FourParameterLogisticCurve Class

public class FourParameterLogisticCurve : NonlinearCurve

Public Class FourParameterLogisticCurve
	Inherits NonlinearCurve

public ref class FourParameterLogisticCurve : public NonlinearCurve

type FourParameterLogisticCurve = 
    class
        inherit NonlinearCurve
    end

Inheritance

Object  →  Curve  →  NonlinearCurve  →  FourParameterLogisticCurve

Use the FourParameterLogisticCurve class to fit a four-parameter logistic curve to data. This is the standard dose-response curve used in pharmacology, immunoassays (ELISA), and bioassays. The 4PL curve is characterized by its symmetric S-shape with upper and lower asymptotes.

Equation:

y = A₂ + (A₁ - A₂) / (1 + (x/x₀)^p)

Parameters:

• A₁ – Upper asymptote (maximum response)
• A₂ – Lower asymptote (minimum response, baseline)
• x₀ – Inflection point (EC₅₀, IC₅₀, or ED₅₀ in pharmacology)
• p – Hill slope (steepness factor; positive for increasing, negative for decreasing curves)

Applications:

• Dose-response analysis in pharmacology
• ELISA and immunoassay standard curves
• EC₅₀/IC₅₀ determination
• Bioassay calibration
• Receptor binding studies

The 4PL curve assumes symmetry around the inflection point. When the data shows asymmetry (e.g., different slopes on ascending vs. descending portions), a FiveParameterLogisticCurve with an additional asymmetry parameter may provide a better fit.

Alternative Parameterizations: The 4PL model is sometimes written as y = D + (A - D) / (1 + (x/C)^B), where A = A₁, D = A₂, C = x₀, and B = p. This is equivalent to the form used here.

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Reference