effect of parameter not being part of design, how to evaluate, treat it as covariate or something else

[#1]

We would like to do response surface design for optimization of two formulation factors… we would like to consider compression force as well as it might have an effect, but could we not have it to be part of the design because it may be adjusted differently for different formulations… in that case could we treat compression force as covariate then, and how?

Compression force would be adjusted to get acceptable friability, and for different formulations different ranges of compression force might be considered acceptable. However, compression force might be important factor for dissolution, our primary response of interest. We might generate for each formulation samples on two levels of compression force but they maybe won't be always same low and high values for all formulations.

@Ben_Ingham 

[#2]

Hi!

This sounds like a constrained factor space DOE. These can be a challenge to design but it is definitely possible.

Let me check that I understand:

• You have 2 formulations factors (we can call them X1,  X2) and a compression factor (X3).
• You know the total range for all factors X1, X2 and X3. This forms a cubic factor space.
• However, the feasible range for X3 is dependent on the formulation factors, X1 and X2. So the feasible factor space is not the whole cube. There are parts of the cube that should be disallowed.

Some questions:

• Is the above all correct?
• Does the feasible range for X3 depend only on X1 or X2, or does it depend on both?
• Can X1 and X2 be varied independently or are they amounts that need to add up to a fixed total? In other words, are they "mixture" factors?

Let me know. I'm confident there will be a solution.

Phil  

[#3]

Yes, X3 is dependent on X1 and X2, and X1 and X2 can be varied independently.

We dont know in advance what X3 we would have for different values of X1 and X2.

[#4]

Hi @TM ,

Would it be feasible to run the study first to determine what the associated X3 values should be when X1 and X2 are at set values in order to gain success? That way when you run the X1 and X2 DoE to alter Y, you simply select the X3 values for each condition that are needed for minimum success?

Thanks,

Ben

[#5]

You say that you don't know in advance what X3 you would have for different values of X1 and X2. But at some point later you do know what X3 is. How do you find out? What is the process of finding out what X3 needs to be?

Also, for a given combination of X1 and X2, is there only 1 possible value for X3? Or is it a range?

[#6]

It will be a range based on in process control of tablets

[#7]

How is the range of X3 determined? Just thinking of how you could pull out an appropriate design - if you can have X3 be one single value (rather than a range) that is 'just enough' to achieve a meaningful output that would make the design easier. How likely is it that X3 could have a value that works for all settings?