Experimental design for parameter estimation through sensitivity analysis

Abstract

Parameter estimates can be obtained by fitting a numerical simulation model to experimental data, but these estimates may be biased and/or imprecise because of noise in the experimental data. Appropriate choice of experimental conditions, such as exposure or substrate concentrations and sampling times, can minimize the effect of experimental noise on parameter estimates, thus reducing bias and improving precision. This article describes a technique for selecting experimental (initial) conditions and measurement times for optimal parameter estimation. The technique makes use of a user‐supplied mathematical simulation model for the process under study with a set of “current” parameter values specified. These “current” parameter values are the best that can be obtained using all available experimental data and/or literature information at the time when design calculations are performed. Early in a modeling study, the “current” parameter values will be tentative— based on a relatively small amount of information. Later in a study, the “current” parameter values may be known to reasonable accuracy, but final confirmation is desired. The technique uses the simulation model to calculate a numerical index for each possible experimental design. The numerical index, or Information Index, is a measure of the response of a simulation model to changes in parameter values, described by Kalogerakis and Luus (1983, 1984). The experimental design with the greatest value of Information Index is the one under which parameters can be most precisely estimated. Computation of the Information Index, described in detail, can be somewhat complicated, depending on the software available. The results, however, are simple to interpret and provide valuable information on the quality of alternate proposed experiments. The technique is applicable to a broad range of dynamical systems. Its use is demonstrated by application to a simulation model being developed to describe the in vitro metabolism of benzene by mouse liver microsomes.