Fitting Curves to Non-Linear Data

See how to create non-linear models for situations where linear models just won’t work and there are exponents in the model parameters. Techniques are useful to uncover interesting relationships where the rate of change over time, concentration, or any number of varying inputs defies characterization with linear models. These situations, and half-life, kinetics for growth or decay, pharmacometrics, and sigmoidal potency responses that often require special handling can be addressed using non-linear models. 

NOTE:  In JMP 18, 19 new curve fits were added to the Fit Curve Platform. The most important one is the Dissolution curve analysis. This is expected to be very popular in the Pharmaceuticals.  Dissolution analysis uses industry-standard methods to compare the dissolution profile of a new drug to a standard/reference drug from the Fit Curve platform, including nonparametric F1 Analysis, F2 Analysis, and multivariate distance, along with eight popular dissolution curve models (Higuchi, Hixson-Crowell, and Korsmeyer-Peppas). Fit Curve includes the ability to handle both stacked data (long) and rows as functions (wide) data and Fit Curve DOE for F2 Analysis.

This webinar uses a pharmacokinetic example related to ICH Q14 guidelines for bioassay development.

See how to:

• Understand curve terminologyy
  • Linear Regression Model
  • Curvilinear Regression Model
  • Non-linear model
• See examples of using non-linear models
  • Interactive dats transformation for adhesive stability
  • First order and equilibrium  & enzyme kinetics 
  • Growth curves for historical data
• Choose specialized JMP Models
  • Fit Curve Capability/Platform - Easy dialog with many useful models
  • Non-Linear Capability/Platform - All the knobs for tuning convergence to create more and more complex models than Fit Curve
• Build model using Fit Curve, where the curve shape is the response.
  • Fit a model to the time course data
  • Then use parameters for responses in the DOE model
    • Dissolution curves and disolution DOE verification runs
• Build model using Non-Linear specialized model              

Questions answered by Byron @Byron_JMP  during the session and questions from previous sessions on this topic.

Q: If we have a nonlinear equation from literature and want to see how well the data fit the equation, how can confidence of the model be determined?

A: Yes you can add and customize models using the Model Library in the Specialized> Nonlinear platform to create a formula column with parameters and initial values. Click the Model Library button on the Nonlinear launch window to open the library. Select a model in the list to see its formula in the Formula box.

Menu to start using custom non-linear models

Q: How do you compare multiple models for the best fit?

A: You can create as many models as you want, one at a time or multiple models using the shortcut key that brings up all options.  Then, you will see the results.  

To select multiple report options:

• On Windows:&nbspPress Alt and right-click a disclosure icon.
• On Mac: Press ^ and Option and click a disclosure icon.

To select multiple analysis options:

• On Windows: Press Alt and click a red triangle icon.
• On Mac: Press Option and click a red triangle icon.

See JMP 18 Keyboard Shortcuts for all shortcuts. 

Q: After fitting the curve, is it possible to calculate area under curve in JMP?

A: Yes, you can definitely get area under the curve  elimination rate and absorption rate, underneath that parameter estimates table  when we use one of the pharmacokinetic models.

Q: Can you get other metrics of model performance under nonlinear? I saw RSME and maybe one other.

A: Yes, see Non-Linear Platform options.

Q: Can add a callout box with the data in the box to each plot?

A: In Graph Builder you can use the Hover Label drill-down.

A: Is the large sample data available?

Q: Yes. Enzyme Modifier data is available. 

Q: You mentioned Functional DOE for analyzing data that doesn’t have a good model.  Is that available?

A: Wavelets DOE is available in JMP Pro .

Resources

• When a Linear Model Just Won’t Do: Fitting Nonlinear Models Using JMP, Discovery Summing presentation by Sue Walsh
• Fitting Non-Linear Curves step-by-step guide and video
• Statistical Details for Fit Curve