Hello,
Is it possible to design a complete factorial experiment for 3 dependent variables (more on that in a second) for one outcome? The variables are dependent as they each represent the % of active mixed ingredient A, B or C, ( A + B + C = 100%) that a patient would receive. For now, assume the dosage of each distinct mix will always be the same.
We are trying to determine the best mix that would maximize the outcome. A is the main ingredient and would be either low (50% of the mix) or high (70% of the mix).
B and C would also be either high or low. It would look like this:
- A:70% - B:20% - C:10%
- A:70% - B:10% - C:20%
- A:50% - B:30% - C:20%
- A:50% - B:20% - C:30%
Although A can be either high/low, B & C high/low values would change when A is either high or low. I can't draw a high/low cube as with three independent variables.
Can this design be modeled as a factorial design? Would you consider a better approach to determine the best mix?
What would the design would be like if we were to set two level of dosages for the mix?
Regards,
Angel
In my opinion, you can approach the above problem based on Response Surface Modeling and Optimization using Mixture Designs type of experimental designs.
detailed coverage of Mixture designs is provided in the following two books :
1) Applied Regression Analysis: Draper and Smith.
2) Response Surface Methodology : Myers, Montogomery and Cook.