Is It Possible To Estimate the Parameters of the Sigmoid Emax Model with Truncated Data Typical of Clinical Studies?

Abstract

Many drug concentration-effect relationships are described by the nonlinear sigmoid E(max) model. Clinical considerations frequently limit the magnitude of effect intensity that may be produced; the most pronounced effect intensity may be considerably below E(max). We have tested and quantified the influence of this limitation on the estimatability of the sigmoid E(max) model parameters. We have used the estimated parameter values to calculate data descriptors (drug concentrations required to produce certain effect intensities) and compared these with concentrations determined by using exact parameter values. We found that when the highest measured effect intensity was less than 95% of E(max), E(max) and EC50 were poorly estimated (high coefficient of variation and pronounced bias). Nevertheless, the fit to the data was quite good and the data descriptors were estimated with precision within the range for which data were available but not beyond. Baseline effect was estimated with good precision but the sigmoidicity parameter (gamma) was highly variable. Thus, where clinical considerations prevent determination of concentration-effect data near the maximum effect intensity, E(max) and EC50 estimations are unreliable. The use of estimable data descriptors is proposed to characterize the concentration-effect relationship under these conditions.