Jérémy Seurat, Hervé Le Nagard, Romain Leroux, France Mentré on behalf of the PFIM group
Université de Paris, INSERM, IAME, F-75018 Paris, France
Introduction: Nonlinear mixed effects models (NLMEM) are widely used in model-based drug development to analyse longitudinal data. The use of the Fisher Information Matrix (FIM) is a good alternative to clinical trial simulation to optimize the design of these studies. PFIM 4.0 was released in 2014 [1] and is one of the tools developed for evaluation and/or optimisation of population designs based on the Fisher information matrix (FIM) in NLMEM.
Objectives: To develop an R package with the object-oriented system S4 of R [2], in order to propose a modernised PFIM tool: PFIM 5. Our goals were to:
- – improve simplicity of use
- – increase readability and modularity to conduct population design evaluation and optimization
- – provide quality control with tests and validation processes
- – display all the results with both clear graphical form and complete data summary, while ensuring their easy manipulation in R.
Methods: PFIM was re-implemented from scratch in R S4 language, following a top-down approach which consists of taking a high-level definition of a problem and then subdivides it into subproblems for knowledge ordering and solving the sole problem. Based on this approach, the object-oriented system S4 has a formal definition of the classes that describe their representation and inheritance link. Thanks to S4, the code of the new PFIM thus offers a great flexibility to conduct population design evaluation and optimization.
Results: In PFIM 5, as in PFIM 4.0, the FIM is evaluated by first order linearization of the model [3]. Individual, population and Bayesian (to give shrinkage predictions [4]) FIM are still available. Under given design constraints and based on the D-criterion, design can be optimised using a multiplicative algorithm as a new feature in PFIM 5 [5]. The standard data visualization package ggplot2 for R is used to display all the results with clear graphical form [6]. A clear data summary is provided. A quality control using a criterion based on the evaluation of the determinant of the FIM is also provided.
This new version of PFIM includes a library of PKPD models implemented in R S4 language. It contains various PK models with different administration routes (e.g., bolus, infusion, first-order absorption), different number of compartments (from 1 to 3), and different types of eliminations (linear or Michaelis-Menten). For PD models, direct effect models (with or without baseline) and indirect response models (turnover model only) are included. Linear and nonlinear (e.g. Emax, sigmoid Emax) PKPD models are included. PFIM handles both analytical and ODE models and offers the possibility to the user to define his own models or to extend models from the library.
Conclusions: There is a need to increase the use of model based optimal design approaches, as it can anticipate ‘fatal’ studies. PFIM 5 fulfils some needs by its user-friendliness, readability, modularity. All features implemented in PFIM 4.0. will soon be part of PFIM 5, such as the Fedorov-Wynn and Simplex algorithms for design optimisation, discrete covariates and Wald test power predictions [7]). Other perspectives are to include new features like alternative methods to evaluate the FIM (e.g. MC/AGQ [8]) for discrete response models. PFIM and the library of PKPD models will be interoperable with other estimation parameter software tools in R.
References:
[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] Yu Y. Monotonic convergence of a general algorithm for computing optimal designs. Ann Stat. 2010;38:1593–606.
[6] Wickham H., ggplot2: Elegant Graphics for Data Analysis, Springer-Verlag New York, 2016; 978-3-319-24277-4.
[7] 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.
[8] 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 29 (2021) Abstr 9671 [www.page-meeting.org/?abstract=9671]
Poster: Study Design