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General guidance on follw-up DOE for DSDs and resources?

BJK_JerseyBoy

Hi I am a newbie in DOE and using JMP. I have pharmaceutical formulation that involves 5 continuous factors and 4 responses to optimize. I have used DSDs to identify the design space that I want to further explore and optimize the formulation.

I fit the model after acquiring the data and remove the effect that is not important (F5 and all quadratic forms and interactions).

By maximizing the desirability parameter, I found the optimal formulation as below.

By looking at the each desirability function, I kind of get the idea that I will have to maximize F1 and minimize F3. F4 barely affect the desirability, so it could be fixed. Also, F2 is not significant factor but combination of F2*F3 is an important factor. This tells me that I would have to vary F2 and F3 for the next round of DOE to optimize the formulation.

The questions is;

1) How should I set the boundary of F2 and F3 to further optimize.

2) What DOE model should I apply for this type of optimization?

3) Lastly, are there any specific tools in JMP that allow me to systemically investigate the factors and design space to follow up for next DOE run rather than relying on my naive observations? I have played around with a graph builder but since I have 4 response that I want to optimize at the same time, it was not that helpful to find a design space to follow up with DOE.

I am sorry if the questions are too basic, but it would be great if you can give general guidance on designing follow up DOE for DSDs. Also some useful tool for finding design space to follow up after initial DSD and related resources would be very appreciated.

Thank you!!

Accepted answers

Victor_G

Hi @BJK_JerseyBoy,

With formulation topics, there are commonly two different approaches :

Either your formulation is a "diluted" solution, and the solvent takes a large amount of the formulation (70-90%+) and/or the solvent is inert or doesn't influence the responses you're measuring : That means you would like to see if some additives show significant effect, synergistic or antagonistic interactions : in this case, since you're not interested in ratios between additives but rather in the influence of small amounts of additives in the formulation (and the solvent will compensate to 100% the total amount of additives introduced), your factors are indepent of each others, and any factorial design may be suited : Screening design, Definitive Screening Design, (Fractional/Full) Factorial Designs, Response Surface Model designs, ... Depending on the complexity of the model and number of runs to estimate effects, you will be able to estimate statistical significance of effects/interactions, and possibly do some optimization (mostly in the case of DSD, RSM).

Or your formulation has no solvent, and/or the solvent is not predominant in the formulation and/or has an influence on the response(s) and/or you're more interested to find the good ratio between additives than their absolute concentration in the formulation : in this case Mixture Designs are more suited, they are not focused on the estimation of statistical significance of your factors, but more on the ratios optimization of additives to match your response(s) objectives. Factors are dependent of each others (if you reduce level of A, you increase level(s) of other additive(s)) and the total amount/part of the formulation is fixed (1 or 100%).

You can look at this great poster to see if your situation requires Mixture Designs (you'll have the explanation I have done before between different types of formulations/mixtures): When Not to Run a Mixture Experiment - JMP User Community

In your case, looking at your example and results, you did some transformations in your inputs (and outputs) to have ratios instead of amount of additives : this seems to be a situation where Mixture Designs would be more suited (or perhaps a custom mixed model, with F1, F2 and F3 as mixture factors, and F4 as continuous factor since its concentration is very low compared to other additives).

Mixture Designs involve frequently more runs than with screening and some factorial designs, but the objective is different. You can have several levels for each factors depending on your model complexity, add any constraints you want (about max ratio for your factors, or constraint about ratio between (some of) them) and the experimental space exploration is quite easy with the mixture Profiler (example in screenshot on the JMP sample data "Donev Mixture Data"). Also if needed, you can fix/block any factor at a specific level if you want to optimize your responses with a "fixed constraint" (like F4 is at 2% for example) : Prediction Profiler Options (jmp.com)

Your approach is interesting (even if theoriticaly debatable for ratios), and it would be nice to check your findings with new runs, to see if you're still able to have correct predictions and validate your model.

Hope this answer will help you,

Mixture-design_example.png

All comments

Victor_G

Hi @BJK_JerseyBoy,

Just to be sure, you're talking about a formulation and doing a DSD, which is a special factorial design assuming independent factors and no constraints on the "total amount". Is this really your case, you can add or reduce "additives" amount without any constraints/dependency between factors and the solvent will compensate the changes in F1, F2, F3 and F4 ?

Or should the amount of F1+F2+F3+F4 always be equal to 100% of the formulation ? If this is the case, a Mixture Designs (jmp.com) would perhaps have been more suited for your needs.

