A distinction should be made between quantification of drugs binding to receptors and drugs producing responses. There may not necessarily be a linear relationship between the two values. In contrast to this article's previous definition of the Hill equation, the IUPHAR defines the Hill equation in terms of the tissue response , as
where  is the drug concentration,  is the Hill coefficient, and  is the drug concentration that produces a 50% maximal response. Dissociation constants (in the previous section) relate to ligand binding, while  reflects tissue response.
This form of the equation can reflect tissue/cell/population responses to drugs and can be used to generate dose response curves. The relationship between  and EC50 may be quite complex as a biological response will be the sum of myriad factors; a drug will have a different biological effect if more receptors are present, regardless of its affinity.
The Del-Castillo Katz model is used to relate the Hill equation to receptor activation by including a second equilibrium of the ligand-bound receptor to an activated form of the ligand-bound receptor.
Statistical analysis of response as a function of stimulus may be performed by regression methods such as the probit model or logit model, or other methods such as the Spearman–Kärber method. Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship.