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Calculation of results

Please read the Directions for Use for product-specific recommendations. 

There are several types of curve-fitting methods for computerized calculation. They can be divided into two categories: linear and non-linear. The choice depends on the shape of the measuring range for the particular assay. Both FDA and EMA recognize that most ligand-binding assays do not have a linear measuring range but often a sigmodial appearance, thus the algorithm used should be non-linear.

When calculating results, the Blank/Calibrator 0 should be seen as a negative control and not be included in the calibration curve.

 

Cubic Spline

The Cubic Spline Regression analysis is a non-linear algorithm that is one of the models recommended by Mercodia.

The Spline method is a piecewise third order polynomial, which has knots at every calibrator concentration. The whole function and its first and second derivates are continuous.

There are two kinds of Spline fitting methods:

  • Smoothed Spline

  • Interpolation Spline

If available, Smoothed Spline is the best method. It selects the degree of smoothing so that it reaches the optimal for a continuous function. An outlying calibrator value within the calibrator curve will not have an effect on the curve fitting.

The curve fitting in the Interpolation Spline method will draw the calibrator curves exactly through all calibrator responses, which could risk creating a function where sample results cannot be evaluated. 

 

Logistic Regression

Logistic regression is another non-linear algorithm recommended by Mercodia. It is suited for use in ligand-biding assays because it can describe sigmoidal relationships accurately.

FOUR PARAMETER LOGISTIC (4PL)

The algoritm will estimate four parameters in order to fit the curve. The model fits data that makes an S-shaped curve. 

FIVE PARAMETER LOGISTIC (5PL)

The model can handle assymtric relationships by adding one parameter compared to the 4PL algoritm. As the name implies five parameters will be estiamted in order to fit the curve.

Depending on the iterative fitting process used by the software and the ability to fit the algorithm to the actual data generated, a weighting function can be added. By doing this the curve will easier converge to the data, even if outlying values are present.

 

Manual CAlculation

If a curve-fitting program is not available, manual calculation can be done with pen and paper or by using Excel. Mercodia provides Excel Evaluation Sheets upon request. These sheets use a simple approximation (interpolation polynomial) to mimic a spline function and can be used for most products. 

For further reading: Findlay JWA and Dilard RF (2007) Appropriate calibration curve fitting in ligand binding assays. AAPS J. 9(2): E260–E267.