Design evaluation and optimisation in nonlinear mixed effects models with the R package PFIM
Romain Leroux , Jérémy Seurat, Hervé Le Nagard, 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 present work describes the R package PFIM 5.0, the new version of PFIM, that provides powerful tools to perform evaluation of the FIM and design optimization under given design constraints in NLMEMs.
The package PFIM 5.0 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: PFIM 5.0 is implemented using the formal object oriented system S4, that defines objects having clear object-oriented programming characteristics including class and argument definitions, inheritance, as well as argument checking, instantiation and implementation methods. PFIM thus offers a great flexibility to conduct population design evaluation and optimisation. The version of this package is available from the Comprehensive R Archive Network at https://cran.r-project.org/web/packages/PFIM/index.html. Documentation with additional detailled examples is provided by a comprehensive user guide from the PFIM website at http://www.pfim.biostat.fr/.
Results: In this new version, the user can write his entire project in a single R script. PFIM 5.0 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.
In the package PFIM 5.0, as its predecessor PFIM 4.0, 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] and the Fedorov-Wynn algorithm [9] that optimise within a discrete design space. It is now possible to optimize both the dose and the measurement times, for example by using the multiplicative algorithm.
The results of an evaluation or design optimization can be exploited using R. The standard data visualization package ggplot2 [10] 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 [11] is used to turn them into high quality reports that can be easily shared. For both evaluation and optimisation a complete summary of the results is provided, notably including the FIM, the D-optimality criterion, and expected SE and RSE of parameters.
Conclusions: : By its user-friendliness, readability, modularity, PFIM 5.0 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 5, such as discrete covariates and Wald test power predictions [12]. Other perspectives are to include new features like alternative methods to evaluate the FIM (e.g. MC/AGQ [13]) for discrete response models. In our permanent concern to facilitate an effective use of the package PFIM, a GUI version of the package PFIM 5.0 is planned to be released for next summer.
References:
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