Parameter Estimability of Biphasic Response Models

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Abstract
Pharmacodynamics of general anesthetic agents generally exhibit biphasic concentration-effect relationships (i.e., an activation phase at low concentrations and inhibition at higher concentrations). These relationships are usually characterized with biphasic models constructed from various combinations and modifications of the nonlinear sigmoid E(MAX) model. We tested and quantified the parameter estimability of the simplest additive biphasic pharmacodynamic models by a Monte Carlo method. The estimated model parameters were used to calculate descriptors of the concentration-effect data. Parameters and descriptors were compared with their true values. When the IC50/EC50 ratio was low (<10), E(MAX), EC50, and IC50 were poorly estimated (high coefficient of variation and pronounced bias). However, the fit to the data was excellent, and the data descriptors calculated from the estimated model parameters demonstrated high precision and accuracy. Baseline effect (E0) was estimated with good precision and accuracy. As the IC50/EC50 ratio was increased, the estimability of model parameters and data descriptors improved, with the data descriptors continuing to be more estimable than model parameters. Thus, model parameters become estimable when there is sufficient separation between EC50 and IC50 to produce a plateauing of peak effect (activation), which can be observed directly from the data signature. Data descriptors are not subject to this limitation and thus may serve as better metrics for summarizing concentration-effect relationships.