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Yamaguchi D, Katsube T, Wajima T. Evaluation and optimization of sample size of neonates and infants for pediatric clinical studies on cefiderocol using a model-based approach. Pharmacol Res Perspect 2024; 12:e70001. [PMID: 39180172 PMCID: PMC11343721 DOI: 10.1002/prp2.70001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Revised: 07/17/2024] [Accepted: 08/06/2024] [Indexed: 08/26/2024] Open
Abstract
When planning pediatric clinical trials, optimizing the sample size of neonates/infants is essential because it is difficult to enroll these subjects. In this simulation study, we evaluated the sample size of neonates/infants using a model-based optimal approach for identifying their pharmacokinetics for cefiderocol. We assessed the usefulness of data for estimation performance (accuracy and variance of parameter estimation) from adults and the impact of data from very young subjects, including preterm neonates. Stochastic simulation and estimation were utilized to assess the impact of sample size allocation for age categories in estimation performance for population pharmacokinetic parameters in pediatrics. The inclusion of adult pharmacokinetic information improved the estimation performance of population pharmacokinetic parameters as the coefficient of variation (CV) range of parameter estimation decreased from 4.9%-593.7% to 2.3%-17.3%. When sample size allocation was based on the age groups of gestational age and postnatal age, the data showed 15 neonates/infants would be necessary to appropriately estimate pediatric pharmacokinetic parameters (<20%CV). By using the postmenstrual age (PMA), which is theoretically considered to be associated with the maturation of organs, the number of neonates/infants required for appropriate parameter estimation could be reduced to seven (one and six with <32 and >32 weeks PMA, respectively) to nine (three and six with <37 and >37 weeks PMA, respectively) subjects. The model-based optimal design approach allowed efficient evaluation of the sample size of neonates/infants for estimation of pediatric pharmacokinetic parameters. This approach to assessment should be useful when designing pediatric clinical trials, especially those including young children.
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Affiliation(s)
- Daichi Yamaguchi
- Clinical Pharmacology & PharmacokineticsShionogi & Co., Ltd.OsakaJapan
| | - Takayuki Katsube
- Clinical Pharmacology & PharmacokineticsShionogi & Co., Ltd.OsakaJapan
| | - Toshihiro Wajima
- Pharmacokinetics/Pharmacodynamics & PharmacometricsJapan Drug Development & Medical Affairs, Eli Lilly Japan K.KKobeJapan
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2
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van Noort M, Ruppert M. Two new user-friendly methods to assess pharmacometric parameter identifiability on categorical and continuous scales. CPT Pharmacometrics Syst Pharmacol 2024; 13:1160-1169. [PMID: 38715388 PMCID: PMC11247123 DOI: 10.1002/psp4.13147] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 03/07/2024] [Accepted: 04/10/2024] [Indexed: 07/16/2024] Open
Abstract
Parameter identifiability methods assess whether the parameters of a model are uniquely determined by the observations. While the success of a model fit can provide some information on this, it can be valuable to determine identifiability before any fit has been attempted, or to separate identifiability from other issues. Two concepts that lean themselves well for identifiability analysis and have been underutilized are the sensitivity matrix (SM) and the Fisher information matrix (FIM). This paper presents two newly developed methods, one based on the SM and one based on the FIM. Both methods can assess local identifiability for a wide set of models, can be used with limited effort, and are freely available. The methods require the proposed model in the form of a set of differential equations, the parameter values, and the study design as input. They can be used a priori, as they do not need observed values or a successful model fit. Traditional methods provide a single categorical (yes/no) answer to the question of identifiability. In many cases, this is not very informative, and identifiability depends on study design (e.g., dose levels or observation times) and parameter values. Indicators on a continuous scale characterizing the level of identifiability would provide more detailed and relevant information, for example, to guide model development. Our two methods provide both categorical and continuous indicators. Both methods indicate which parameter combinations are difficult to identify by calculating the directions in parameter space that are least identifiable. The methods were validated with an example problem.
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3
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van Noort M, Ruppert M, DeJongh J, Marostica E, Bosch R, Mešić E, Snelder N. Navigating the landscape of parameter identifiability methods: A workflow recommendation for model development. CPT Pharmacometrics Syst Pharmacol 2024; 13:1170-1179. [PMID: 38715385 PMCID: PMC11247124 DOI: 10.1002/psp4.13148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 03/07/2024] [Accepted: 04/10/2024] [Indexed: 07/16/2024] Open
Abstract
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.
