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Design optimality for models defined by a system of ordinary differential equations
Author(s) -
RodríguezDíaz Juan M.,
SánchezLeón Guillermo
Publication year - 2014
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201300145
Subject(s) - ordinary differential equation , ode , optimal design , estimator , mathematics , linearization , mathematical optimization , sensitivity (control systems) , fisher information , differential equation , nonlinear system , statistics , physics , quantum mechanics , mathematical analysis , electronic engineering , engineering
Many scientific processes, specially in pharmacokinetics (PK) and pharmacodynamics (PD) studies, are defined by a system of ordinary differential equations (ODE). If there are unknown parameters that need to be estimated, the optimal experimental design approach offers quality estimators for the different objectives of the practitioners. When computing optimal designs the standard procedure uses the linearization of the analytical expression of the ODE solution, which is not feasible when this analytical form does not exist. In this work some methods to solve this problem are described and discussed. Optimal designs for two well‐known example models, Iodine and Michaelis–Menten, have been computed using the proposed methods. A thorough study has been done for a specific two‐parameter PK model, the biokinetic model of ciprofloxacin and ofloxacin, computing the best designs for different optimality criteria and numbers of points. The designs have been compared according to their efficiency, and the goodness of the designs for the estimation of each parameter has been checked. Although the objectives of the paper are focused on the optimal design field, the methodology can be used as well for a sensitivity analysis of ordinary differential equation systems.