Five Parameter logistic model

The topic of nonlinear calibration for LBAs, such as immunoassays, has been reviewed in detail in a number of publications [4,8,9,15 17]. Typically, immunoassay calibration curves are inherently nonlinear [9]. Because the response error relationship is a nonconstant function of the mean response, weighting is needed to account for the heterogeneity in response variances. The four- or five-parameter logistic models are accepted widely as the standard models for fitting nonlinear sigmoidal calibration data [3 5,8,9,16,17], This model can be described... 

The most frequently used nonlinear calibration curve models [18] are the four- and five-parameter logistic models (4PL and 5PL). For example, the four-parameter logistic model is expressed mathematically as follows ... 

A calibration (standard) curve describes the concentration-response curve typically including more than eight calibrators and additional ones serving as anchor points thus facilitating curve fitting. All calibrators are prepared in duplicates in the matrix analyzed. The concentration-response relationship is most often fitted with a four- to five-parameter logistic model. 

Physico-chemical measurements using chromatographic methods produce responses that are linear to the concentrations. As IA measures the resulting signals of a reaction, however, the response is a nonlinear function of the analyte concentration. Often, the regression model used to describe this relationship is a four- or five-parameter logistic function, as shown in the sigmoid shape standard curve in Fig. 6.4. 

When the curve is asymmetric around the two sides of the EDS0, another term is introduced to provide an estimate for this asymmetry and a better fit. This becomes the five-parameter logistic (5PL) model ... 

Figure 3.4 Modelled maltose attenuation data (MG, modified Gompertz IBF, incomplete 3-function 5P, five-parameter logistic). The residuals for each model are depicted on the right.

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