RSM based on CCD is supposed to be applied for finding the optimum value of some independent variables. There are two dependent variables. Can we use sum of the response signals obtained for these two dependent variables as a function of independent variables and find only one fitted model (equation) for the problem?
There are many examples of this kind in the literature. An example is the work attached, in which the sum of HPLC peak area of two drugs (AT and VAS) has been fitted with the second-order quadratic model, function of pH, sorbent amount, and sorption time, because these two drugs are used together for treatment and control of hypertension.
Can we use such a manner for approaching the problems by experimental design? If not, why?
Ahmad Hosseini-Bandegharaei
You may get your answer by considering some numerical examples. Apply the idea in some numerical examples and observe the results. It might be helpful.
Yes, you can --I think -- if you are interested in the sum.
Otherwise, use a polynomial (metamodel) per dependent variable.
Also see either constrained RSM or multi-objective Pareto RSM; see my 2015 book or website.
It is wiser to transform the results than to do the direct sum of the responses. I suggest using multiple response optimization. See this article:
Costa, Nuno Ricardo, and Zulema Lopes Pereira. "Multiple response optimization: a global criterion‐based method." Journal of chemometrics 24.6 (2010): 333-342.
I hope i helped you.
As you know each component gives different response even they have same concentration. Especially affects of high potent pharmaceuticals at low concentration may extremely high and according to NIOSH each of the antineoplastic drugs have different biological affect. So it is more accurate to take multiple response. Conversion factor can be use to calculate concentration but the biological affect may not be at the same proportion. I hope I helped you.
I think it depends on the dependent variables. If the two dependent variables can be added to give a meaningful entity, then there is no problem in this approach. As your model is actually predicting and optimizing a third variable which is the sum of two variables. But in many cases, the dependent variables are unrelated and different entities, and adding them will not make any sense. In such cases, multi-objective optimization is more preferred.
Dear Hosseini-Bandegharaei
You can apply normalized peak area in Design matrix. For this purpose, normalized peak area for each run is chosen as the response objective for the study. To normalize the peak areas, all the experiments are first done according to design matrix and then, the peak area of each analyte is divided by its smallest peak area, which is achieved in all the experiments. Normalized peak areas for analytes are subsequently added for each run and employed in calculation of the total normalized peak area.
I think we cannot say in general. Objectives of the study are important to decide it. However some properties of the variables can help us. These two dependent variables (let say outputs) need to have summability and same metrics. The interpretation of the sum should be more meaningful than the interpretation of the dependent variables individually. Comparing the shape of the response surface for each dependent variable and sum, we mustn't lose important information when using the sum.
From optimization aspect if we can’t use the sum these dependent variables, we can use multi-objective optimization techniques.
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