FiveParameterLogisticCurve Class

public class FiveParameterLogisticCurve : NonlinearCurve

Public Class FiveParameterLogisticCurve
	Inherits NonlinearCurve

public ref class FiveParameterLogisticCurve : public NonlinearCurve

type FiveParameterLogisticCurve = 
    class
        inherit NonlinearCurve
    end

Inheritance

Object  →  Curve  →  NonlinearCurve  →  FiveParameterLogisticCurve

Use the FiveParameterLogisticCurve class to fit a five-parameter logistic curve to asymmetric dose-response data. This extends the standard 4PL model by adding an asymmetry parameter (s) that allows the curve to have different slopes on the ascending and descending portions.

Equation:

y = A₂ + (A₁ - A₂) / (1 + (x/x₀)^p)^s

Parameters:

• A₁ – Upper asymptote (maximum response)
• A₂ – Lower asymptote (minimum response, baseline)
• x₀ – Inflection point (EC₅₀, IC₅₀, or ED₅₀)
• p – Hill slope (steepness factor)
• s – Asymmetry factor (s = 1 reduces to 4PL; s ≠ 1 creates asymmetry)

Applications:

• Asymmetric dose-response curves in pharmacology
• ELISA curves with asymmetric behavior
• Bioassays with non-standard kinetics
• Receptor binding with complex mechanisms
• Growth curves with asymmetric transitions

The asymmetry parameter (s) provides flexibility for data that doesn't follow the symmetric pattern of the standard 4PL curve. When s = 1, the 5PL reduces to the 4PL model. Values of s > 1 create a sharper transition on one side, while s < 1 creates a more gradual transition.

When to Use 5PL vs 4PL: Use the 5PL model when visual inspection or residual analysis of a 4PL fit shows systematic deviation indicating asymmetry. However, be aware that the additional parameter increases the risk of overfitting with limited data. Compare model fit statistics (AIC, BIC) to determine if the additional complexity is justified.

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For details on how to fit a curve of this type, see the NonlinearCurveFitter class.

Reference