Best design for a DOE with 3 variables and one 4 level categorical

[#1]

dear all

I am looking to find the best design with the following: 3 variables and 4 level categoricals. I have for now a custom design RSM with 28 sets. is there anything better?

Ideally I would like to reduce it to 15 sets.

Many Thanks in advance

Kind regards

Stephanie

[#2]

There are many metrics for the performance of a design. The purpose of the design is ultimately to provide the best data to support estimating the parameters of the linear model. Which metrics are most important to you for this experiment? What is the purpose of this experiment?

The minimum number of runs is equal to the number of parameters to be estimated, unless you plan a super-saturated design. Also, the number of runs is one way to achieve the desired power for the tests of the estimates if tests are important at this time. Does the design with 15 runs provide sufficient power for you? Are you using wide ranges for the continuous factors to illicit a large effect? That strategy will also maximize power for any design.

So you have three continuous factors? How many categorical factors with four levels?

[#3]

Dear Mark

Thank you so much for your answer.

The purpose of the experiment is to screen which parameters have the most influence on the output. I have 3 continuous variables and one 4 level categorical

I would say that the categorical at 4 level will provide the answer. It is quite possible that there will have a synergy in between the categorical and the continuous variable. There is definitely some 2 way interactions. But I will try as you suggested with one way to start with.

Thank you for helping!

[#4]

Stephanie,

If you are screening variables, I am curious as to why you have a 4-level categorical?  Can you use 2 of the categories that are farthest apart, thereby increasing the inference space to draw conclusions about all 4 variables?  As Mark suggests, try to use bold settings for all variables.  You are not trying to "pick the winner", you are trying to get an unbiased estimate of the effects of each factor.  When you test one variable at 4-levels, you have biased the study to that variable (3 degrees of freedom vs. 1 for the others).  If you are able to choose 2 of the 4-levels for your first design, you could run those 4 in a res IV fractional factorial in 8 treatments.  I would also suggest you think about noise and some strategy to handle noise during the experiment (no matter what the design, there are always more variables not controlled than controlled).

[#5]

thank you for your support.

I would like to test the following:

Variable 1: continuous: High and Low

Variable 2: continuous: High and Low

Variable 3: continuous: High and Low

Variable 4: excipient 1, excipient 2, excipient 3, excipient 4.

I do not think I can use continuous for variable 4, as each excipient are different.

do you have suggestions to reduce the biais?

I have for now a 28 sets at the best.

Thank you again to help.

Kind regards

Stephanie

[#6]

I don't know what the response variable is?  I assume the excipient is a substance used to do something to the active ingredient (bind, carry, dilute, bulk, stabilize, etc) What specifically do you want it to do and how will you measure this?  What is the excipient formulation?  If you consider the excipient formulation, you may be able to hypothesize as to why the excipients would perform differently.  If you consider this, you might be able to choose 2 extreme excipients to increase the inference space to cover most different types of excipient formulations.  If you already know excipients are more significant than the other variables in your study and you are trying to understand what is the best combination of factors and second order effects for each excipient, that would be a different type of study.  If you are truly screening, then you don't need to test all possible excipients in the first study, just enough to get a representative sample of the possible variation due to excipient.

[#7]

Hi,

Your objective is to screen for the most important factors. The general advice is to start with a small design for screening. Then you can augment with more runs later to find out more about the most important factors.

So it would make sense to start with a small custom design for this screening objective.

You think that there could be important synergistic effects between the 4-level categorical and the 3 continuous factors. In the Custom Design platform you can add these "interaction" effects to the model that you want to test.

Custom Design will tell you the minimum number of runs and a recommended number of runs. It is up to you to decide. But remember that you can augment with more runs later.

I can share an example Custom Design data table, if that would help. This would have the DOE Dialog script so that you can see how the design was created in the Custom Design interface.

Regards,

Phil

[#8]

Dear Phil

Could you share an example? thank you very much.

Kind regards

Stephanie

[#9]

The example is attached.

To be clear: I am not recommending that you should use this design. It is an example to help you to explore the design choices that you need to think about to work towards a solution.

The 3 continuous factors are X1...X3 and the 4-level categorical is X4. I selected a model with all main effects and the interactions between X4 and the continuous factors. The number of runs is the minimum for this model. The optimality criterion is D-optimal. Again, I am not recommending these choices - you need to decide.

You can run the DOE Dialog script in the table to see the Custom Design interface where the design choices were selected.

I hope this helps.

Regards,

Phil

[#10]

Something to consider...While the custom design may generate the most efficient use of resources to understand the design factors, it does not do anything about the noise factors associated with your situation.  Aliasing can be quite complex (e.g., partial aliasing).