Nowadays Quality by Design is a huge topic - especially in pharmaceutical appliocations. Not only being the recommended method for drug development by the FDA, it even gives you that much more flexibility in production and much more knowledge about your process than many other methods. In this piece I will go through the process of finding a design space using the QbD-methodology supported by Design-Expert. The whole example will be based on data provided by the FDA.


Recently we developed a whole new training on the statistical aspects - especially the Design-of-Experiments-part (DoE) - of QbD. I started familiarizing with the topic by reading the ICH-Guidlines (Q8-Q10) and was a bit disappointed. The guidelines seemed to be very liberal, allowing you to do what ever you want as long as it makes some sense. I - as a statistician - was hoping to find clear guidelines stating that you shall use Design of Experiments (DoE) as a very important tool when developing a drug. 

If you read a bit further you will of course see that using DoE is the strong recommendation by ICH. Later on a colleague pointed me to a very nice example of the recommended QbD-approach - using DoE - by the FDA. On 107 pages the document (Quality by Design for ANDAs: An Example for Immediat-Release Dosage Forms) goes through the whole process of the development of a ANDA(Abbreviated New Drug Application)-drug-product. The document contains many examples of how to apply DoE in pharmaceutical applications. We decided to use multiple of those examples for our training and I want to use one of those in here, to show step by step how to reproduce the results in the document using Design-Expert. I will use Formulation Development Study #1 (starting on page 33) as our example.



One of the most important steps when doing DoE is to select the right factors and the right ranges for those factors. In this example we are trying to find a design space that grants sufficient quality for the following response variables

  • Dissolution at 30 min [Target: Maximize >= 80%]
  • Tablet Content Uniformity CU [Target: Minimize % Relative SD < 5%]
  • Powder blend flow function coefficient ffc. [Target: Maximize >6]
  • Tablet Hardness at 10 kN [Target: Maximize >9kP]

Based on a formal risk assessment and previous screening-experiments the following factors have been chosen to be researched:

  • Drug Substance PSD (Particle Size Distribution - d90, µm) in the range of 10 to 30
  • Disintegrant (%) in the range of 1 to 5
  • %MCC in MCC/Lactose combination in the range of 33.3 to 66.7 
As this is rather an optimization problem than a screening-problem the power-analysis was skipped. A full-factorial design with 3 center points was chosen.

Setting up the Design

It's fairly simple to set up this design in Design-Expert. Just hit the New Design link, select the Factorial tab and in there Regular Two-Level. The design we need is the one for three factors using 8 experiments.

Don't forget to enter the three center points in the bottom part of the dialog. Hit Continue to enter the factors (ignore the warning for a moment - in this example we don't care for the power):
The next step is to enter the responses. Again we are not doing power analysis here, thus you might remove the numbers for signal and noise.
Finally you should end up with something like that:
Of course your order of experiments could be different because the design is randomized. I copied the data from the document to end up with this:
You can download the prepared file here.


Now we want to analyze the data. Design-Expert guides you nicely through the process. Just select the first of the responses on the left hand side and iterate with me through the individual steps. 

  • Transform Initially we don't want to transform our data. This might be an option if we detect specific problems with our models later on in the Diagnostics
  • Effects All effects that are in the top right of the half-normal-plot and do not fit to the line of the effects in the bottom left will be the important ones. Here it's quite obvious that PSD, Disintegrant and their interaction are important.
  • ANOVA Here I just want to compare the FDAs report with our results (we'll only consider the blue, the adjusted model):
Design Expert Report
Both are essentially the same. PSD, Disintegrant and their interaction are significant. So is the overall model. At the same time we cannot detect curvature or a lack-of-fit. Thats good!
  • Diagnostic There is nothing suspicious in the diagnostics-tab, thus we might continue with the interpretation of the model in the model graphs. Design-Expert provides exactly the graph from the FDA-report (page 38).


Obviously we are able to get a good result in terms of dissolution, as long as we take care that PSD is on a low level. It sounds reasonable for me that the dissolution is increased if you have smaller particles.
Disintegrant does not seem to be that important for the dissolution. Of course we should keep our goals in mind, here. We need at least 80% dissolution after 30 minutes. Thus most of the factor-settings are actually ok. Only the dark-blue-part in the bottom-right is not acceptable.


After going through the modeling step for each response we now can go on with the optimization or more precisely the definition of the design space. First we need to tell Design-Expert the acceptable ranges for each response. We do that in the Optimization => Graphical section on the left hand side in Design-Expert.

First enter the accepted ranges for each individual factor, like I did it here for the Dissolution 
Now Design-Expert will try to find a design space that grants sufficient quality for all of these responses. The FDA-example looks like this:
If you go to the next step in Design-Expert your graph will look like that:
Again it is exactly the same. The yellow area is our design space. Inside it all quality requirements are fulfilled. But be careful: This is just a 2-dimensional graph, while our design space is actually 3-dimensional. You can see the effect of factor C (MCC% of MCC/Lactose) by using the Factors Tool in Design-Expert.
Just move the red bar for factor C to the left and right to see what happens with your design space.
Design Space for low levels of %MCC of MCC/Lactose

Design Space for high levels of %MCC in MCC/Lactose

If you enjoyed this intro to QbD and Design-Expert check out our free webinars that might go a bit deeper - especially on Design-Expert and DoE!