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Affiliation(s)
| | | | | | | | | | - Emir Mešić
- LAP&P Consultants BV, Leiden, The Netherlands
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4
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Mc Laughlin AM, Milligan PA, Yee C, Bergstrand M. Model-informed drug development of autologous CAR-T cell therapy: Strategies to optimize CAR-T cell exposure leveraging cell kinetic/dynamic modeling. CPT Pharmacometrics Syst Pharmacol 2023; 12:1577-1590. [PMID: 37448343 PMCID: PMC10681459 DOI: 10.1002/psp4.13011] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Revised: 06/23/2023] [Accepted: 07/10/2023] [Indexed: 07/15/2023] Open
Abstract
Autologous Chimeric antigen receptor (CAR-T) cell therapy has been highly successful in the treatment of aggressive hematological malignancies and is also being evaluated for the treatment of solid tumors as well as other therapeutic areas. A challenge, however, is that up to 60% of patients do not sustain a long-term response. Low CAR-T cell exposure has been suggested as an underlying factor for a poor prognosis. CAR-T cell therapy is a novel therapeutic modality with unique kinetic and dynamic properties. Importantly, "clear" dose-exposure relationships do not seem to exist for any of the currently approved CAR-T cell products. In other words, dose increases have not led to a commensurate increase in the measurable in vivo frequency of transferred CAR-T cells. Therefore, alternative approaches beyond dose titration are needed to optimize CAR-T cell exposure. In this paper, we provide examples of actionable variables - design elements in CAR-T cell discovery, development, and clinical practice, which can be modified to optimize autologous CAR-T cell exposure. Most of these actionable variables can be assessed throughout the various stages of discovery and development as part of a well-informed research and development program. Model-informed drug development approaches can enable such study and program design choices from discovery through to clinical practice and can be an important contributor to cell therapy effectiveness and efficiency.
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Affiliation(s)
| | | | - Cassian Yee
- Department of Melanoma Medical OncologyThe University of Texas MD Anderson Cancer CenterHoustonTexasUSA
- Department of ImmunologyThe University of Texas MD Anderson Cancer CenterHoustonTexasUSA
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5
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Kim S, Hooker AC, Shi Y, Kim GHJ, Wong WK. Metaheuristics for pharmacometrics. CPT Pharmacometrics Syst Pharmacol 2021; 10:1297-1309. [PMID: 34562342 PMCID: PMC8592519 DOI: 10.1002/psp4.12714] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 08/06/2021] [Accepted: 09/07/2021] [Indexed: 12/22/2022] Open
Abstract
Metaheuristics is a powerful optimization tool that is increasingly used across disciplines to tackle general purpose optimization problems. Nature-inspired metaheuristic algorithms is a subclass of metaheuristic algorithms and have been shown to be particularly flexible and useful in solving complicated optimization problems in computer science and engineering. A common practice with metaheuristics is to hybridize it with another suitably chosen algorithm for enhanced performance. This paper reviews metaheuristic algorithms and demonstrates some of its utility in tackling pharmacometric problems. Specifically, we provide three applications using one of its most celebrated members, particle swarm optimization (PSO), and show that PSO can effectively estimate parameters in complicated nonlinear mixed-effects models and to gain insights into statistical identifiability issues in a complex compartment model. In the third application, we demonstrate how to hybridize PSO with sparse grid, which is an often-used technique to evaluate high dimensional integrals, to search for D -efficient designs for estimating parameters in nonlinear mixed-effects models with a count outcome. We also show the proposed hybrid algorithm outperforms its competitors when sparse grid is replaced by its competitor, adaptive gaussian quadrature to approximate the integral, or when PSO is replaced by three notable nature-inspired metaheuristic algorithms.
