One derivation of the 5PL equation may be expressed as follows:
4PL vs. 5PL
The type of logistic equation that will yield the best fit through a set of points is dependent on the response or the shape of the standard curve of an assay. Three different types of response curves may be encountered when analyzing Bio-Plex cytokine immunoassays: a sigmoidal or S-shaped curve (Figure 3A), a low-response curve (Figure 3B), or a high-response curve (Figure 3C). If the curve is S-shaped and symmetrical (i.e., similar shapes on both ends of the S), a 4PL or 5PL regression will yield similar results. When the curve is not symmetrical, as in Figures 3B and 3C, a better fit will be achieved using a 5PL regression.
Measuring Goodness of Fit
Goodness of fit is a term that describes how well a curve fits a given set of data. Goodness of fit using linear regression is commonly assessed by the R2 value (Motulsky 1996). When using logistic regression, there are other statistical parameters for measuring goodness of fit, such as fit probability and residual variance. Two methods more practical for measuring goodness of fit are typically used, backcalculation of standards and spiked recovery (Nix and Wild 2001, Davies 2001).
Backcalculation of Standards (Standards Recovery)
A practical method for assessing the quality of a curve fit is to calculate the concentrations of the standards after the regression has been completed (Nix and Wild 2001, Baud 1993). This procedure is also known as standards recovery and is performed by