Design of Experiments for Estimating Enzyme and Pharmacokinetic Parameters

Abstract

Principles are described for optimally estimating precise model parameters. D-optimized designs, which minimize the volumes of joint confidence regions for the parameters, generally replicate p sampling points. (p is the number of parameters.) The observations are repeated at equal frequency when the estimation of all model parameters is essential, but often in unequal proportions if only some of the parameters are of interest. Usually, one of the design points yields the maximal experimentally attainable response. In the presence of constant relative errors another point measures the smallest possible response. The principles of optimization are applied to simple enzyme and pharmacokinetic models, and designs yielding the most precise parameters are described. These designs provide guidelines, and not rules, for experimentation. In practice, a few observations could test the validity of the model while others could be obtained close to the proposed design points. The usefulness of the strategy is demonstrated by the substantially reduced estimating efficiency (larger parameter variance) of frequently applied experimental designs, especially when the number of measurements is increased.