You can try to see what optimization JMP does with your several responses by clicking on the red dot next to Profiler, "Optimization and Desirability", "and then "Maximize Desirability". Keep in mind that by default each of your 4 responses will have the same importance (1), but you can change this in "Set Desirability", if you want to give more/less importance to a response.
If you want to build a deeper understanding of your system by adding experiments to your DoE, I think the platform "Augment Design" could really help you : Augment Designs (jmp.com). This way, you keep (or augment) your existing model and experiments but you can augment the precision with new added experiments, or change the range of your factors to explore a broader/smaller experimental space.
Perhaps something interesting to try would be to augment some of the ranges of your factors space (if you are in exploration phase, else in an optimization phase it would be best to concentrate in a smaller optimal experimental space), to see for example :
- What happens if you have a lower level for factors F2 and F3 (and/or a higher level for factor F1) : do you still have to keep F2 and F3 at their lowest level and F1 et its highest level ?
- What happens if F4 has a broader range, does it change its impact on the responses ?

I hope these first thoughts will help you,

BJK_JerseyBoy

Thanks @Victor_G,

You sound like you are familiar with pharmaceutical formulation work so I will give you bit more details.

Yes, it is a pure mixture problem where I have fixed total quantity and vary the amount of each factor.

So as you said, F1+F2+F3+F4 should be 100. I wanted to have 'at least' 3 levels for each factor and tried custom design but with that I could not achieve the orthogonality of main factors. I remember reading something like "make the model fit the problem does not make the problem fit the model." in one of postings in JMP community. However, I really wanted to employ DSD as it enables orthogonal evaluation of each factor on responses.

So, I made little trick to be able to apply DSD on this problem. I converted % of each factor to ratios and this way you can independently change the level of each factor. For instance, when you look at the screen shot of maximizing the desirability on my initial posting, JMP tells me that at F1:30, F2:5, F3:10, F4: 1 I can maximize the responses. This is the ratios, but I can convert this ratio to F1: 65%, F2: 11%, F3:22%, F4: 2%, then use this mixture to screen the formulations.

I know it is not strict forward and not sure if it is correct way to do it, but at least JMP fit this data nicely with p-value of predictive plot of R1&R2 ~0.01 and R3&R4 ~ 0.06.

I have never explored Mixture Design but will do if that enables the orthogonal design and less runs for initial screening compared to DSD.

Below I aggregated my response to your answer 1,2, and 3.

I have rated the importance of each response and applied "Maximize Desirability" to find desirability that is shown in my initial posting (2nd screenshot). As you have suggested, my goal is to definitely optimize the formulation by looking at the smaller design space. The question is what is smart ways to set up the boundary of design space to follow up. Assuming that subject matter expert wants me to fix F1 and F4 at the value suggested by desirability function of JMP (2nd screenshot) and further investigate the different ratio of F2 and F3. How should I set the boundary of F2 and F3 to look at? I see some people use 3D scatter plot to figure this out but since I would like to consider 4 responses (simultaneously) to optimize, it is not viable option. But I was thinking JMP should have some smart tool to help users to identify the design space to follow up even though there are multiple responses. In terms of designing method, I was not aware of Augment Design tool. Thanks for letting me know, I will look into it.

Thanks for your input and suggestions. I am very new to DOE and JMP so I am in the active learning phase. Any additional advice would be appreciated.

Victor_G

Hi @BJK_JerseyBoy,

With formulation topics, there are commonly two different approaches :

Either your formulation is a "diluted" solution, and the solvent takes a large amount of the formulation (70-90%+) and/or the solvent is inert or doesn't influence the responses you're measuring : That means you would like to see if some additives show significant effect, synergistic or antagonistic interactions : in this case, since you're not interested in ratios between additives but rather in the influence of small amounts of additives in the formulation (and the solvent will compensate to 100% the total amount of additives introduced), your factors are indepent of each others, and any factorial design may be suited : Screening design, Definitive Screening Design, (Fractional/Full) Factorial Designs, Response Surface Model designs, ... Depending on the complexity of the model and number of runs to estimate effects, you will be able to estimate statistical significance of effects/interactions, and possibly do some optimization (mostly in the case of DSD, RSM).

Or your formulation has no solvent, and/or the solvent is not predominant in the formulation and/or has an influence on the response(s) and/or you're more interested to find the good ratio between additives than their absolute concentration in the formulation : in this case Mixture Designs are more suited, they are not focused on the estimation of statistical significance of your factors, but more on the ratios optimization of additives to match your response(s) objectives. Factors are dependent of each others (if you reduce level of A, you increase level(s) of other additive(s)) and the total amount/part of the formulation is fixed (1 or 100%).

Hope this answer will help you,

Mixture-design_example.png

BJK_JerseyBoy

@Victor_G,

Thank you so much for sharing your experience and knowledge. It really helps on understanding basics of Mixture Design and how you apply that to optimize formulations. I will study more of Mixture Design based on the resources you have provided.

All the best!