Estimating potency for the Emax-model without attaining maximal effects

The most widely applied model relating drug concentrations to effects is the E-max 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 E-max model can only be estimated with reasonable precision if the curve shows sign of reaching a maximum, otherwise both EC50 and E-max estimates may be extremely imprecise. This paper provides a solution by introducing a new parameter (S-0) equal to E-max/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.