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Seurat J, Gerbino KR, Meyer JR, Borin JM, Weitz JS. Design, optimization, and inference of biphasic decay of infectious virus particles. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.02.23.581735. [PMID: 38464262 PMCID: PMC10925204 DOI: 10.1101/2024.02.23.581735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2024]
Abstract
Virus population dynamics are driven by counter-balancing forces of production and loss. Whereas viral production arises from complex interactions with susceptible hosts, the loss of infectious virus particles is often approximated as a first-order kinetic process. As such, experimental protocols to measure infectious virus loss are not typically designed to identify non-exponential decay processes. Here, we propose methods to evaluate if an experimental design is adequate to identify multiphasic virus particle decay and to optimize the sampling times of decay experiments, accounting for uncertainties in viral kinetics. First, we evaluate synthetic scenarios of biphasic decays, with varying decay rates and initial proportions of subpopulations. We show that robust inference of multiphasic decay is more likely when the faster decaying subpopulation predominates insofar as early samples are taken to resolve the faster decay rate. Moreover, design optimization involving non-equal spacing between observations increases the precision of estimation while reducing the number of samples. We then apply these methods to infer multiple decay rates associated with the decay of bacteriophage ('phage') Φ D 9 , an evolved isolate derived from phage Φ 21 . A pilot experiment confirmed that Φ D 9 decay is multiphasic, but was unable to resolve the rate or proportion of the fast decaying subpopulation(s). We then applied a Fisher information matrix-based design optimization method to propose non-equally spaced sampling times. Using this strategy, we were able to robustly estimate multiple decay rates and the size of the respective subpopulations. Notably, we conclude that the vast majority (94%) of the phage Φ D 9 population decays at a rate 16-fold higher than the slow decaying population. Altogether, these results provide both a rationale and a practical approach to quantitatively estimate heterogeneity in viral decay.
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Affiliation(s)
- Jérémy Seurat
- Institut de Biologie, Ecole Normale Superieure, Paris, 75005, France
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, 30332, GA, USA
| | - Krista R. Gerbino
- Division of Biological Sciences, University of California San Diego, La Jolla, 92093, CA, USA
| | - Justin R. Meyer
- Division of Biological Sciences, University of California San Diego, La Jolla, 92093, CA, USA
| | - Joshua M. Borin
- Division of Biological Sciences, University of California San Diego, La Jolla, 92093, CA, USA
| | - Joshua S. Weitz
- Institut de Biologie, Ecole Normale Superieure, Paris, 75005, France
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, 30332, GA, USA
- Department of Biology, University of Maryland, College Park, 20742, MD, USA
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Mwangi M, Verbeke G, Njagi EN, Florez AJ, Mwalili S, Ivanova A, Bukania ZN, Molenberghs G. Evaluation of a flexible piecewise linear mixed-effects model in the analysis of randomized cross-over trials. Pharm Stat 2024; 23:370-384. [PMID: 38146135 DOI: 10.1002/pst.2357] [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: 03/30/2023] [Revised: 10/15/2023] [Accepted: 11/29/2023] [Indexed: 12/27/2023]
Abstract
Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.
