Estimating the parameters of the operational model of pharmacological agonism.

The aim of this work is practical. We show that the parameters of the widely used operational model of pharmacological agonism are difficult to estimate from single dose-response curves. The parameters can be estimated using pairs of dose-response curves (usually treatment and control) sharing some parameters. Confidence bands for the estimators are developed. In the case of multiple dose-response curve pairs one can employ a non-linear mixed effects model to allow for inter-individual variation. The point estimates and the confidence intervals thus obtained are similar to the more naive construction based on mean and standard errors of parameter estimates. To test for difference of certain parameters between treatment and control we employ a permutation test and Wald's test. Copyright 2005 John Wiley & Sons, Ltd.