Estimating potency for the Emax-model without attaining maximal effects.

The most widely applied model relating drug concentrations to effects is the Emax model. In practice, concentration-effect relationships often deviate from a simple linear relationship but without reaching a clear maximum because a further increase in concentration might be associated with unacceptable or distorting side effects. The parameters for the Emax model can only be estimated with reasonable precision if the curve shows sign of reaching a maximum, otherwise both EC50 and Emax estimates may be extremely imprecise. This paper provides a solution by introducing a new parameter (S0) equal to Emax/EC50 that can be used to characterize potency adequately even if there are no signs of a clear maximum. Simulations are presented to investigate the nature of the new parameter and published examples are used as illustration.