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Affiliation(s)
- Moses Mwangi
- I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium
- Center for Public Health Research, Kenya Medical Research Institute, Nairobi, Kenya
| | - Geert Verbeke
- I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium
- L-BioStat, Katholieke Universiteit (KU) Leuven, Leuven, Belgium
| | - Edmund Njeru Njagi
- Non-Communicable Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Alvaro Jose Florez
- School of Statistics, Universidad del Valle, Cali, Colombia
- Data Science Institute, I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium
| | - Samuel Mwalili
- Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture & Technology, Nairobi, Kenya
| | - Anna Ivanova
- I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium
- L-BioStat, Katholieke Universiteit (KU) Leuven, Leuven, Belgium
| | - Zipporah N Bukania
- Center for Public Health Research, Kenya Medical Research Institute, Nairobi, Kenya
| | - Geert Molenberghs
- I-BioStat, Universiteit Hasselt, Diepenbeek, Belgium
- L-BioStat, Katholieke Universiteit (KU) Leuven, Leuven, Belgium
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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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Nonlinear Mixed-Effect Pharmacokinetic Modeling and Distribution of Doxycycline in Healthy Female Donkeys after Multiple Intragastric Dosing-Preliminary Investigation. Animals (Basel) 2021; 11:ani11072047. [PMID: 34359175 PMCID: PMC8300337 DOI: 10.3390/ani11072047] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 06/22/2021] [Accepted: 07/02/2021] [Indexed: 12/27/2022] Open
Abstract
Doxycycline (DXC) is a broad-spectrum antibacterial antimicrobial administered to horses for the treatment of bacterial infections which may also affect donkeys. Donkeys have a different metabolism than horses, leading to differences in the pharmacokinetics of drugs compared to horses. This study aimed to describe the population pharmacokinetics of DXC in donkeys. Five doses of DXC hyclate (10 mg/kg) were administered via a nasogastric tube, q12 h, to eight non-fasted, healthy, adult jennies. Serum, urine, synovial fluid and endometrium were collected for 72 h following the first administration. Doxycycline concentration was measured by competitive enzyme immunoassay. Serum concentrations versus time data were fitted simultaneously using the stochastic approximation expectation-maximization algorithm for nonlinear mixed effects. A one-compartment model with linear elimination and first-order absorption after intragastric administration, best described the available pharmacokinetic data. Final parameter estimates indicate that DXC has a high volume of distribution (108 L/kg) as well as high absorption (10.3 h-1) in donkeys. However, results suggest that oral DXC at 10 mg/kg q12 h in donkeys would not result in a therapeutic concentration in serum, urine, synovial fluid or endometrium by comparison to the minimum inhibitory concentration of common equine pathogens. Further studies are recommended to identify appropriate dosage and dosing intervals of oral DXC in donkeys.
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Percie du Sert N, Ahluwalia A, Alam S, Avey MT, Baker M, Browne WJ, Clark A, Cuthill IC, Dirnagl U, Emerson M, Garner P, Holgate ST, Howells DW, Hurst V, Karp NA, Lazic SE, Lidster K, MacCallum CJ, Macleod M, Pearl EJ, Petersen OH, Rawle F, Reynolds P, Rooney K, Sena ES, Silberberg SD, Steckler T, Würbel H. Reporting animal research: Explanation and elaboration for the ARRIVE guidelines 2.0. PLoS Biol 2020; 18:e3000411. [PMID: 32663221 PMCID: PMC7360025 DOI: 10.1371/journal.pbio.3000411] [Citation(s) in RCA: 989] [Impact Index Per Article: 247.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Improving the reproducibility of biomedical research is a major challenge. Transparent and accurate reporting is vital to this process; it allows readers to assess the reliability of the findings and repeat or build upon the work of other researchers. The ARRIVE guidelines (Animal Research: Reporting In Vivo Experiments) were developed in 2010 to help authors and journals identify the minimum information necessary to report in publications describing in vivo experiments. Despite widespread endorsement by the scientific community, the impact of ARRIVE on the transparency of reporting in animal research publications has been limited. We have revised the ARRIVE guidelines to update them and facilitate their use in practice. The revised guidelines are published alongside this paper. This explanation and elaboration document was developed as part of the revision. It provides further information about each of the 21 items in ARRIVE 2.0, including the rationale and supporting evidence for their inclusion in the guidelines, elaboration of details to report, and examples of good reporting from the published literature. This document also covers advice and best practice in the design and conduct of animal studies to support researchers in improving standards from the start of the experimental design process through to publication.
