Diagnosis of Model Applicability by Identification of Incompatible Data Sets Illustrated on a Pharmacokinetic Model for Dioxins in Mammals

Abstract

When calibrating a model the problem often arises that different data sets (e.g. different outputs of the same system; data obtained under different conditions) are incompatible: parameter values that give an acceptable fit to one data set provide an unacceptable fit to another set. Occasionally, a previously calibrated model fits poorly to a new data set, but it may be possible to re-calibrate the model to both data sets. However, if data sets are in fact incompatible, calibration of the model to all available data may simply result in a poor compromise-fit without any insight into the cause of the problem. This paper discusses how the situation can be analysed as a multi-objective optimization problem, with the goodness of fit values to the different data sets as optimization goals. It is shown that the set of Pareto-optimal solutions (i.e. where an increase in fit to a particular data set must necessarily lead to a decrease elsewhere) provides an efficient way to analyse the situation. If there is only a single Pareto-optimal point, the same set of parameter values can be used for all ap­plications. If this is not the case, it will be shown how trade-offs between goodness of fit values can be indicated, and clusters of mutually compatible data sets (i.e. those that can be fitted by single set of parameter values) can be identified. Analysis of parameter values corresponding to the different clusters provides insight to arrive at a more generally applicable model. The method proposed in this paper is illustrated on a simple growth model with artificial data sets as well as on a pharmacokinetic model for dioxins using data from a number of independent experiments using mice, rats and cows. The present analysis provides valuable insight for the further development of generic toxicokinetic models that can be used for interspecies extrapolations.