Estimating Potency for the E max-Model Without Attaining Maximal Effects

The most widely applied model relating drug concentrations to effects is the E_maxmodel. 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_maxmodel can only be estimated with reasonable precision if the curve shows sign of reaching a maximum, otherwise both EC₅₀and E_maxestimates may be extremely imprecise. This paper provides a solution by introducing a new parameter (S₀) equal to E_max/EC₅₀that 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.