Statistical Details for the Fit Curve Platform
Model Formulas
Table 13.1 provides the formulas for the models on the Fit Curve red triangle menu.
|
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. |
