Performance of the SAEM and FOCEI algorithms in the open-source non-linear mixed effect modelling tool nlmixr
Rik Schoemaker(1), Matthew Fidler(2), Christian Laveille(3), Justin J. Wilkins(1), Richard Hooijmaijers(4), Teun M. Post(4), Mirjam N. Trame(5), Yuan Xiong(6), and Wenping Wang(7)
(1) Occams, The Netherlands, (2) Novartis, Fort Worth, TX, USA, (3) Calvagone, France, (4) LAP&P Consultants, The Netherlands, (5) Novartis, Cambridge, MA, USA, (6) Certara, Princeton, NJ, USA, (7) Novartis, East Hanover, NJ, USA
Objectives:
nlmixr is a freely available open-source package for R [1] that does not depend on any commercial software, and is available on CRAN [2] and GitHub [3]. The package allows structural models to be implemented using a system of ordinary differential equations (ODEs), and allows fully flexible dosing definitions in terms of the type (e.g. bolus doses or infusions), the timing, the number of doses, and their amount, which can vary between individuals. nlmixr builds on RxODE [4], a fast and efficient R package for simulating nonlinear mixed effect models using ODEs, with rapid execution due to compilation in C. Comprehensive online documentation is available [5], and an nlmixr tutorial is in preparation. The package comes with its dedicated project manager shinyMixR [6] that runs in a web-browser, and is linked to xpose [7, 8] for graphical exploration and goodness of fit plots.
nlmixr implements a number of parameter estimation algorithms that can be accessed through a common model definition language. These algorithms currently comprise nlme [9], stochastic approximation expectation maximization (SAEM) [10], and first-order conditional estimation with interaction (FOCEI) [11]. Further algorithms and parallel computation are in active development.
For a new tool to be accepted by the pharmacometric modelling and simulation community, it is essential that its estimation algorithms can be demonstrated to perform well and provide results comparable to widely used standards. The question is, can one switch from another package to an nlmixr estimation algorithm and obtain similar results?
Methods:
Performances of the SAEM and FOCEI algorithms in nlmixr were compared to those found in the industry standards, Monolix [12] and NONMEM [11], using two scenarios: a simple model fit to 500 sparsely-sampled datasets, and a range of more complex compartmental models with linear and non-linear clearance fit to datasets with rich sampling.
Estimation with sparsely sampled data was investigated for a first-order absorption model with one-compartmental disposition and linear elimination. Single-dose data for 10,000 subjects were simulated, split into four equal-sized dose groups, and four time points were randomly sampled within the 24 hours after the dose. Using the bootstrap tool of PsN [13], 500 datasets containing 120 subjects each were resampled from these 10,000 subjects, stratified by dose so that 30 subjects in each resampled dataset received one of the four doses.
Each resampled dataset was then analysed using the same structural model that was used for simulation, using Monolix's SAEM algorithm, NONMEM’s FOCEI algorithm, and nlmixr's SAEM and FOCEI algorithms, to allow a paired comparison for each simulated data set of the analysis outcomes.
Richly sampled profiles were simulated for 4 different dose levels of 30 subjects each, for a range of test models with one- or two-compartmental disposition, oral (first-order absorption), intravenous bolus, or intravenous infusion administration, with either linear or Michaelis-Menten clearance. Inter-individual variability was applied to all pharmacokinetic parameters. Data were simulated for a single administration with sampling over 72 hours (19 samples), seven repeated daily administrations, with 15 samples over 24 hours after the 4th dose, 19 samples over 72 hours after the 7th dose, and 5 trough samples, and the combined single and multiple dose profiles (58 samples). These combinations provided a total of 36 test cases. A similar set of models and data sets was previously used to compare NONMEM and Monolix [14].
Results:
Single-thread computational speed was higher for nlmixr/FOCEI compared to NONMEM, but lower for nlmixr/SAEM compared to Monolix. Estimation results obtained from nlmixr for FOCEI and SAEM matched corresponding output from NONMEM/FOCEI and Monolix/SAEM closely, both in terms of parameter estimates and associated standard errors, both for the repeated sparse data sets, and for the wide range of models and inputs with rich data sets.
Conclusions:
The FOCEI and SAEM algorithms in nlmixr provide near-identical results to those obtained from NONMEM and Monolix for the same models and data. These results indicate that nlmixr may provide a viable alternative to existing tools for pharmacometric parameter estimation.
References:
[1] R Development Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
[2] https://cran.r-project.org/web/packages/nlmixr/index.html
[3] https://github.com/nlmixrdevelopment/nlmixr
[4] Wang W, Hallow KM, James DA. A Tutorial on RxODE. CPT:PSP (2016) 5:3–10.
[5] https://nlmixrdevelopment.github.io/nlmixr
[6] https://github.com/RichardHooijmaijers/shinyMixR
[7] https://github.com/nlmixrdevelopment/xpose.nlmixr
[8] https://github.com/UUPharmacometrics/xpose
[9] Pinheiro J, Bates D, DebRoy S, Sarkar D and R Core Team. nlme: Linear and Nonlinear Mixed Effects Models. [R package (2018)] https://CRAN.R-project.org/package=nlme
[10] Kuhn E and Lavielle MM. Maximum likelihood estimation in nonlinear mixed effects models. Comput Stat Data An (2005) 49:1020–1038.
[11] Beal S, Sheiner LB, Boeckmann A, and Bauer RJ. 1989-2013. NONMEM Users Guides. Version 7.4.3. Icon Development Solutions, USA.
[12] Monolix version 2019R1. Antony, France: Lixoft SAS, 2019. http://lixoft.com/products/monolix/
[13] Lindbom L, Pihlgren P, Jonsson EN. 2005. PsN-Toolkit--a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput Methods Programs Biomed (2005) 79(3): 241-57.
[14] Laveille C, Lavielle M, Chatel K, and Jacqmin P. Evaluation of the PK and PK-PD libraries of MONOLIX: A comparison with NONMEM. PAGE 17 (2008) Abstr 1356 [www.page-meeting.org/?abstract=1356]
