Predictive and Specialized Modeling > Fit Curve > Statistical Details for the Fit Curve Platform
Publication date: 05/24/2021

Statistical Details for the Fit Curve Platform

Model Formulas

Table 14.1 provides the formulas for the models on the Fit Curve red triangle menu.

Table 14.1 Fit Curve Model Formulas

Model

Formula

Polynomials

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Equation shown here

where k is the order of the polynomial. These models can also be fit using the Fit Model and Fit Y by X platforms.

Logistic 2P

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Equation shown here

a = Growth Rate

b = Inflection Point

Available only when all response values are between zero and one.

Logistic 3P

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Asymptote

Logistic 4P

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Logistic 4P Rodbard

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Available only when the regressor values are positive.

Logistic 4P Hill

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Logistic 5P

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Asymptote 1

d = Asymptote 2

f = Power

Probit 2P

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Equation shown here

a = Growth Rate

b = Inflection Point

Φ = Normal Distribution CDF

Available only when all response values are between zero and one.

Probit 4P

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Equation shown here

a = Growth Rate

b = Inflection Point

c = Asymptote 1

d = Asymptote 2

Φ = Normal Distribution CDF

Gompertz 3P

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Equation shown here

a = Asymptote

b = Growth Rate

c = Inflection Point

Gompertz 4P

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Equation shown here

a = Lower Asymptote

b = Upper Asymptote

c = Growth Rate

d = Inflection Point

Weibull Growth

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Equation shown here

a = Upper Asymptote

b = Growth Rate

c = Inflection Point

Available only when both the response values and regressor values are non-negative.

Exponential 2P

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Equation shown here

a = Scale

b = Growth Rate

Exponential 3P

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Equation shown here

a = Asymptote

b = Scale

c = Growth Rate

Biexponential 4P

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Equation shown here

a = Scale 1

b = Decay Rate 1

c = Scale 2

d = Decay Rate 2

Available only when the response values are positive.

Biexponential 5P

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Equation shown here

a = Asymptote

b = Scale 1

c = Decay Rate 1

d = Scale 2

f = Decay Rate 2

Mechanistic Growth

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Equation shown here

a = Asymptote

b = Scale

c = Growth Rate

Cell Growth 4P

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Equation shown here

a = Peak value if mortality rate, d, is zero

b = Response at time zero

c = Cell Division Rate

d = Cell Mortality Rate

Available only when the response values are positive and the regressor values are non-negative.

Gaussian Peak

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Equation shown here

a = Peak Value

b = Critical Point

c = Growth Rate

Lorentzian Peak

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Equation shown here

a = Peak Value

b = Growth Rate

c = Critical Point

One Compartment Oral Dose

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Image shown here

Equation shown here

a = Area Under Curve

b = Elimination Rate

c = Absorption Rate

Available only when the response values and the regressor values are all positive.

Two Compartment IV Bolus Dose

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Image shown here

Equation shown here

α =Equation shown here

β =Equation shown here

a = Initial Concentration

b = Transfer Rate In

c = Transfer Rate Out

d = Elimination Rate

Available only when the response values and the regressor values are all positive.

Michaelis-Menten

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Equation shown here

a = Max Reaction Rate

b = Inverse Affinity

Available only when the response values and the regressor values are all positive.

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