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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020 Epub Dec 05, 2020
https://doi.org/10.15446/rce.v43n2.81938
Original articles of research
An Optimal Design Criterion for Within-Individual Covariance Matrices Discrimination and Parameter Estimation in Nonlinear Mixed Effects Models
Un criterio de diseño optimal para discriminación de matrices de covarianza intra-individual y estimación de parámetros en modelos de efectos mixtos no lineales
1Instituto de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Medellin, Colombia
2Escuela de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Medellin, Colombia
In this paper, we consider the problem of finding optimal population designs for within-individual covariance matrices discrimination and parameter estimation in nonlinear mixed effects models. A compound optimality criterion is provided, which combines an estimation criterion and a discrimination criterion. We used the D-optimality criterion for parameter estimation, which maximizes the determinant of the Fisher information matrix. For discrimination, we propose a generalization of the T-optimality criterion for fixed-effects models. Equivalence theorems are provided for these criteria. We illustrated the application of compound criteria with an example in a pharmacokinetic experiment.
Key words: Compound criteria; D-optimality; Mixed effects models; Optimal designs; T-optimality
En este artículo se considera el problema de encontrar diseños óptimos poblacionales para discriminación entre matrices de covarianza intra-individual y estimación de parámetros en modelos de efectos mixtos no lineales. Se propone un criterio compuesto que combina un criterio para estimación y otro para discriminación. Para estimación se usa el criterio de D-optimalidad el cual maximiza el determinante de la matriz de información de Fisher. Para discriminación se propone una generalización del criterio de T-optimalidad para modelos de efectos fijos. Para estos criterios se proporcionan los respectivos teoremas de equivalencia. La aplicación del criterio compuesto se ilustra con un ejemplo en un experimento de farmacocinética.
Palabras clave: Criterios compuestos; Diseños óptimos; D-optimalidad; Modelo de efectos mixtos; T-optimalidad
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Received: September 2019; Accepted: April 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
