Regression model

Regression models define how PLA 3.0 fits dose-response curves and calculates values from your assay data. Use them to set up regression analysis for your assay elements. Selecting the appropriate regression model is an important step in defining your assay.

About regression models

In dose-response analysis, regression models translate experimental data into meaningful metrics by mathematically describing the relationship between dose and response. In PLA 3.0, selecting a regression model is a central part of the analysis workflow:

  • For multi-dose samples, PLA 3.0 fits a regression curve to the dilution sequence. This curve is then used to calculate parameters such as EC50 and other curve characteristics.

  • For single-dose samples, PLA 3.0 uses the regression curve fitted to the Standards to interpolate a dose value from the measured response.

Dose-response analysis documents support the following regression models, each designed for specific curve characteristics:

  • Linear model
  • Hill equation
  • 2-parameter logistic fit model with fixed asymptotes
  • 3-parameter logistic fit model with fixed upper asymptote
  • 3-parameter logistic fit model with fixed lower asymptote
  • 4-parameter logistic fit model
  • 5-parameter logistic fit model

Linear model

Uses the linear regression model.

The model is defined by the following equation:

Where:
  • z = logb(x)
  • b = logarithm base (e, 2, 10)
  • x = working concentration
  • m = slope
  • n = intercept
The following figure shows a sample plot created with this model:
Figure 1. Sample plot created with the linear regression model of the Dose-response analysis document type

Hill equation

Uses the 2-parameter logistic-fit regression model with upper asymptote fixed at 1 and lower asymptote fixed at 0 to span a response range from 0 to 100 %.

The model is defined by the following equation:

Where:
  • B = effect strength (dynamic width)
  • z = logb(x)
  • b = logarithm base (e, 2, 10)
  • x = working concentration
The following figure shows a sample plot created with this model:
Figure 2. Sample plot created with the hill equation regression model of the Dose-response analysis document type

2-parameter logistic fit model with fixed asymptotes

Uses the 2-parameter logistic-fit regression model with fixed upper and lower asymptote.

The model is defined by the following equation:

Where:
  • A = fixed upper asymptote
  • D = fixed lower asymptote
  • B = effect strength (dynamic width)
  • C = logb(EC50)
  • z = logb(x)
  • x = working concentration
  • b = logarithm base (e, 2, 10)
The following figure shows a sample plot created with this model:
Figure 3. Sample plot created with the 2-parameter logistic fit model using undiluted Controls to fix the upper and lower asymptotes

3-parameter logistic fit model with fixed upper asymptote

Uses the 3-parameter logistic-fit regression model with fixed upper asymptote.

The model is defined by the following equation:

Where:
  • A = fixed upper asymptote
  • D = lower asymptote
  • B = effect strength (dynamic width)
  • C =logb(EC50)
  • z = logb(x)
  • x = working concentration
  • b = logarithm base (e, 2, 10)
The following figure shows a sample plot created with this model:
Figure 4. Sample plot created with the 3-parameter logistic fit model with fixed upper asymptote using an undiluted Control to fix the upper asymptote

3-parameter logistic fit model with fixed lower asymptote

Uses the 3-parameter logistic-fit regression model with fixed lower asymptote.

The model is defined by the following equation:

Where:
  • A = upper asymptote
  • D = fixed lower asymptote
  • B = effect strength (dynamic width)
  • C = logb(EC50)
  • z = logb(x)
  • x = working concentration
  • b = logarithm base (e, 2, 10)

4-parameter logistic fit model

Uses the 4-parameter logistic-fit regression model.

The model is defined by the following equation:

Where:
  • A = upper asymptote
  • D = lower asymptote
  • B = effect strength (dynamic width)
  • C = logb(EC50)
  • z = logb(x)
  • x = working concentration
  • b = logarithm base (e, 2, 10)
The following figure shows a sample plot created with this model:
Figure 5. Sample plot created with the 4-parameter logistic fit model of the Dose-response analysis document type

5-parameter logistic fit model

Uses the 5-parameter logistic-fit regression model.

The model is defined by the following equation:

Where:
  • A = upper asymptote
  • D = lower asymptote
  • B, C = nonlinear parameters without scientific meaning
  • G = asymmetry parameter
  • z = logb(x)
  • x = working concentration
  • b = logarithm base (e, 2, 10)

Calculation of the EC50 no longer depends on C only:

The following figure shows a sample plot created with this model:
Figure 6. Sample plot created with the 5-parameter logistic fit model of the Dose-response analysis document type

Work with regression models

For details on how to create and work with regression models, see the Select a regression model topic.