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.

Quantitative response assay documents currently support the following regression models:

Linear parallel-line
3-parameter logistic fit (fixed upper asymptote)
3-parameter logistic fit (fixed lower asymptote)
4-parameter logistic fit
5-parameter logistic fit
Slope ratio assay

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.

Linear parallel-line

Uses the Linear parallel-line regression model to estimate relative potency.

The model is defined by the following equation:

Response = Slope \cdot {log}_{b} (Dose) + Intercept

3-parameter logistic fit with fixed upper asymptote

Uses the 3-parameter logistic fit regression model with fixed upper asymptote to estimate relative potency.

The model is defined by the following equation:

Response = D + \frac{fixed value - D}{1 + b^{- B \cdot ({log}_{b} (Dose) - C)}}

3-parameter logistic fit with fixed lower asymptote

Uses the 3-parameter logistic fit regression model with fixed lower asymptote to estimate relative potency.

The model is defined by the following equation:

Response = fixed value + \frac{A - fixed value}{1 + b^{- B \cdot ({log}_{b} (Dose) - C)}}

4-parameter logistic fit

Uses the 4-parameter logistic fit regression model to estimate relative potency.

The model is defined by the following equation:

Response = D + \frac{A - D}{1 + b^{- B \cdot ({log}_{b} (Dose) - C)}}

To refine the characteristics of your assay, you can include a control line. If you do so, PLA 3.0 performs an extra semi-restricted regression and uses the values of the control line to calculate the upper or lower margin. This adds an extra term to the Analysis of Variance.

Note:

You set up the control line as an extra element. To include it, add the Include control line element to you analytical model and select the control line you set up.

5-parameter logistic fit

Uses the 5-parameter logistic fit regression model to estimate relative potency.

The model is defined by the following equation:

Response = D + \frac{A - D}{{(1 + b^{- B \cdot ({log}_{b} (Dose) - C)})}^{G}}

Slope ratio

Uses the Slope ratio regression model to estimate relative potency.

The model is defined by the following equation:

Response = Dose \cdot Dose + Intercept

To refine the characteristics of your assay, you include a control line. If you do so, PLA 3.0 performs an extra semi-restricted regression and uses the values of the control line to estimate the intercept. This adds an extra term to the Analysis of Variance.

Note:

You set up the control line as an extra element. To include it, add the Include control line element to you analytical model and select the control line you set up.

Examples

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