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Affiliation(s)
- Seongho Kim
- Department of OncologyWayne State UniversityDetroitMichiganUSA
| | | | - Yu Shi
- Department of BiostatisticsUniversity of California Los AngelesLos AngelesCaliforniaUSA
| | - Grace Hyun J. Kim
- Department of BiostatisticsUniversity of California Los AngelesLos AngelesCaliforniaUSA
| | - Weng Kee Wong
- Department of BiostatisticsUniversity of California Los AngelesLos AngelesCaliforniaUSA
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6
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Germovsek E, Barker CIS, Sharland M, Standing JF. Pharmacokinetic-Pharmacodynamic Modeling in Pediatric Drug Development, and the Importance of Standardized Scaling of Clearance. Clin Pharmacokinet 2020; 58:39-52. [PMID: 29675639 PMCID: PMC6325987 DOI: 10.1007/s40262-018-0659-0] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Pharmacokinetic/pharmacodynamic (PKPD) modeling is important in the design and conduct of clinical pharmacology research in children. During drug development, PKPD modeling and simulation should underpin rational trial design and facilitate extrapolation to investigate efficacy and safety. The application of PKPD modeling to optimize dosing recommendations and therapeutic drug monitoring is also increasing, and PKPD model-based dose individualization will become a core feature of personalized medicine. Following extensive progress on pediatric PK modeling, a greater emphasis now needs to be placed on PD modeling to understand age-related changes in drug effects. This paper discusses the principles of PKPD modeling in the context of pediatric drug development, summarizing how important PK parameters, such as clearance (CL), are scaled with size and age, and highlights a standardized method for CL scaling in children. One standard scaling method would facilitate comparison of PK parameters across multiple studies, thus increasing the utility of existing PK models and facilitating optimal design of new studies.
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Affiliation(s)
- Eva Germovsek
- Infection, Inflammation and Rheumatology Section, UCL Great Ormond Street Institute of Child Heath, University College London, London, UK. .,Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University, PO Box 591, 751 24, Uppsala, Sweden.
| | - Charlotte I S Barker
- Infection, Inflammation and Rheumatology Section, UCL Great Ormond Street Institute of Child Heath, University College London, London, UK.,Paediatric Infectious Diseases Research Group, Institute for Infection and Immunity, St George's, University of London, London, UK.,St George's University Hospitals NHS Foundation Trust, London, UK
| | - Mike Sharland
- Paediatric Infectious Diseases Research Group, Institute for Infection and Immunity, St George's, University of London, London, UK.,St George's University Hospitals NHS Foundation Trust, London, UK
| | - Joseph F Standing
- Infection, Inflammation and Rheumatology Section, UCL Great Ormond Street Institute of Child Heath, University College London, London, UK.,Paediatric Infectious Diseases Research Group, Institute for Infection and Immunity, St George's, University of London, London, UK
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7
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Hill AC, Rower JE, White HS. The pharmacokinetics of oral carbamazepine in rats dosed using an automated drug delivery system. Epilepsia 2019; 60:1829-1837. [DOI: 10.1111/epi.16293] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 06/28/2019] [Accepted: 06/28/2019] [Indexed: 12/25/2022]
Affiliation(s)
- A. Cameron Hill
- Department of Pharmacology & Toxicology University of Utah Salt Lake City Utah
| | - Joseph E. Rower
- Department of Pharmacology & Toxicology University of Utah Salt Lake City Utah
| | - H. Steve White
- School of Pharmacy University of Washington Seattle Washington
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8
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Dumont C, Lestini G, Le Nagard H, Mentré F, Comets E, Nguyen TT. PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2018; 156:217-229. [PMID: 29428073 DOI: 10.1016/j.cmpb.2018.01.008] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 12/22/2017] [Accepted: 01/10/2018] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Cyrielle Dumont
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France; University of Lille, EA 2694, Public Health: Epidemiology and Healthcare Quality, ILIS, Lille, F-59000, France
| | - Giulia Lestini
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France
| | - Hervé Le Nagard
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France
| | - France Mentré
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France
| | - Emmanuelle Comets
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France
| | - Thu Thuy Nguyen
- IAME, UMR 1137, INSERM and University Paris Diderot, Sorbonne Paris Cité, Paris, F-75018, France.