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Affiliation(s)
| | - Amrita Ahluwalia
- The William Harvey Research Institute, London, United Kingdom
- Barts Cardiovascular CTU, Queen Mary University of London, London, United Kingdom
| | - Sabina Alam
- Taylor & Francis Group, London, United Kingdom
| | - Marc T. Avey
- Health Science Practice, ICF, Durham, North Carolina, United States of America
| | - Monya Baker
- Nature, San Francisco, California, United States of America
| | | | | | - Innes C. Cuthill
- School of Biological Sciences, University of Bristol, Bristol, United Kingdom
| | - Ulrich Dirnagl
- QUEST Center for Transforming Biomedical Research, Berlin Institute of Health & Department of Experimental Neurology, Charite Universitätsmedizin Berlin, Berlin, Germany
| | - Michael Emerson
- National Heart and Lung Institute, Imperial College London, London, United Kingdom
| | - Paul Garner
- Centre for Evidence Synthesis in Global Health, Clinical Sciences Department, Liverpool School of Tropical Medicine, Liverpool, United Kingdom
| | - Stephen T. Holgate
- Clinical and Experimental Sciences, University of Southampton, Southampton, United Kingdom
| | - David W. Howells
- Tasmanian School of Medicine, University of Tasmania, Hobart, Australia
| | | | - Natasha A. Karp
- Data Sciences & Quantitative Biology, Discovery Sciences, R&D, AstraZeneca, Cambridge, United Kingdom
| | | | | | | | - Malcolm Macleod
- Centre for Clinical Brain Sciences, University of Edinburgh, Edinburgh, United Kingdom
| | | | - Ole H. Petersen
- Academia Europaea Knowledge Hub, Cardiff University, Cardiff, United Kingdom
| | | | - Penny Reynolds
- Statistics in Anesthesiology Research (STAR) Core, Department of Anesthesiology, College of Medicine, University of Florida, Gainesville, Florida, United States of America
| | - Kieron Rooney
- Discipline of Exercise and Sport Science, Faculty of Medicine and Health, University of Sydney, Sydney, Australia
| | - Emily S. Sena
- Centre for Clinical Brain Sciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Shai D. Silberberg
- National Institute of Neurological Disorders and Stroke, Bethesda, Maryland, United States of America
| | | | - Hanno Würbel
- Veterinary Public Health Institute, Vetsuisse Faculty, University of Bern, Bern, Switzerland
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Seurat J, Nguyen TT, Mentré F. Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes. Stat Methods Med Res 2019; 29:934-952. [DOI: 10.1177/0962280219850588] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.
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Affiliation(s)
- Jérémy Seurat
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
| | - Thu Thuy Nguyen
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
| | - France Mentré
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
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Yang J, Ma P, Bullman J, Nicholls A, Chen C. Adjustment of the area under the concentration curve by terminal rate constant for bioequivalence assessment in a parallel-group study of lamotrigine. Br J Clin Pharmacol 2019; 85:563-569. [PMID: 30511473 PMCID: PMC6379210 DOI: 10.1111/bcp.13826] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2018] [Revised: 11/06/2018] [Accepted: 11/23/2018] [Indexed: 11/30/2022] Open
Abstract
AIM A new strength of lamotrigine extended-release formulation unexpectedly failed to show bioequivalence with the existing strengths at the same dose in a parallel-group study. We report the post-hoc analyses conducted to identify the cause and propose an approach for future evaluations in similar situations. METHODS A seemingly bimodal distribution of the half-life among the study participants prompted the use of terminal-phase-rate-constant-adjusted area under the concentration curve as the endpoint for bioequivalence assessment. Population pharmacokinetic modelling was also performed to assess the bimodal distribution of apparent clearance and the potential treatment effects on bioavailability. RESULTS The cause for failing to achieve bioequivalence appeared to be a biased representation of a bimodal clearance distribution between the groups. The pharmacokinetic modelling with a mixture routine identified two subpopulations: 88% had a mean clearance of 1.99 l h-1 ; 12% had a mean clearance of 0.64 l h-1 . The low-clearance population was unequally represented by 13% and 4% of subjects in the reference and test groups, respectively, and treatment appeared to have no significant effect on oral bioavailability. The bioequivalence comparison using the adjusted area concluded with a 90% confidence interval of 0.91-1.06, suggesting that treatment had no significant effect on bioavailability and the formulations would meet regulatory criteria for bioequivalence. CONCLUSIONS The adjustment of the area under the concentration curve adjusted by terminal-phase rate constant should be considered for situational application in bioequivalence assessment when there are multiple clearance subpopulations in a parallel-group study.
