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]

Hi @BenoitM,

Welcome in the Community !

I see at least two options that could lead to a design appropriate for your needs:

• You could add a 3-levels categorical "Hard-to-change" factor for subplot replicate (A, B and C or 1, 2 and 3 levels), adding the main effect for this subplot replicate factor in the model panel, changing Temperature as "Very Hard to Change" factor, checking the option "Hard to change factors can vary independently of Very Hard to change factors", and specify an appropriate number of whole plots (depending on the number of bioreactor platforms you want to use) and number of subplot (multiple of 3, I choose 3 so that each subplot experiment is replicated 2 times, like you want). This design will create replicate runs in the subplots, but there is no certainty that each run of each subplot will be triplicated.
  
  
• You could also design first the subplot matrices, by creating 6 RSM designs for 4 factors with 16 runs, and then replicating them each up to 48 runs with the Augment Designs. After this step, you can combine the designs (by concatenating the tables), adding a Whole Plot factor column and applying Temperature factor levels to each of the 6 Whole Plots, and it should lead to the design you want. This option is perhaps more tedious, but it is sure that the replicates constraint will be enforced by having each run of each subplot triplicated. Make sure at the end of this process to randomize order of the runs inside each whole plot, using the workaround found here Randomize rows from a datatable by using Create a Subset Data Table with sampling rate of 1, and then sort the datatable by whole plot order to keep the split-plot structure.
  
  

Either one or the other option should create a design that respect your needs, you may only have to change the assumed model from the "Model" script in the datatable (to remove any effects linked to "subplot replicate" factor and the subplot random effect for option 1 for example). 
Please find attached an example of such design, with 288 total runs, 48 runs per whole plot, and 3 replicates for each subplot experiment for both options. Some scripts are also saved in the datatable with the corresponding model assumed "Model (refined)" and some visualization of the design structure.

The comparison of the two designs performance shows similar results:

• Power analysis:
  
• Prediction variance and FDS:
  
• Correlation map and design diagnostics:
  

Hope this answer will help you,

[#3]

Hi @Victor_G 

Thank you so much for the detailed explanation and the example designs! I think I need to clarify my situation a bit better to make sure we're on the same page:

I’m working with three bacterial species (M. sporium, M. buryatense, and M. acidophila). So far, I’ve been creating separate DOE files for each species (I’ve attached these in case that’s useful). Within each whole plot, I have the five subplot treatment combinations. I’m planning three biological replicates per subplot treatment. Across all three species, that gives me a total of 45 treatment conditions (5 subplots × 3 replicates × 3 species) for 1 out of 6 whole plots — which fits well into a single 48-well BioLector plate.

My Main Questions:

1. How do my 45 wells (15 wells per species) compare to your 48 wells per whole plot? I'm trying to understand if we're talking about the same thing or if there's a fundamental difference in our design structures.
2. How does having 3 separate species affect the split-plot design? Should "Species" be treated as an additional factor in the design, or is it acceptable to keep them as completely separate designs?
3. Can I keep my three DOE files separate, or do they need to be combined into a single design file?

I hope this is clear. Thanks again for taking the time to explain this!

Benoît

[#4]

Indeed, I  had some infos missing from the first post and question. I'm not entirely sure to follow :
How many factors do you have in total ? :

• Temperature (Continuous, 3 levels, Hard to change),
• Species (Categorical, 3 levels, Easy to change),
• pH (Continuous, 3 levels, Easy to change),
• TN (Continuous, 3 levels, Easy to change),
• TN/TP (Continuous, 3 levels, Easy to change),
• C/N (Continuous, 3 levels, Easy to change) ?

Do you confirm you would like to create a design with maximum 288 runs with 6 whole plots of 48 runs each ?

The designs options I have posted contained Temperature and 4 continuous factors (pH, TN, TN/TP and CN), but not the "species" factor.

Even if "bacterial species" is missing in my design option 2, you can still use the process used to create your final design:

1. Create individual subplot matrices for the 5 Easy-to change factors, specifying a model for each matrix with 16 (or 15) runs, and replicate each subplot design to get to the 45/48 subplot parts.
2. Concatenate the subplot parts to get the final design structure.
3. Link 2 whole plots to each temperature conditions.
4. Make sure all column properties and model script are ready for analysis (whole plot random effect column and attribute in model, Hard to change property for Temperature, etc...).