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9
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Alam MI, Bogacka B, Coad DS. Pharmacokinetically guided optimum adaptive dose selection in early phase clinical trials. Comput Stat Data Anal 2017. [DOI: 10.1016/j.csda.2017.02.009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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10
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Bellanti F, Di Iorio VL, Danhof M, Della Pasqua O. Sampling Optimization in Pharmacokinetic Bridging Studies: Example of the Use of Deferiprone in Children With β-Thalassemia. J Clin Pharmacol 2016; 56:1094-103. [PMID: 26785826 DOI: 10.1002/jcph.708] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2015] [Accepted: 01/13/2016] [Indexed: 01/19/2023]
Abstract
Despite wide clinical experience with deferiprone, the optimum dosage in children younger than 6 years remains to be established. This analysis aimed to optimize the design of a prospective clinical study for the evaluation of deferiprone pharmacokinetics in children. A 1-compartment model with first-order oral absorption was used for the purposes of the analysis. Different sampling schemes were evaluated under the assumption of a constrained population size. A sampling scheme with 5 samples per subject was found to be sufficient to ensure accurate characterization of the pharmacokinetics of deferiprone. Whereas the accuracy of parameters estimates was high, precision was slightly reduced because of the small sample size (CV% >30% for Vd/F and KA). Mean AUC ± SD was found to be 33.4 ± 19.2 and 35.6 ± 20.2 mg · h/mL, and mean Cmax ± SD was found to be 10.2 ± 6.1 and 10.9 ± 6.7 mg/L based on sparse and frequent sampling, respectively. The results showed that typical frequent sampling schemes and sample sizes do not warrant accurate model and parameter identifiability. Expectation of the determinant (ED) optimality and simulation-based optimization concepts can be used to support pharmacokinetic bridging studies. Of importance is the accurate estimation of the magnitude of the covariate effects, as they partly determine the dose recommendation for the population of interest.
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Affiliation(s)
- Francesco Bellanti
- Division of Pharmacology, Leiden Academic Centre for Drug Research, London, UK
| | | | - Meindert Danhof
- Division of Pharmacology, Leiden Academic Centre for Drug Research, London, UK
| | - Oscar Della Pasqua
- Division of Pharmacology, Leiden Academic Centre for Drug Research, London, UK.,Clinical Pharmacology Modelling & Simulation, GlaxoSmithKline, Stockley Park, UK.,Clinical Pharmacology & Therapeutics, University College London, London, UK
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11
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Nguyen TT, Bénech H, Delaforge M, Lenuzza N. Design optimisation for pharmacokinetic modeling of a cocktail of phenotyping drugs. Pharm Stat 2015; 15:165-77. [DOI: 10.1002/pst.1731] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2015] [Indexed: 12/24/2022]
Affiliation(s)
- Thu Thuy Nguyen
- CEA, LIST; Data Analysis and Systems Intelligence Laboratory; Gif-sur-Yvette France
| | | | | | - Natacha Lenuzza
- CEA, LIST; Data Analysis and Systems Intelligence Laboratory; Gif-sur-Yvette France
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12
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Perera V, Bies RR, Mo G, Dolton MJ, Carr VJ, McLachlan AJ, Day RO, Polasek TM, Forrest A. Optimal sampling of antipsychotic medicines: a pharmacometric approach for clinical practice. Br J Clin Pharmacol 2015; 78:800-14. [PMID: 24773369 DOI: 10.1111/bcp.12410] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Accepted: 04/19/2014] [Indexed: 11/28/2022] Open
Abstract
AIM To determine optimal sampling strategies to allow the calculation of clinical pharmacokinetic parameters for selected antipsychotic medicines using a pharmacometric approach. METHODS This study utilized previous population pharmacokinetic parameters of the antipsychotic medicines aripiprazole, clozapine, olanzapine, perphenazine, quetiapine, risperidone (including 9-OH risperidone) and ziprasidone. d-optimality was utilized to identify time points which accurately predicted the pharmacokinetic parameters (and expected error) of each drug at steady-state. A standard two stage population approach (STS) with MAP-Bayesian estimation was used to compare area under the concentration-time curves (AUC) generated from sparse optimal time points and rich extensive data. Monte Carlo Simulation (MCS) was used to simulate 1000 patients with population variability in pharmacokinetic parameters. Forward stepwise regression analysis was used to determine the most predictive time points of the AUC for each drug at steady-state. RESULTS Three optimal sampling times were identified for each antipsychotic medicine. For aripiprazole, clozapine, olanzapine, perphenazine, risperidone, 9-OH risperidone, quetiapine and ziprasidone the CV% of the apparent clearance using optimal sampling strategies were 19.5, 8.6, 9.5, 13.5, 12.9, 10.0, 16.0 and 10.7, respectively. Using the MCS and linear regression approach to predict AUC, the recommended sampling windows were 16.5-17.5 h, 10-11 h, 23-24 h, 19-20 h, 16.5-17.5 h, 22.5-23.5 h, 5-6 h and 5.5-6.5 h, respectively. CONCLUSION This analysis provides important sampling information for future population pharmacokinetic studies and clinical studies investigating the pharmacokinetics of antipsychotic medicines.
