Regression analysis

Use regression models and simultaneous regression to set up regression analysis for your assay elements.

Regression models

Regression analysis runs two regressions using a full and a restricted model. PLA 3.0 uses the difference between full and restricted models to analyze the suitability of a system in suitability testing.

  • The full regression model finds the best fit for the system. Regression parameters are defined separately for the Standard and each Test sample.

  • The restricted regression model focuses the regression on relative potency. The restricted model approximates the Standard sample and Test samples together. Only the regression parameter used to determine relative potency is assumed to differ. Other regression parameters are assumed to be equal in the Standard and Test samples.

PLA 3.0 currently supports the following regression models:

  • Parallel-line assay (linear parallel-line)

  • 4-parameter logistic fit

  • 5-parameter logistic fit

  • 3-parameter logistic fit (fixed upper asymptote)

  • 3-parameter logistic fit (fixed lower asymptote)

  • Slope ratio assay

Tip: In regression models for 4-parameter logistic fit and slope ratio, you can include control lines. If you do so, an additional semi-restricted regression is performed. This adds an additional term to the Analysis of Variance.
The following table shows examples of restricted regression models:
Regression model Number of parameters Parameters equal in Standard and Test samples Differentiating parameters
Parallel-line assay with one Test sample 3 slope y-intercept of the Standard sample, y-intercept of the Test sample
Parallel-line assay with three Test samples 5 slope y-intercept of the Standard sample, 3 y-intercepts of the 3 Test samples
4-parameter logistic fit with one Test sample 5 upper asymptote, lower asymptote, slope inflection point of the Standard sample, inflection point of the Test sample
4-parameter logistic fit with three Test samples 7 upper asymptote, lower asymptote, slope inflection point of the Standard sample, 3 inflection points of the 3 Test samples

Simultaneous regression

Use simultaneous regression, if you want to address incomplete data in individual assay elements. Quantitative response assays normally perform all assay regressions one by one, that is, all regression is done in pairs. In the case of simultaneous regression, all regressions are performed together in a single model.

Note: If you use simultaneous regression with the configuration optimizer, you create a very large number of configurations. Your system may not be able to calculate all configurations in a timely manner.