Detalle Publicación

D-optimal experimental designs for a mixture of Adair models
Autores: López Fidalgo, Jesús Fernando; Rodríguez-Hernández, M. M.
ISSN: 0169-7439
Volumen: 154
Páginas: 150 - 161
Fecha de publicación: 2016
In a Pharmacokinetic reaction a ligand may be bound to different types of macro-molecules, each with different number of binding sites. They are frequently involved in certain diseases diagnostics. Adair equation is used very often to model the reactions of biological macro-molecules with a ligand. This equation relates the saturation ratio with the free ligand concentration when the equilibrium is reached and it depends on some association constants of the chemical reaction, which have to be estimated. The main problem considered in this paper is the computation of optimal experimental designs for a mixture of Adair models when different types of macromolecules are mixed in the experiment. The main contribution of this work is obtaining the Fisher Information Matrix for a model with a mixture of probability distributions. Since this is not anymore in the Exponential family the expectation cannot be obtained analytically. Then the computation of optimal designs through the information matrix cannot be done with traditional methods. In data analysis when one has the data this expectation can be computed empirically from the data. But in experimental design data are not available when the experiment is being scheduled. Assuming nominal values of the parameters, as is usually done for nonlinear models, simulations were performed for each point in a suitable discretized design space. The number of simulations and the sample size used in each simulation were empirically tuned...