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Affiliation(s)
- Vidya Perera
- School of Pharmacy and Pharmaceutical Sciences, School of Pharmacy, SUNY at Buffalo, Buffalo, NY, USA; Schizophrenia Research Institute, Sydney, Australia
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13
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Simultaneous optimal experimental design for in vitro binding parameter estimation. J Pharmacokinet Pharmacodyn 2013; 40:573-85. [PMID: 23943088 DOI: 10.1007/s10928-013-9330-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Accepted: 08/03/2013] [Indexed: 10/26/2022]
Abstract
Simultaneous optimization of in vitro ligand binding studies using an optimal design software package that can incorporate multiple design variables through non-linear mixed effect models and provide a general optimized design regardless of the binding site capacity and relative binding rates for a two binding system. Experimental design optimization was employed with D- and ED-optimality using PopED 2.8 including commonly encountered factors during experimentation (residual error, between experiment variability and non-specific binding) for in vitro ligand binding experiments: association, dissociation, equilibrium and non-specific binding experiments. Moreover, a method for optimizing several design parameters (ligand concentrations, measurement times and total number of samples) was examined. With changes in relative binding site density and relative binding rates, different measurement times and ligand concentrations were needed to provide precise estimation of binding parameters. However, using optimized design variables, significant reductions in number of samples provided as good or better precision of the parameter estimates compared to the original extensive sampling design. Employing ED-optimality led to a general experimental design regardless of the relative binding site density and relative binding rates. Precision of the parameter estimates were as good as the extensive sampling design for most parameters and better for the poorly estimated parameters. Optimized designs for in vitro ligand binding studies provided robust parameter estimation while allowing more efficient and cost effective experimentation by reducing the measurement times and separate ligand concentrations required and in some cases, the total number of samples.
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Chakrabarty A, Buzzard GT, Rundell AE. Model-based design of experiments for cellular processes. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2013; 5:181-203. [PMID: 23293047 DOI: 10.1002/wsbm.1204] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Ankush Chakrabarty
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
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15
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Taneja A, Nyberg J, Danhof M, Della Pasqua O. Optimised protocol design for the screening of analgesic compounds in neuropathic pain. J Pharmacokinet Pharmacodyn 2012. [PMID: 23197246 DOI: 10.1007/s10928-012-9277-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
We have previously shown how screening experiments for neuropathic pain can be optimised taking into account parameter and model uncertainty. Here we demonstrate how optimised protocols can be used to screen and rank candidate molecules. The concept is illustrated by pregabalin as a new chemical entity and gabapentin as a reference compound. ED-optimality was applied to a logistic regression model describing the relationship between drug exposure and response to evoked pain in the complete Freund's adjuvant (CFA) model in rats. Design variables for optimisation of the experimental protocol included dose levels and sampling times. Prior information from the reference compound was used in conjunction with relative in vitro potency as priors. Results from simulated scenarios were then combined with fitting of experimental data to estimate precision and bias of model parameters for the empirical and optimised designs. The pharmacokinetics of pregabalin was described by a two-compartment model. The expected value of EC(50) of pregabalin was 637.5 ng ml(-1). Model-based analysis of the data yielded median (range) of EC(50) values of 1,125 (898-2412) ng ml(-1) for the empirical protocol and 755 (189-756) ng ml(-1) for the optimised design. In contrast to current practice, optimal design entails different sampling schedule across dose levels. ED-optimised designs should become standard practice in the screening of candidate molecules. It ensures lower bias when estimating the drug potency, facilitating accurate ranking and selection of compounds for further development.
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Affiliation(s)
- A Taneja
- Division of Pharmacology, LACDR, Leiden University, Leiden, The Netherlands
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16
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Nyberg J, Höglund R, Bergstrand M, Karlsson MO, Hooker AC. Serial correlation in optimal design for nonlinear mixed effects models. J Pharmacokinet Pharmacodyn 2012; 39:239-49. [PMID: 22415637 DOI: 10.1007/s10928-012-9245-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2011] [Accepted: 02/26/2012] [Indexed: 10/28/2022]
Abstract
In population modeling two sources of variability are commonly included; inter individual variability and residual variability. Rich sampling optimal design (more samples than model parameters) using these models will often result in a sampling schedule where some measurements are taken at exactly the same time point, thereby maximizing the signal-to-noise ratio. This behavior is a result of not appropriately taking into account error generation mechanisms and is often clinically unappealing and may be avoided by including intrinsic variability, i.e. serially correlated residual errors. In this paper we extend previous work that investigated optimal designs of population models including serial correlation using stochastic differential equations to optimal design with the more robust, and analytic, AR(1) autocorrelation model. Further, we investigate the importance of correlation strength, design criteria and robust designs. Finally, we explore the optimal design properties when estimating parameters with and without serial correlation. In the investigated examples the designs and estimation performance differs significantly when handling serial correlation.
