , CL i , V i ) follow the log-normal distribution (6) with the mean vector γ 0 = (1, 0.15, 8) and the diagonal covariance matrix Ω = Diag(ω …”

Section: Software Comparisonmentioning

confidence: 99%

“…The discussion of different software tools for population PK/PD optimal designs started at PODE 2007 and continued at every workshop since then. The discussed software packages include PFIM (see B a z z o l i et al [6]), PkStaMp (see A l i e v et al [2]), PopDes (see G u e o r g u i e v a et al [13]), PopED (see N y b e r g et al [20]), and WinPOPT (see D u f f u l l et al [7]). …”

Section: Introductionmentioning

confidence: 99%

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Optimal design for population pk/pd models

Leonov

Aliev

2012

Tatra Mountains Mathematical Publications

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Section: Modelmentioning

confidence: 99%

Section: Software Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal design for population pk/pd models

Leonov

Aliev

2012

Tatra Mountains Mathematical Publications

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“…To avoid simulations, which are time consuming, designs can be evaluated using the Fisher information matrix (M F ) and the optimization of its determinant. [8] The calculation of the M F for the non-linear mixed-effects model was first developed by Mentré et al [7] and Retout et al [9] for uniresponse non-linear mixed-effects modelling and then extended to multi-response population pharmacokinetic/pharmacodynamic models [8,10] using a first-order Taylor expansion of the population pharmacokinetic model around the random effect. [7,11,12] The calculation of the M F for non-linear mixed-effects modelling used in population pharmacokinetics is performed in software packages, including PFIM developed in R, dedicated to design evaluation and optimization.…”

Section: Introductionmentioning

confidence: 99%

Optimal Sampling Times for a Drug and its Metabolite using SIMCYP® Simulations as Prior Information

et al. 2012

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Background: Since 2007, it is mandatory for the pharmaceutical companies to submit a Paediatric Investigation Plan to the Paediatric Committee at the European Medicines Agency for any drug in development in adults, and it often leads to the need to conduct a pharmacokinetic study in children. Pharmacokinetic studies in children raise ethical and methodological issues. Because of limitation of sampling times, appropriate methods, such as the population approach, are necessary for analysis of the pharmacokinetic data. The choice of the pharmacokinetic sampling design has an important impact on the precision of population parameter estimates. Approaches for design evaluation and optimization based on the evaluation of the Fisher information matrix (M F ) have been proposed and are now implemented in several software packages, such as PFIM in R.Objectives: The objectives of this work were to (i) develop a joint population pharmacokinetic model to describe the pharmacokinetic characteristics of a drug S and its active metabolite in children after intravenous drug administration from simulated plasma concentration-time data produced using physiologically based pharmacokinetic (PBPK) predictions; (ii) optimize the pharmacokinetic sampling times for an upcoming clinical study using a multi-response design approach, considering clinical constraints; and iii) evaluate the resulting design taking data below the lower limit of quantification (BLQ) into account.Methods: Plasma concentration-time profiles were simulated in children using a PBPK model previously developed with the software SIMCYP ® for the parent drug and its active metabolite. Data were analysed using non-linear mixed-effect models with the software NONMEM ® , using a joint model for the parent drug and its metabolite. The population pharmacokinetic design, for the future study in 82 children from 2 to 18 years old, each receiving a single dose of the drug, was then optimized using PFIM, assuming identical times for parent and metabolite concentration measurements and considering clinical constraints. Design evaluation was based on the relative standard errors (RSEs) of the parameters of interest. In the final evaluation of the proposed design, an approach was used to assess the possible effect of BLQ concentrations on the design efficiency. This approach consists of rescaling the M F , using, at each sampling time, the probability of observing a concentration BLQ computed from Monte-Carlo simulations.Results: A joint pharmacokinetic model with three compartments for the parent drug and one for its active metabolite, with random effects on four parameters, was used to fit the simulated PBPK concentration-time data. A combined error model best described the residual variability. Parameters and dose were expressed per kilogram of bodyweight. Reaching a compromise between PFIM results and clinical constraints, the optimal design was composed of four samples at 0.1, 1.8, 5 and 10 h after drug injection. This design predicted RSE lower than 30 % for the fo...

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“…This approach relies on the Cramer-Rao inequality, which states that the inverse of the MF is the lower bound of the variance-covariance matrix of any unbiased estimator of the parameters. Expressions of the expected individual (MIF) and population Fisher information matrix (MPF) using first-order (FO) approximation [5,6] have been developed and implemented in several software programs [7,8] to evaluate and optimize 4 designs for standard individual regression or population analysis, respectively. Beside MIF and MPF, the expected Bayesian Fisher information matrix (MBF) was also developed to evaluate the estimation error of individual parameters obtained by MAP [9,10].…”

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confidence: 99%

Individual Bayesian Information Matrix for Predicting Estimation Error and Shrinkage of Individual Parameters Accounting for Data Below the Limit of Quantification

Nguyen

Nguyễn

2017

Pharm Res

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Purpose: In mixed models, the relative standard errors (RSE) and shrinkage of individual parameters can be predicted from the individual Bayesian information matrix (MBF).We proposed an approach accounting for data below the limit of quantification (LOQ) in MBF.Methods: MBF is the sum of the expectation of the individual Fisher information (MIF) which can be evaluated by First-Order linearization and the inverse of random effect variance.We expressed the individual information as a weighted sum of predicted MIF for every possible design composing of measurements above and/or below LOQ. When evaluating MIF, we derived the likelihood expressed as the product of the likelihood of observed data and the 2 probability for data to be below LOQ. The relevance of RSE and shrinkage predicted by MBF in absence or presence of data below LOQ were evaluated by simulations, using a pharmacokinetic/viral kinetic model defined by differential equations. Results:Simulations showed good agreement between predicted and observed RSE and shrinkage in absence or presence of data below LOQ. We found that RSE and shrinkage increased with sparser designs and with data below LOQ. Conclusions:The proposed method based on MBF adequately predicted individual RSE and shrinkage, allowing for evaluation of a large number of scenarios without extensive simulations. KEYWORDS: Bayesian Fisher information matrix; Data below the limit of quantification;Nonlinear mixed effect models; Optimal design; Shrinkage. ABBREVIATIONS: FO

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Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

Cited by 30 publications

References 35 publications

Optimal design for population pk/pd models

Optimal design for population pk/pd models

Optimal Sampling Times for a Drug and its Metabolite using SIMCYP® Simulations as Prior Information

Individual Bayesian Information Matrix for Predicting Estimation Error and Shrinkage of Individual Parameters Accounting for Data Below the Limit of Quantification

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