A practical algorithm for practical parameter identifiability analysis
Yasunori Aoki (1), Ben Holder (2), Hans De Sterck (1), and Ken Hayami (3)
(1) University of Waterloo, (2) Ryerson University, (3) National Institute of Informatics
Objectives: When constructing a mathematical model in biology, we often face the problem of parameter identifiability. As the reliability of predictions based on a parameterized mathematical model depends on the reliability of the estimated parameters, being able to identify the parameters based on the experimental data is crucial. Thus parameter identifiability analysis is an essential stage in model building and designing experiment. We aim to conduct this identifiability analysis by finding multiple sets of parameters that are consistent with the experimental data. If these multiple parameter values are well-constrained, then we can say the parameter is most likely identifiable, and otherwise it is not identifiable. Although this approach to identifiability analysis is known to be reliable, its existing implementation in the Monte Carlo method is known to be computationally intensive and often considered to be impractical.
Methods: Conventionally, multiple sets of parameters that are consistent with the experimental data are found one-by-one using a local optimization algorithm such as the Levenberg-Marquardt method. We propose a new algorithm for parameter identifiability analysis by modifying the Cluster Newton method for parameter identification presented in [1], which simultaneously finds multiple sets of consistent parameters, hence reducing the computation time significantly.
Results: We have conducted numerical experiments using three finitely-parameterized systems of ordinary differential equations models in biology: an influenza viral kinetics model, an HIV viral kinetics model, and a three-step biochemistry pathway model. We have observed that our algorithm reliably estimates parameter identifiability at 1/10th to 1/50th the computational cost of the conventional Monte Carlo simulation.
Conclusions: With the proposed algorithm, parameter identifiability analysis of nonlinear mathematical models can be done significantly faster than using the Monte Carlo simulation, and gives more robust result than the local linearization-based identifiability analysis using the Fischer Information matrix. As parameter identifiability can be used for experimental design evaluation, we wish to incorporate the proposed algorithm into an optimal experimental design workflow in the future.
References:
[1] Yasunori Aoki, Ken Hayami, Hans De Sterck and Akihiko Konagaya: Cluster Newton Method for Sampling Multiple Solutions of an Underdetermined Inverse Problem: Parameter Identification for Pharmacokinetics, submitted to Inverse Problems, 2011; also appeared as a technical report, see http://www.nii.ac.jp/TechReports/11-002E.html.
