Predictive and Specialized Modeling > Fit Curve > Statistical Details for the Fit Curve Platform
Publication date: 11/10/2021

# 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

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

a = Growth Rate

b = Inflection Point

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

Logistic 3P

a = Growth Rate

b = Inflection Point

c = Asymptote

Logistic 4P

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Logistic 4P Rodbard

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Available only when the regressor values are positive.

Logistic 4P Hill

a = Growth Rate

b = Inflection Point

c = Lower Asymptote

d = Upper Asymptote

Logistic 5P

a = Growth Rate

b = Inflection Point

c = Asymptote 1

d = Asymptote 2

f = Power

Probit 2P

a = Growth Rate

b = Inflection Point

Φ = Normal Distribution CDF

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

Probit 4P

a = Growth Rate

b = Inflection Point

c = Asymptote 1

d = Asymptote 2

Φ = Normal Distribution CDF

Gompertz 3P

a = Asymptote

b = Growth Rate

c = Inflection Point

Gompertz 4P

a = Lower Asymptote

b = Upper Asymptote

c = Growth Rate

d = Inflection Point

Weibull Growth

a = Upper Asymptote

b = Growth Rate

c = Inflection Point

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

Exponential 2P

a = Scale

b = Growth Rate

Exponential 3P

a = Asymptote

b = Scale

c = Growth Rate

Biexponential 4P

a = Scale 1

b = Decay Rate 1

c = Scale 2

d = Decay Rate 2

Available only when the response values are positive.

Biexponential 5P

a = Asymptote

b = Scale 1

c = Decay Rate 1

d = Scale 2

f = Decay Rate 2

Mechanistic Growth

a = Asymptote

b = Scale

c = Growth Rate

Cell Growth 4P

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

a = Peak Value

b = Critical Point

c = Growth Rate

Lorentzian Peak

a = Peak Value

b = Growth Rate

c = Critical Point

One Compartment Oral Dose

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

α =

β =

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

a = Max Reaction Rate

b = Inverse Affinity

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