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Principles of Curve Fitting for Multiplex Sandwich Immunoassays, Rev B

r fit. A linear regression with an R2 value >0.99 is considered a very good fit (Nix and Wild 2001). The primary advantage of this method is that it is extremely simple. Once the linear range of an assay is determined, additional standard concentrations within the specified range may be added to improve the accuracy of the fit.

Logistic Regression
Immunoassay data may also be modeled using a nonlinear regression routine, most commonly known as a logistic regression (Baud 1993). An example of a logistic regression of a standard curve from a Bio-Plex cytokine assay, with the log of the concentration plotted on the x-axis and the response (relative median fluorescence intensity, or MFI) plotted on the y-axis, is presented in Figure 2. The logistic regression is commonly used for many assays, including sandwich immunoassays (Baud 1993). Two common logistic equations are used, four-parameter (4PL) and fiveparameter (5PL) (Baud 1993). Depending on the data, one regression may yield better results than another.

Four-Parameter Logistic (4PL)
The 4PL equation contains four parameters or variables related to the graphical properties of the curve, as illustrated in Figure 2.

One derivation of the 4PL equation may be expressed as follows (Baud 1993):

Once a 4PL equation is created from a set of data, values for all four of the parameters will be determined. The equation may then be used to calculate unknown concentrations (x) from the assay data (y), much like the well-known linear equation y = mx + b.

Five-Parameter Logistic (5PL)
The 5PL equation is equivalent to the 4PL equation with an additional parameter add
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