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DOE including events that occur or not occur on a certain time during the experimental run

martindemel

How would you integrate events in a DOE? e.g. an event occurs on day 4 or day 5 or not at all . And if the event occurs there is a range to what extent this event occurs (30-100%). (let's assume you can control the event to occur or not to occur and to what extent, otherwise you would not add it to the design, but just record if it occurred and to what amount)

Simply adding factors will add the extent of the event to each experiment, even if the event does not occur. Unless you add disallowed combinations.

Is there a better, more efficient, or with more power way? e.g. using covariates?

Accepted answers

SamGardner

There is an approach to do this, described in one of Brad Jones' papers: https://www.tandfonline.com/doi/full/10.1080/00401706.2018.1562986

Don't have time right now to mock up and example, but if you want I can walk you through, I have used this approach previously.

All comments

Mark_Bailey

Martin,

Are you talking about using a Uncontrolled factor, which is filled in after the run?

Can you use 0% for the case of no event?

martindemel

It is more like you start your experiment which last let's say 1 week, and you might add something to the process, like adding some oxigen to a culture. It could be on day 4 or day 5 or never. So it is kind of controlled when or if you add it, but it is not from the beginning. So staying with the oxigen example. The first 3 days the oxigen would be 0% and then on day 4 e.g. 40% (of potential 100% oxigen level) will be added. In another run there is no oxigen at all, and in another run on day 5 e.g. 60%, and so forth.

I understand you suggest to say if there will not be an event (adding oxigen) then use amount of 0%. To do this one would need for the day 3 levels (0,4,5) and a disallowed combination (if day == 4 or 5, then amount == 0 not allowed). And one saying (if day == 0, then amount !=0 not allowed)?

Phil_Kay

Sounds complicated, @martindemel .

I've had questions like this from people in upstream biopharma, i.e. fermentation. They talk about different feeding regimes. I never had a good answer for them.

It could be handled as a functional input variable. But that might be over-complicating.

I think it depends how many different feeding regimes they want to explore. It might be easier just to code these as different levels of a single categorical factor. But that would depend on what questions they are trying to answer.

Sorry. I'm not sure if that helps much! I will be interested to know what they decide to do.

Phil

Mark_Bailey

It seems unnecessarily complicated. I do not think that a constraint is necessary. Just a data column for Oxygen level. As long as you know the amount present (0 if absent) for each run, it is just another potential factor. Regression can handle it. It might not be optimal data for estimating the intended model, but it should work.

I do not know of a principled method or tool to augment columns, only rows.

DonMcCormack

Why not treat the feeding regime factor as categorical? For the analysis, you could still break out the %O2 by day, assuming data was collected daily.

SamGardner

There is an approach to do this, described in one of Brad Jones' papers: https://www.tandfonline.com/doi/full/10.1080/00401706.2018.1562986

Don't have time right now to mock up and example, but if you want I can walk you through, I have used this approach previously.

martindemel

Thanks for all your suggestions, I will discuss this further with the customer and provide an update probably within the next two weeks. @SamGardner I will take a look at this paper and may come back if I have questions.

martindemel

@SamGardner : Thanks, the chicken experiment with the enzymes was mirroring the problem, though their enzymes are Days a temp shift occurs, and the Log Dose is the temperature it is shifted to.

I created 3 different design options (attached). Though the nested works I think it is easier to create a candidate set and use this, especially if there are additional process parameters.

The main challenge which makes this complicated is to remove model terms which would imply linear dependent effects due to the nested setup. I hope I did it correct in my examples here. May you take this as starting point and fine tune to your needs.

There are 3 examples, all have 3 additional process factors included:

CD CovariateDays.jmp ... has a candidate set in a structure similar to the nested setup Day4 (yes/no), Day5 (yes/no), Temp (37 if both are 0, otherwise between 33 and 35, and no Day4 and Day5 at 1 at the same time
CD CovariatesSimple.jmp ... has a candidate set with just DayNr and Temp
CD NestedFactors.jmp ... Nested setup using Day4, Day5, and Temp
ScriptDesigns.jsl ... the three designs as scripts
CovariateDays.jmp and CovariatesSimple.jmp ... Covariate tables if you want to setup the design from scratch.

CD CovariateSimple.jmp