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Affiliation(s)
- Joakim Nyberg
- Department of Pharmaceutical Biosciences, Uppsala University, Box 591, SE-751 24 Uppsala, Sweden.
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17
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Duffull SB, Graham G, Mengersen K, Eccleston J. Evaluation of the Pre-Posterior Distribution of Optimized Sampling Times for the Design of Pharmacokinetic Studies. J Biopharm Stat 2011; 22:16-29. [DOI: 10.1080/10543406.2010.500065] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
| | | | - Kerrie Mengersen
- c Mathematical Sciences , Queensland University of Technology , Brisbane , Australia
| | - John Eccleston
- d School of Physical Sciences , University of Queensland , Brisbane , Australia
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Nguyen TT, Bazzoli C, Mentré F. Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models. Stat Med 2011; 31:1043-58. [PMID: 21965170 DOI: 10.1002/sim.4390] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Revised: 07/13/2011] [Accepted: 08/04/2011] [Indexed: 01/15/2023]
Abstract
Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or changing between periods. We use the expected standard errors of treatment effect to compute the power for the Wald test of comparison or equivalence and the number of subjects needed for a given power. We perform various simulations mimicking crossover two-period trials to show the relevance of these developments. We then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3.2 of the r function PFIM.
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19
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Ogungbenro K, Aarons L. Population Fisher information matrix and optimal design of discrete data responses in population pharmacodynamic experiments. J Pharmacokinet Pharmacodyn 2011; 38:449-69. [PMID: 21660504 DOI: 10.1007/s10928-011-9203-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2010] [Accepted: 05/30/2011] [Indexed: 11/26/2022]
Affiliation(s)
- Kayode Ogungbenro
- Centre for Applied Pharmacokinetic Research, The University of Manchester, Oxford Road, Manchester, UK.
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20
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Ogungbenro K, Dokoumetzidis A, Aarons L. Application of optimal design methodologies in clinical pharmacology experiments. Pharm Stat 2010; 8:239-52. [PMID: 19009585 DOI: 10.1002/pst.354] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Pharmacokinetics and pharmacodynamics data are often analysed by mixed-effects modelling techniques (also known as population analysis), which has become a standard tool in the pharmaceutical industries for drug development. The last 10 years has witnessed considerable interest in the application of experimental design theories to population pharmacokinetic and pharmacodynamic experiments. Design of population pharmacokinetic experiments involves selection and a careful balance of a number of design factors. Optimal design theory uses prior information about the model and parameter estimates to optimize a function of the Fisher information matrix to obtain the best combination of the design factors. This paper provides a review of the different approaches that have been described in the literature for optimal design of population pharmacokinetic and pharmacodynamic experiments. It describes options that are available and highlights some of the issues that could be of concern as regards practical application. It also discusses areas of application of optimal design theories in clinical pharmacology experiments. It is expected that as the awareness about the benefits of this approach increases, more people will embrace it and ultimately will lead to more efficient population pharmacokinetic and pharmacodynamic experiments and can also help to reduce both cost and time during drug development.
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Affiliation(s)
- Kayode Ogungbenro
- Centre for Applied Pharmacokinetics Research, The University of Manchester, Manchester, UK.
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21
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Bazzoli C, Retout S, Mentré F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2010; 98:55-65. [PMID: 19892427 DOI: 10.1016/j.cmpb.2009.09.012] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2009] [Revised: 09/16/2009] [Accepted: 09/18/2009] [Indexed: 05/28/2023]
Abstract
Nonlinear mixed effect models (NLMEM) with multiple responses are increasingly used in pharmacometrics, one of the main examples being the joint analysis of the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug. Efficient tools for design evaluation and optimisation in NLMEM are necessary. The R functions PFIM 1.2 and PFIMOPT 1.0 were proposed for these purposes, but accommodate only single response models. The methodology used is based on the Fisher information matrix, developed using a linearisation of the model. In this paper, we present an extended version, PFIM 3.0, dedicated to both design evaluation and optimisation for multiple response models, using a similar method as for single response models. In addition to handling multiple response models, several features have been integrated into PFIM 3.0 for model specification and optimisation. The extension includes a library of classical analytical pharmacokinetics models and allows the user to describe more complex models using differential equations. Regarding the optimisation algorithm, an alternative to the Simplex algorithm has been implemented, the Fedorov-Wynn algorithm to optimise more practical D-optimal design. Indeed, this algorithm optimises design among a set of sampling times specified by the user. This R function is freely available at http://www.pfim.biostat.fr. The efficiency of this approach and the simplicity of use of PFIM 3.0 are illustrated with a real example of the joint PKPD analysis of warfarin, an oral anticoagulant, with a model defined by ordinary differential equations.
