Custom Split Plot Design Replicates

[#1]

Hi everyone — I’m planning BioLector (a 48 well bioreactor platform) runs and need advice on implementing my design in JMP. I should note up-front that biological triplicates are applied at the subplot (treatment) level (i.e., three biological replicate wells/runs for each unique combination of the subplot factors A–D within a whole-plot temperature setting).

Experiment context (what I want to do)

• Temperature must be constant during a BioLector run, so it is a hard-to-change / whole-plot factor.

• Four additional factors A, B, C, D are easy to change and are subplot factors.

• The analysis model should include all two-way interactions among the five factors and second-order (quadratic) terms for continuous factors (building a RSM).

• I will use biological triplicates at the subplot level (three biological replicates of each A–D treatment combination inside each whole plot / temperature run).

• I plan to use JMP Custom Design → split-plot → 6 whole plots (two for each temperature level)and 5 subplots per whole plot, but I noticed the Replicate option in “Augment Design” is greyed out for custom split-plot designs. 

What I'd love some guidance on

• How to include biological triplicates at the subplot level, given that the usual replicate augment option isn’t available for split-plot designs.

• Any general advice or common pitfalls to watch out for. Are there more suitable alternatives out there for my specific case.

Any help is very much appreciated!

[#2 · Accepted solution]

Hi @BenoitM,

Of course, it is a sensible approach and make the design generation a lot easier.
Here are the steps I followed:

1.  Create a split-plot design with Temperature (Hard to change), 4 continuous factors (Easy to change), specify a RSM model, and create 6 whole plots with 30 runs in total.
2. Copy-paste this design 2 times, to enter the Bacterial species factor in the design as a new column and allocate one initial design per species.
3. Copy-paste the previous design by species 2 times, to get the final design with triplicates for the three species in the final design. You should get at the end a 270 runs DoE with 6 Whole plots, each Whole plots with 45 runs (15 runs by species, and each species having triplicates of 5 unique treatments).
   Make sure to randomize the runs inside each whole plot, and to order the runs by Whole plots, to respect the restriction randomization.

Here is how the final design looks like with a Cell plot visualization and a Parallel plot (unrandomized, just sorted by Whole Plots to better understand the pattern repetition accross species and Whole Plots):

Please find attached the design proposed with all scripts (visualizations, models, and randomized version of the DOE).

Hope this answer will finally help you get to your final design,

[#3]

Hi @Victor_G,

Thanks a lot, this is exactly what I needed! :)

One last detail I forgot to mention: the pH levels differ between species (4 - 5.5 - 7 for M. acidophila ; 8 - 9 - 10 for M. buryatense ; 6.5 - 7.5 - 8.5 for M. sporium). I assume it’s fine if I just manually adjust those pH values in the data table for each species?

My sincere thanks again for all your help. I really appreciate the time you’ve taken to guide me through this!

Benoît

[#4]

Is the pH a factor you would (and could) like to vary for each (or some) species ? Or is it a characteristic of the species ?

In the latter case, pH and species will be confounded, so you can still record the value, but it won't impact the analysis (each species has its pH value).
In the first case, depending on how you can vary this factor (independantly like any other subplot factor, or it's a "result" of the different factors combination), you can either treat it as a factor during design generation (independant factor) or record the values in a new column and treat is as Uncontrolled factor in the analysis/modeling (dependant factor of the other conditions).

If the ranges of pH are different for the species but you can still control it, this pH factor can be introduced in the design as a nested factor within species. You can use the method presented in Nested DOE with continous factors? to build your design with a nested factor, or use a candidate set approach: create all possible combinations of factors, remove the unfeasible ones, and let the Custom design platform choose the relevant and most informative treatments to create your design.

The candidate set approach has been extensively discussed on various use cases in this forum, here are some links to know more:
Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-784) 
DOE with two type of constraints 
Optimizing a Mixture of maximum 3 Ingredients, with 5 ingredients to be Evaluated. 
Using the Disallowed Combination Script to define factor constraints in DOE 
...

Hope this answer may help you,

[#5]

Hi @Victor_G,

Thanks again for the detailed explanation.

Just to clarify, I’ll actually be fitting separate models for each species, so I don’t need to estimate cross-species effects. Given that, I assume I don’t need to set up any nesting in the design? My understanding is that nesting would only be necessary if I wanted to create one combined design (and single model) that enforces species-specific pH ranges within the same design table.

Since I’ll analyze each species independently, I suppose I can simply define the pH range differently in each species’ design and keep everything straightforward, does that sound right? Given this context, does it make more sense to simply replace the pH values with the species-specific levels, as I mentioned earlier?

The final design would then be the one you proposed earlier ("Custom Split Plot Design Replicates_F.jmp"), where the pH levels 4 – 5.5 – 7 are kept for M. acidophila, replaced with 6.5 – 7.5 – 8.5 for M. sporium, and with 8 – 9 – 10 for M. buryatense.

Thanks again for all your help,
Benoît

[#6 · Accepted solution]

Hi @BenoitM,

Exactly, if you plan to analyze the results separately by species, you won't need any nesting in the design, as there will be separate models and pH ranges ( and/or any other factors ranges) for each species. So you can simply replace the values for pH by the ones used for each specific species. You can then modify the last design proposed "Custom Split Plot Design Replicates_F.jmp" with the actual values for each species.

If you plan on generalizing your analysis and seeing different impacts of pH variations depending on species and other factors, you can then use nesting in the model.

All the best for your experimentation and analysis !