* Goal is characterization/optimization of a fermentation process. * 6 factors (X1-X6), independent and controllable for each experimental unit (their Custom design setup needs 53 runs) * want to include a factor "cultivation time" (ct). This means taking a sample on three different times and analyze it (kind of repeated measure). This is lot of work for the analytic department, so they want to reduce the number of tests/samples. * Challenge: How to best select the ct samples and set up the design? Ideas from customer: use custom designer and factors X1-X6 as covariates to be selected from model effects are just main effects testing different number of runs until collinearities of the main effects X1-X6 are minimal or acceptable (they hope that this will resolve 2-factor interactions (X1-X6)*ct ) Alternatively using a split plot already in the first design How to approach this kind of situation best? I think the idea with the covariates should work. This would help to find a subset of runs where they test all three ct timepoints and get a decent information if ct will have an effect and also if there is some potential interaction. But can we easily assess how the power is for these model effects? I do not think split plot will work here, but may you have other ideas. Another spontaneous idea would be to take these samples and use FDE and as supplementary variables the DOE factors and see if there is some relationship between X1-X6 and the profile of the ct values. 3 points are not much but depending on the shape it might be enough. What do you think? Any ideas?

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DOE challenge

martindemel

Goal is characterization/optimization of a fermentation process.
6 factors (X1-X6), independent and controllable for each experimental unit (their Custom design setup needs 53 runs)
want to include a factor "cultivation time" (ct). This means taking a sample on three different times and analyze it (kind of repeated measure). This is lot of work for the analytic department, so they want to reduce the number of tests/samples.
Challenge: How to best select the ct samples and set up the design?

Ideas from customer:

use custom designer and factors X1-X6 as covariates to be selected from
model effects are just main effects
testing different number of runs until collinearities of the main effects X1-X6 are minimal or acceptable (they hope that this will resolve 2-factor interactions (X1-X6)*ct )
Alternatively using a split plot already in the first design

How to approach this kind of situation best?

I think the idea with the covariates should work. This would help to find a subset of runs where they test all three ct timepoints and get a decent information if ct will have an effect and also if there is some potential interaction. But can we easily assess how the power is for these model effects?

I do not think split plot will work here, but may you have other ideas.

Another spontaneous idea would be to take these samples and use FDE and as supplementary variables the DOE factors and see if there is some relationship between X1-X6 and the profile of the ct values. 3 points are not much but depending on the shape it might be enough.

What do you think? Any ideas?

Accepted answers

Phil_Kay

HI Martin,

Thanks for the clarification.

First of all, a 53-run CCD including 9 center points seems like a strange choice, but maybe they have their reasons. For now, we should assume this is the design they will use.

I am still a bit confused about the number of analytic measurements that they can afford. I was assuming that they can afford to run at least one analytic measurement for each of the 53 runs, presumably at the final time point (the "end point"). But I understand that they can't afford to run analytic measurements at 3 time points for all 53 runs.

So there is some small number of runs for which they can take analytic measurement on 2 or 3 time points. And therefore a smaller number of runs that they can use to estimate the effects of the factors on the slope and/or curvature of Y vs cultivation time.

Just doing multiple time points for the 12 axial points is not the worst idea, although all 2-factor interactions are aliased with each other, so they will only be able estimate the main and quadratic effects of the factors on Y vs and cultivation time. Also, the power to detect main effects is low because you are not exploring the extremes of factor space.

If they wish to estimate the effects of 2-factor interactions on Y vs cultivation time then using a covariate custom design approach to select the subset of runs for multiple time points seems like a good idea. This is also a better approach for getting the best power to detect effects.

I get the sense that they lean more towards classical rather than custom design. I would encourage them to look at the benefits of custom design. Especially for complex situations like this one.

This presentation from the most recent Discovery Americas should be really useful for how they can model the resulting data using FDE or Fit Curve. I think Curve DOE could be really useful here. Actually I think Curve DOE should be really useful in lots of applications and we should make more people aware of it.

I hope that helps,

Phil

All comments

Phil_Kay

Hi Martin,

Interesting. Can you explain a bit more about "their Custom design setup needs 53 runs"? Are the factors, X1 - X6, all continuous?

Do you mean that they will carry out a 53-run DOE on the 6 factors and the question is how they should sample vs time over those 53 runs?

If so, it sounds like they can't afford 159 (=53*3) timepoint samples. How many could they afford?

Cheers,

Phil

DonMcCormack

Will all experimental units be run for the same amount of time or will it depend on the level of ct (i.e., is ct a treatment)?

Mark_Bailey

Are any of the factors hard to change? Or will they restrict randomization for convenience sake?

Do they already know that these six factors affect the response?

It sounds like repeated measures to me! I would suggest that they consider a range of CT with the nominal value at the center.

Why use covariates? Do you mean to say that they already have data for some experimental units? Why not use Custom Design from scratch?

What did they specify in Custom Design so that 53 runs are required? That number seems excessive to me.

Are they sure that there will only be a linear change in the response? That is not often the case in biological systems such as fermentation.

I like the idea of FDOE with CT as the function. Not sure if 3 time points will provide much information, but once they have the data they can try lots of different analytical approaches.

I wish I had more answers than questions - sorry!

martindemel

Hi, thank you all for all your suggestions and questions

I have some more details and try to answer your questions:

to be corrected: The design is not a custom design but a orthogonal CCD (incl. 9 center points), therefore the 53=46+9 runs (he told me that he was wrong and a colleague used another design), 6 continuous factors
it's a batch process (similar to a titer process) and the cultivation time is measured 3 times during this process for a batch, so on the one hand a repeated measure but no treatment, but in my eyes perfect for a FDOE
They can afford maybe 30-40 analytics measurements max, right now they want to do this for the axial points of the CCD to assess how cultivation time interacts with the other DOE factors.
They are in a process characterization and the ultimate goal is to find the best cultivation time and how they then have to control the other parameters to stay in their quality range.
They have some idea of what's likely to be important, however the process is different each time.

If I treat the resulting data in a mixed model, I would see the repeated measures in that way:

batch would be the fixed effect
cultivation time the random effect as well batch*ct (an the other factors in a similar way)

If I would try to set up a custom design, I would go for a functional response (with timepoints of ct) and do a design with 6 cont. factors. This would lead to a 34 run design, adding some additional (CP) ones they would still be below 40 (>13 less than now, still with the need to select about 12-13 only for the analytics department (as they have to measure 3 times.

I still don't see how you would use a split plot in such a case as the customer asked for. And treating ct as factor does not get into my head as it does not make sense to have just one measure in one batch to e.g. the lower ct and in another batch a measure for a higher ct.

Hope I could uncover some unknowns.

Phil_Kay

HI Martin,

Thanks for the clarification.

First of all, a 53-run CCD including 9 center points seems like a strange choice, but maybe they have their reasons. For now, we should assume this is the design they will use.

I get the sense that they lean more towards classical rather than custom design. I would encourage them to look at the benefits of custom design. Especially for complex situations like this one.

I hope that helps,

Phil