Levy Batista(1,3), Thierry Bastogne(1,2,3), and El-Hadi Djermoune(1)
(1) CRAN CNRS UMR 7039, Nancy, France (2) INRIA BIGS, Vandoeuvre-lès-Nancy, France (3) CYBERnano, Villers-lès-Nancy, France
Objectives: With the advent of realtime biotechnologies, most of biological responses measured during in-vitro or in- vivo experiments exhibit non-linear behaviors and mixed effects models are often used to better characterize the responses. Parameter and confidence intervals estimation involve numerical integration, linearization or stochastic approximation algorithms [1]. Instead of modeling the response we propose a method in which each biological process is regarded as a dynamical system with input-ouput variables and cofactors. We show that this approach allows to use classical linear methods.
Methods: Firstly, we suppose that the response of each biological unit is the output of a linear time invariant system described by an autoregressive model structure with external input (ARX) [2]. The drug administration is considered as the input signal. To account for the variability within and between biological units, we introduce mixed effects in the ARX model. Data are assumed to be recorded at a constant sampling rate. The basic EM algorithm is implemented without approximation to estimate the model parameters under the likelihood function [3]. Moreover, Fisher information matrix is determined by using Louis method [4].
Results: We show how mixed-effects can be introduced in black-box modeling for the identification of a population of dynamic systems. We have determined parameter estimation and confidence intervals of an ARX model structure. We show relevance of the proposed solution in simulation and using real in-vitro data coming from realtime cell impedance measurements.
Conclusions: New biotechnologies allow to use system identification models where the response of individuals is seen as the output of a system with unknown parameters. The proposed method suggests that, in some cases, it is possible to use linear mixed-effects estimation methods to characterize non-linear responses.
References:
[1] M. Lavielle, Mixed Effects Models for the Population Approach. Models, Tasks, Methods & Tools. Chapman & Hall/CRC Biostatistics Series, 2014.
[2] L. Ljung, System Identification, Theory for the User. PreWiley-Hall, 1987.
[3] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the royal statistical society, Serie B, vol. 39, no. 1, pp. 1–38, 1977.
[4] T. A. Louis, “Finding the observed information matrix when using the em algorithm,” Journal of the Royal Statistical Society. Series B (Methodological), vol. 44, no. 2, pp. pp. 226–233, 1982.
Reference: PAGE 25 (2016) Abstr 5807 [www.page-meeting.org/?abstract=5807]
Poster: Methodology - New Modelling Approaches