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22
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Zamuner S, Di Iorio VL, Nyberg J, Gunn RN, Cunningham VJ, Gomeni R, Hooker AC. Adaptive-Optimal Design in PET Occupancy Studies. Clin Pharmacol Ther 2010; 87:563-71. [DOI: 10.1038/clpt.2010.9] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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24
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D-optimal designs for parameter estimation for indirect pharmacodynamic response models. J Pharmacokinet Pharmacodyn 2009; 36:523-39. [PMID: 19904585 DOI: 10.1007/s10928-009-9135-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2008] [Accepted: 10/09/2009] [Indexed: 10/20/2022]
Abstract
This report generates efficient experimental designs (dose, sampling times) for parameter estimation for four basic physiologic indirect pharmacodynamic response (IDR) models. The principles underlying IDR models and their response patterns have been well described. Each IDR model explicitly contains four parameters, k (in) (production), k (out) (loss), I (max)/S (max) (capacity) and IC (50)/SC (50) (sensitivity). The pharmacokinetics of an IV dose of drug described by a monoexponential function of time with two parameters, V and k (el), is assumed. The random errors in the response variable are assumed to be additive, independent, and normal with zero mean and variance proportional to some power of the mean response. Optimal design theory was used extensively to assess the role of both dose and sampling times. Our designs were generated in Mathematica (ADAPT 5 typically produces identical results). G-optimality was used to verify that the generated designs were indeed D-optimal. Such designs are efficient and robust when good prior knowledge of the estimated parameters is available. The efficiency of unconstrained D-optimal designs (4 dose, sampling time pairs) does not improve much when the drug doses are allowed to differ, compared with constrained single dose designs (4 sampling times) with one maximal feasible dose. Also, explored were efficiencies of alternative study designs and results from parameter misspecification. This analysis substantiates the importance of larger doses yielding greater certainty in parameter estimation in pharmacodynamics.
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25
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Bazzoli C, Retout S, Mentré F. Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model. Stat Med 2009; 28:1940-56. [PMID: 19266541 DOI: 10.1002/sim.3573] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic-pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation-maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first-order linearization estimation methods implemented in the NONMEM software (first-order (FO), first-order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.
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26
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Nyberg J, Karlsson MO, Hooker AC. Simultaneous optimal experimental design on dose and sample times. J Pharmacokinet Pharmacodyn 2009; 36:125-45. [PMID: 19319484 DOI: 10.1007/s10928-009-9114-z] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2008] [Accepted: 03/10/2009] [Indexed: 10/21/2022]
Abstract
Optimal experimental design can be used for optimizing new pharmacokinetic (PK)-pharmacodynamic (PD) studies to increase the parameter precision. Several methods for optimizing non-linear mixed effect models has been proposed previously but the impact of optimizing other continuous design parameters, e.g. the dose, has not been investigated to a large extent. Moreover, the optimization method (sequential or simultaneous) for optimizing several continuous design parameters can have an impact on the optimal design. In the sequential approach the time and dose where optimized in sequence and in the simultaneous approach the dose and time points where optimized at the same time. To investigate the sequential approach and the simultaneous approach; three different PK-PD models where considered. In most of the cases the optimization method did change the optimal design and furthermore the precision was improved with the simultaneous approach.
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Affiliation(s)
- Joakim Nyberg
- Department of Pharmaceutical Biosciences, Uppsala University, Sweden.
