2023 - A Coruña - Spain

PAGE 2023: Methodology - Study Design
Romain Leroux

Design evaluation and optimisation in nonlinear mixed effects models with the R package PFIM 6.0

Romain Leroux , Jérémy Seurat, Nguyen Tran Bach, France Mentré on behalf of the PFIM group

Université de Paris, INSERM, IAME, F-75018 Paris, France

Objectives: Nonlinear mixed effects models (NLMEMs) are widely used in model-based drug development to analyse longitudinal data. For optimising the design of longitudinal studies in pharmacometrics, the use of the Fisher information matrix (FIM) is a good alternative to time-consuming clinical trial simulations. PFIM 4.0 was released in 2014 [1] and is one of the tools developed for FIM-based evaluation and/or optimisation of in NLMEMs. The next version PFIM 5.0 was an R package releasead on the CRAN. The present work describes the R package PFIM 6.0 that provides powerful tools to perform evaluation of the FIM and design optimization under given design constraints in NLMEMs. The package PFIM 6.0 allows the users to:
- use a library of PKPD models as well as user-defined models,
- evaluate the FIM (individual, population and bayesian) and give its determinant as quality control,
- generate D-optimal designs under given design constraints,
- display all the results with both clear graphical form and complete data summary and turn them into high quality reports that can be easily shared.

Methods: In our permanent concern to facilitate an effective use of the package PFIM, we have entirely rewritten the package, keeping the formal object oriented system S4. Thanks to these major changes, PFIM 6.0 provide users with the easiest possible scripts to use but also facilitate the modularity with the next features and improve the code performances for design evaluation and optimization. The version of this package is avalaible from the Comprehensive R Archive Network at: https://cran.r-project.org/web/packages/PFIM/index.html. Documentation with additional detailed examples is provided by a comprehensive user guide from the PFIM website at http://www.pfim.biostat.fr/.

Results: PFIM 6.0 still handles both user-defined analytical and ODE models and also includes a library of models implemented using the object-oriented system S4 of R, which makes it easier to use and add new models to the library. It contains libraries of pharmacokinetic (PK) and pharmacodynamic (PD) models. The PK library includes different administration routes (bolus, infusion, oral), 1- and 2-compartment models. The PD library contains direct and indirect, linear and nonlinear models. The PK/PD models are obtained with combination of the models from the PK and PD libraries. In the current version of PFIM, parameters with different distributions (normal and lognormal) can now be defined within the same project. The FIM is evaluated by first order linearisation of the model [3]. Individual, population and Bayesian (to give shrinkage predictions [4]) designs can be evaluated or optimised. It includes also several algorithms to conduct design optimisation based on the D-criterion, given design constraints: the simplex algorithm (Nelder-Mead) [5], PSO (Particle Swarm Optimisation) [6] and PGBO (Population Genetics Based Optimiser) [7] that optimise within a continuous design space, and the multiplicative [8,9] and the Fedorov-Wynn algorithm [10] that optimise within a discrete design space.  It is now possible to optimise both the dose and the measurement times, for example by using the multiplicative algorithm. The results of an evaluation or design optimisation can be exploited using R. The standard data visualization package ggplot2 [11] is used to display the results in clear graphical form (sensitivity graphs, responses over time and optimal design, SE and RSE obtained with the evaluated or the optimised design) and the package rmarkdown [12] is used to turn them into high quality reports that can be easily shared. 

Conclusions: By its user-friendliness, readability, modularity, PFIM 6.0 fulfills the need to increase the use of model based optimal design approaches. All features implemented in PFIM 4.0 will soon be part of PFIM 6.0, such as discrete covariates and Wald test power predictions [13]. Other perspectives are to include new features like alternative methods to evaluate the FIM (e.g. MC/AGQ [14]) for discrete response models. 

[1] Dumont C, Lestini G, Le Nagard H, Mentré F, Comets E, Nguyen TT, et al. PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models. Comput Methods Programs Biomed. 2018;156:217–29.
[2] Chambers JM. Object-Oriented Programming, Functional Programming and R. Stat Sci. 2014;29:167–80.
[3] Mentré F, Mallet A, Baccar D. Optimal Design in Random-Effects Regression Models. Biometrika. 1997;84:429–42. 
[4] Combes FP, Retout S, Frey N, Mentré F. Prediction of shrinkage of individual parameters using the bayesian information matrix in non-linear mixed effect models with evaluation in pharmacokinetics. Pharm Res. 2013;30:2355–67.
[5] Nelder JA, Mead R. A simplex method for function minimization. Comput J. 1965;7:308–13.
[6] Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. Proc. of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, 4-6 October 1995;39-43.
[7] Le Nagard H, Chao L, Tenaillon O. The emergence of complexity and restricted pleiotropy in adapting networks. BMC Evol Biol 2011;11-326.
[8] Yu Y. Monotonic convergence of a general algorithm for computing optimal designs. Ann Stat. 2010;38:1593–606.                                                                                                                [9] Seurat J, Tang Y, Mentré F, Nguyen, TT. Finding optimal design in nonlinear mixed effect models using multiplicative algorithms. Comput Methods Programs Biomed. 2021;207.106–126. 
[10] Fedorov, VV. Theory of Optimal Experiments. Academic Press, New York, 1972.
[11] Wickham H., ggplot2: Elegant Graphics for Data Analysis, Springer-Verlag New York, 2016;978-3-319-24277-4.
[12] Allaire J, Xie Y, McPherson J, Luraschi J, Ushey K, Atkins A, Wickham H, Cheng J, Chang W, Iannone R. rmarkdown: Dynamic Documents for R. R package version 2.13, 2022.
[13] Retout S, Comets E, Samson A, Mentré F. Design in nonlinear mixed effects models: optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates. Stat Med. 2007;26:5162–79.
[14] Ueckert S, Mentré F. A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature. Comput Stat Data Anal. 2017;111:203–19.

Reference: PAGE 31 (2023) Abstr 10510 [www.page-meeting.org/?abstract=10510]
Poster: Methodology - Study Design
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