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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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Comparing the performance of FOCE and different expectation-maximization methods in handling complex population physiologically-based pharmacokinetic models. J Pharmacokinet Pharmacodyn 2016; 43:359-70. [DOI: 10.1007/s10928-016-9476-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Accepted: 05/13/2016] [Indexed: 11/26/2022]
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10
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Riviere MK, Ueckert S, Mentré F. An MCMC method for the evaluation of the Fisher information matrix for non-linear mixed effect models. Biostatistics 2016; 17:737-50. [PMID: 27166250 DOI: 10.1093/biostatistics/kxw020] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Accepted: 03/16/2016] [Indexed: 11/13/2022] Open
Abstract
Non-linear mixed effect models (NLMEMs) are widely used for the analysis of longitudinal data. To design these studies, optimal design based on the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. In recent years, estimation algorithms for NLMEMs have transitioned from linearization toward more exact higher-order methods. Optimal design, on the other hand, has mainly relied on first-order (FO) linearization to calculate the FIM. Although efficient in general, FO cannot be applied to complex non-linear models and with difficulty in studies with discrete data. We propose an approach to evaluate the expected FIM in NLMEMs for both discrete and continuous outcomes. We used Markov Chain Monte Carlo (MCMC) to integrate the derivatives of the log-likelihood over the random effects, and Monte Carlo to evaluate its expectation w.r.t. the observations. Our method was implemented in R using Stan, which efficiently draws MCMC samples and calculates partial derivatives of the log-likelihood. Evaluated on several examples, our approach showed good performance with relative standard errors (RSEs) close to those obtained by simulations. We studied the influence of the number of MC and MCMC samples and computed the uncertainty of the FIM evaluation. We also compared our approach to Adaptive Gaussian Quadrature, Laplace approximation, and FO. Our method is available in R-package MIXFIM and can be used to evaluate the FIM, its determinant with confidence intervals (CIs), and RSEs with CIs.
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Affiliation(s)
- Marie-Karelle Riviere
- INSERM, IAME, UMR 1137, F-75018 Paris, France and Univ Paris Diderot, Sorbonne Paris Cité, F-75018 Paris, France
| | - Sebastian Ueckert
- INSERM, IAME, UMR 1137, F-75018 Paris, France and Univ Paris Diderot, Sorbonne Paris Cité, F-75018 Paris, France
| | - France Mentré
- INSERM, IAME, UMR 1137, F-75018 Paris, France and Univ Paris Diderot, Sorbonne Paris Cité, F-75018 Paris, France
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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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Dumont C, Chenel M, Mentré F. Influence of covariance between random effects in design for nonlinear mixed-effect models with an illustration in pediatric pharmacokinetics. J Biopharm Stat 2014; 24:471-92. [PMID: 24697342 DOI: 10.1080/10543406.2014.888443] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
Nonlinear mixed-effect models are used increasingly during drug development. For design, an alternative to simulations is based on the Fisher information matrix. Its expression was derived using a first-order approach, was then extended to include covariance and implemented into the R function PFIM. The impact of covariance on standard errors, amount of information, and optimal designs was studied. It was also shown how standard errors can be predicted analytically within the framework of rich individual data without the model. The results were illustrated by applying this extension to the design of a pharmacokinetic study of a drug in pediatric development.
