The Quest Graph™ IC50 Calculator attempts to model an experimental set using a four parameter logistic regression model, so called because it has four key parameters in an equation of the form:

This model typically resolves as a sigmoid function, or "S"-shaped curve. For biological promotion, the Hill coefficient of the equation will be (-) negative, with the slope of the curve rising ("S"). For biological inhibition, the Hill coefficient of the equation will be (+) positive, with the slope of the curve falling ("Ƨ").

With regards to IC50, the sigmoid function itself is a special case of the log-logistic distribution, which is part of a broader family of logistic distributions and functions. In contrast to standard logistic distributions, however, a primary distinction of this calculator is that it does not necessitate prior normalization of data, nor does it enforce these boundaries in the modeling of an experimental set. That is to say, in a standard logistic distribution, the response values (Y) range from 0 to 1 probability values. This is typically what is seen in probit/logit analysis and what is commonly used when modeling population survival rates. In this calculator, response values can be any positive real number, which may result in regression models which do not adhere to the 0 to 1 logistic distribution boundaries. This is especially the case where the controls of an experimental set do not make clear the upper and lower bounds of the data. In such cases, it is not uncommon to generate a regression model which extends far into the negative Y-axis or rises exponentially.

Because negative response values are typically incoherent in biological contexts, it is often desirable to analytical restrict regression models to the positive response domain. This can be achieved computational by fixing the minimum response value to zero. This reduces the four parameter logistic model into a three parameter logistic model with the simplified equation as follows:

With this form, the regression model has a lower-bounds fixed at zero, eliminating any models which may otherwise extend into the negative response domain. There are two final points to make about this calculator. The first is that the four parameter logistic curve is a symmetric regression model around the inflection point, that is, the IC₅₀. Roughly translated, this implies that the shape of the sigmoid function on one side of the inflection point will mirror that of the other side. In order to model an experimental set which is asymmetric in nature, a five parameter logistic curve is required. Second, it is inadequate to utilize R² when discussing the goodness of fit of a four parameter regression model. As has been demonstrated in several papers, R² can be used when describing linear regression models, but fails to capture the degree of noise and variability in non-linear models.

For additional reading, please see the following: