JMP's "Contour Profile"
In JMP, the "contour profile" feature allows you to display the prediction formula of a fitted model as contour lines and examine the relationship between factors (X) and characteristic values (Y).
In particular, during the development and manufacturing stages of pharmaceuticals, the Quality by Design (QbD) concept recommends representing the relationship between factors and characteristics using contour lines through experimental design methods to construct a design space*. In this context, the "contour profile" shown earlier is frequently used in JMP.
*Multiple combinations and interactions of input variables (such as raw material properties) and process parameters that have been proven to ensure quality (from ICH Q8)
Occasionally, we receive requests from our Japanese customers to display predicted response values in the "contour profile" using a color gradient, as shown below .
fig1.png
Unfortunately, JMP does not have an option to apply a color gradient like the one shown above in its "Contour Profile" feature.
Even when there are multiple characteristics (multiple Y values), the "contour profile" can be drawn by overlaying multiple characteristics as follows:
nao_masukawa_0-1685406975970.png
In this case, if we can apply a color gradient to multiple properties,The resulting graph will be difficult to understand.
Contour lines with color gradients drawn on a contour map.
Drawing contour lines with the color gradient shown earlier in JMP requires a bit of ingenuity.
As an example, let's say we use the JMP sample data "Bounce Data.jmp" and fit a response surface model to characteristic Y "coefficient of restitution," and then want to represent the response surface as contour lines with a color gradient.
We'll start from the point where we've displayed the "Contour Profile" in the [Model Fitting] report.
The contour lines displayed here are plotted with the value of the factor "silane" fixed at 50, with "silica" on the horizontal axis and "silane" on the vertical axis.
nao_masukawa_0-1685408217397.png
Operation to create contour lines with a color gradient
1. From the red triangle button to the left of the "Contour Profile" report, select [Simulator] . As shown in the figure below, set the "Number of repetitions" to 1, change the silica and sulfur sequences to "Arithmetic progression of position parameters," and set the number of steps to 100. (In this example, silane is a factor with a fixed value, so the sequence remains "Fixed.")
2. Click the [Create Table] button at the bottom of the "Simulator".
nao_masukawa_1-1685408605349.png
This will output the data table shown on the right side of the diagram above. This data table is created as follows:
The "silica" range (0.7-1.7) is divided into 100 equal intervals.
The range of "sulfur" (1.8-2.8) is divided into 100 equal intervals.
⇒ Create a grid of 10,000 squares (=100 x 100) with silica on the horizontal axis and sulfur on the vertical axis, and input the predicted value for each grid into the "coefficient of restitution" field.
3. Select [Graph] > [Contour Plot] for the data table created in step 2, specify [X] and [Y] as follows, and check "Fill display area".
nao_masukawa_2-1685409679151.png
A contour map will be created. If necessary, right-click on the legend displayed on the right and specify the color theme, the number of labels (how many to color-code), etc.
nao_masukawa_3-1685410345348.png
To display value labels on the contour lines, select "Contour Labels" from the red triangle button in the upper left corner of the report.
Contour lines with color gradients drawn using GraphBuilder
The above instructions demonstrate the operation using the "Contour Map" platform, but you can also create it using the "Graph Builder" on the data table created in step 2.
nao_masukawa_4-1685410786322.png
Which is better depends on your preference, but please note that "Graph Builder" has display limitations compared to "Contour Maps," such as not being able to add value labels to contour lines.
by Naohiro Masukawa, JMP Japan