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Affiliation(s)
- Cyrielle Dumont
- a Université Paris Diderot, Sorbonne Paris Cité , UMR 738, INSERM, Paris , France
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13
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Nguyen TT, Mentré F. Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature. Comput Stat Data Anal 2014. [DOI: 10.1016/j.csda.2014.06.011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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14
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Dumont C, Chenel M, Mentré F. Two-stage Adaptive Designs in Nonlinear Mixed Effects Models: Application to Pharmacokinetics in Children. COMMUN STAT-SIMUL C 2014. [DOI: 10.1080/03610918.2014.930901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Cyrielle Dumont
- IAME, UMR 1137, INSERM, Paris, France
- Univ Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - Marylore Chenel
- Division of Clinical Pharmacokinetics, Institut de Recherches Internationales Servier, Suresnes, France
| | - France Mentré
- IAME, UMR 1137, INSERM, Paris, France
- Univ Paris Diderot, Sorbonne Paris Cité, Paris, France
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Kloprogge F, Simpson JA, Day NPJ, White NJ, Tarning J. Statistical power calculations for mixed pharmacokinetic study designs using a population approach. AAPS JOURNAL 2014; 16:1110-8. [PMID: 25011414 PMCID: PMC4147042 DOI: 10.1208/s12248-014-9641-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Accepted: 06/19/2014] [Indexed: 11/30/2022]
Abstract
Simultaneous modelling of dense and sparse pharmacokinetic data is possible with a population approach. To determine the number of individuals required to detect the effect of a covariate, simulation-based power calculation methodologies can be employed. The Monte Carlo Mapped Power method (a simulation-based power calculation methodology using the likelihood ratio test) was extended in the current study to perform sample size calculations for mixed pharmacokinetic studies (i.e. both sparse and dense data collection). A workflow guiding an easy and straightforward pharmacokinetic study design, considering also the cost-effectiveness of alternative study designs, was used in this analysis. Initially, data were simulated for a hypothetical drug and then for the anti-malarial drug, dihydroartemisinin. Two datasets (sampling design A: dense; sampling design B: sparse) were simulated using a pharmacokinetic model that included a binary covariate effect and subsequently re-estimated using (1) the same model and (2) a model not including the covariate effect in NONMEM 7.2. Power calculations were performed for varying numbers of patients with sampling designs A and B. Study designs with statistical power >80% were selected and further evaluated for cost-effectiveness. The simulation studies of the hypothetical drug and the anti-malarial drug dihydroartemisinin demonstrated that the simulation-based power calculation methodology, based on the Monte Carlo Mapped Power method, can be utilised to evaluate and determine the sample size of mixed (part sparsely and part densely sampled) study designs. The developed method can contribute to the design of robust and efficient pharmacokinetic studies.
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Affiliation(s)
- Frank Kloprogge
- Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, 420/6 Rajvithi Road, Bangkok, 10400, Thailand,
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Random-Effects Linear Modeling and Sample Size Tables for Two Special Crossover Designs of Average Bioequivalence Studies: The Four-Period, Two-Sequence, Two-Formulation and Six-Period, Three-Sequence, Three-Formulation Designs. Clin Pharmacokinet 2013; 52:1033-43. [DOI: 10.1007/s40262-013-0103-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Gibiansky L, Gibiansky E, Bauer R. Comparison of Nonmem 7.2 estimation methods and parallel processing efficiency on a target-mediated drug disposition model. J Pharmacokinet Pharmacodyn 2011; 39:17-35. [PMID: 22101761 DOI: 10.1007/s10928-011-9228-y] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2011] [Accepted: 10/27/2011] [Indexed: 11/29/2022]
Abstract
The paper compares performance of Nonmem estimation methods--first order conditional estimation with interaction (FOCEI), iterative two stage (ITS), Monte Carlo importance sampling (IMP), importance sampling assisted by mode a posteriori (IMPMAP), stochastic approximation expectation-maximization (SAEM), and Markov chain Monte Carlo Bayesian (BAYES), on the simulated examples of a monoclonal antibody with target-mediated drug disposition (TMDD), demonstrates how optimization of the estimation options improves performance, and compares standard errors of Nonmem parameter estimates with those predicted by PFIM 3.2 optimal design software. In the examples of the one- and two-target quasi-steady-state TMDD models with rich sampling, the parameter estimates and standard errors of the new Nonmem 7.2.0 ITS, IMP, IMPMAP, SAEM and BAYES estimation methods were similar to the FOCEI method, although larger deviation from the true parameter values (those used to simulate the data) was observed using the BAYES method for poorly identifiable parameters. Standard errors of the parameter estimates were in general agreement with the PFIM 3.2 predictions. The ITS, IMP, and IMPMAP methods with the convergence tester were the fastest methods, reducing the computation time by about ten times relative to the FOCEI method. Use of lower computational precision requirements for the FOCEI method reduced the estimation time by 3-5 times without compromising the quality of the parameter estimates, and equaled or exceeded the speed of the SAEM and BAYES methods. Use of parallel computations with 4-12 processors running on the same computer improved the speed proportionally to the number of processors with the efficiency (for 12 processor run) in the range of 85-95% for all methods except BAYES, which had parallelization efficiency of about 70%.
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