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27
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McGree JM, Eccleston JA, Duffull SB. Simultaneous versus sequential optimal design for pharmacokinetic-pharmacodynamic models with FO and FOCE considerations. J Pharmacokinet Pharmacodyn 2009; 36:101-23. [PMID: 19224348 DOI: 10.1007/s10928-009-9113-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2007] [Accepted: 02/03/2009] [Indexed: 10/21/2022]
Abstract
We consider nested multiple response models which are used extensively in the area of pharmacometrics. Given the conditional nature of such models, differences in predicted responses are a consequence of different assumptions about how the models interact. As such, sequential versus simultaneous and First Order (FO) versus First Order Conditional Estimation (FOCE) techniques have been explored in the literature where it was found that the sequential and FO approaches can produce biased results. It is therefore of interest to determine any design consequences between the various methods and approximations. As optimal design for nonlinear mixed effects models is dependent upon initial parameter estimates and an approximation to the expected Fisher information matrix, it is necessary to incorporate any influence of nonlinearity (or parameter-effects curvature) into our exploration. Hence, sequential versus simultaneous design with FO and FOCE considerations are compared under low, typical and high degrees of nonlinearity. Additionally, predicted standard errors of parameters are also compared to empirical estimates formed via a simulation/estimation study in NONMEM. Initially, design theory for nested multiple response models is developed and approaches mentioned above are investigated by considering a pharmacokinetic-pharmacodynamic model found in the literature. We consider design for situations where all responses are continuous and extend this methodology to the case where a response may be a discrete random variable. In particular, for a binary response pharmacodynamic model, it is conjectured that such responses will offer little information about all parameters and hence a sequential optimization, in the form of product design optimality, may yield near optimal designs.
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Affiliation(s)
- J M McGree
- University of Queensland, St. Lucia, Brisbane, Australia.
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28
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Ogungbenro K, Graham G, Gueorguieva I, Aarons L. Incorporating Correlation in Interindividual Variability for the Optimal Design of Multiresponse Pharmacokinetic Experiments. J Biopharm Stat 2008; 18:342-58. [DOI: 10.1080/10543400701697208] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Kayode Ogungbenro
- a Centre for Applied Pharmacokinetics Research, University of Manchester , Manchester, United Kingdom
| | | | | | - Leon Aarons
- d School of Pharmacy and Pharmaceutical Sciences, University of Manchester , Manchester, United Kingdom
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Gueorguieva I, Ogungbenro K, Graham G, Glatt S, Aarons L. A program for individual and population optimal design for univariate and multivariate response pharmacokinetic-pharmacodynamic models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2007; 86:51-61. [PMID: 17292995 DOI: 10.1016/j.cmpb.2007.01.004] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2006] [Revised: 11/24/2006] [Accepted: 01/03/2007] [Indexed: 05/13/2023]
Abstract
The design of pharmacokinetic and pharmacodynamic experiments concerns a number of issues, among which are the number of observations and the times when they are taken. Often a model is used to describe these data and the pharmacokinetic-pharmacodynamic behavior of a drug. Knowledge of the data analysis model at the design stage is beneficial for collecting patient data for parameter estimation. A number of criteria for model-oriented experiments, which maximize the information content of the data, are available. In this paper we present a program, Popdes, to investigate the D-optimal design of individual and population multivariate response models, such as pharmacokinetic-pharmacodynamic, physiologically based pharmacokinetic, and parent drug and metabolites models. A pre-clinical and clinical pharmacokinetic-pharmacodynamic model describing the concentration-time profile and effect of an oncology compound in development is used for illustration.
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Affiliation(s)
- Ivelina Gueorguieva
- Lilly Research Centre, Global PK/PD, Erl Wood Manor, Sunninghill Road, Windlesham, Surrey GU20 6PH, United Kingdom.
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30
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Ogungbenro K, Gueorguieva I, Majid O, Graham G, Aarons L. Optimal design for multiresponse pharmacokinetic-pharmacodynamic models - dealing with unbalanced designs. J Pharmacokinet Pharmacodyn 2007; 34:313-31. [PMID: 17285361 DOI: 10.1007/s10928-006-9048-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2006] [Accepted: 12/19/2006] [Indexed: 10/23/2022]
Abstract
This paper addresses the problem of determining D-optimal designs for multiresponse pharmacokinetic-pharmacodynamic (PKPD) experiments where data on each response variable can be collected at different times. Most previous multiresponse model optimal design applications have considered the case where all response variables are measured at the same time points. However in practice it may not be possible to have all responses measured at the same sampling times. We propose an optimal design method to take into account the unbalanced nature of the problem. The method developed was applied to a PKPD problem that involved describing the time course of drug plasma concentrations, heart rate and mean arterial blood pressure for both a fixed effects and mixed effects regression model. Additionally a simulation study was carried out in NONMEM for one such population optimal design problem.
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Affiliation(s)
- Kayode Ogungbenro
- Centre for Applied Pharmacokinetic Research, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
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