Concerning your two other questions:

---

@BenoitM wrote:
How does having 3 separate species affect the split-plot design? Should "Species" be treated as an additional factor in the design, or is it acceptable to keep them as completely separate designs

---

Yes, if species is an easy to randomize/change factor, I think it should be included in the subplot designs matrices. This way, it will make sure that the individual species are facing different levels of the other factors in a randomized way. However, if you want to triplicate each run of your subplot runs, you won't be able to have a full RSM model in only 16 runs with these 5 factors (minimum is 25). You might have to change the estimability of some higher order terms to "If Possible" and/or delete some model terms to reduce the number of runs to 16/15.

---

@BenoitM wrote:
Can I keep my three DOE files separate, or do they need to be combined into a single design file?

---

It depends on what you want to do in terms of objectives, modeling/statistical analysis, and practical realization of the experiments.
Will the DoEs be run independantly ? Or by batches ? Do you want to learn/analyze from them globally ? Or incrementally, "DoE by DoE" ? By species or globally ?

The design(s) structure(s) and analysis should reflect your objectives and goals.

Hope this follow-up answer will help you,

[#5]

To answer some of your questions.

1) How many factors do I have in total?

• Whole-plot (hard-to-change): Temperature — continuous (3 target levels).

• Subplot (easy-to-change, per-species DoE): four continuous factors — pH, TN, TN/TP, C/N.

• Species: I have 3 bacterial species, but I do not want species as a subplot factor, since I would like to analyze each species independently.  So, per-species design/model will include Temperature + the four subplot factors (and their two-way interactions / quadratic terms as planned).

2) How the DoEs will be run

• The DoEs will not be run independently. Each BioLector run takes roughly a week and will complete a single whole plot (at a fixed temperature) that contains one species block (5 subplots x 3 replicates = 15 wells) from each of the three species’ DoEs for a total of 45 wells (48 is max capacity). 

• After all runs are complete, I will analyze by species.

• I do not want subplot treatments randomized across species, if that makes sense.

Given this setup, I think my question boils down to: Can I keep the attached DoEs separate for each species? If so, what is the most efficient way to include the biological triplicates? Would it be reasonable to simply copy each subplot row twice (to get three replicates per treatment) and then randomize only within each species block on the plate?

I hope this additional context helps in answering my question.

Benoît

[#6]

Ok, I think I understand what you want to design.
In fact, the three replicates are each allocated to one bacterial species, and that's why you want the runs to be triplicated in each whole plot, to make the visualization and comparison easier.

So using the design option 2 shared before, I have added a column for bacterial species in order to identify the "triplicates" so that each run is allocated to one different species. If you want to create the design from scratch, you can follow the process of design option 2, but keep the replicate runs identification to save some time at the end and be able to attribute the replicates to each species.

I have modified the model script (to analyze by species) and some visualizations, this design should now meet your requirements ?

Let me know if I missed something,

[#7]

These discussions would be so much easier if the factor relationships with each other and noise were presented graphically.

Sanders, D., & Coleman, J. (2003). “Recognition and Importance of Restrictions on Randomization in Industrial Experimentation”. Quality Engineering, 15(4), 533–543

Bergerud, Wendy A. (1996) “Displaying Factor Relationships in Experimentation”, The American Statistician, Vol. 50, No. 3

[#8]

Hi @Victor_G — thanks, this is very close and I really appreciate the changes (and the model-by-species script).

One small point I think we still need to clarify: in the current table, the species column nicely tags the three replicate rows, but it seems that the actual treatment conditions inside a single whole plot aren’t truly triplicated. For a given treatment combination within one whole plot, I don’t see three biological replicate rows of that same treatment — instead, the replicates are distributed across species.

To make sure we’re aligned, what I’d like is that for each unique subplot treatment combination, there are three rows of that same treatment (the three biological replicates), and those are labeled with the three species names.

This would mean that for every whole plot, there are only six unique treatment conditions per species (instead of eighteen). This might not be feasible in practice, but if that’s the case, I’m wondering why, when looking at a single species alone (as in my attached DOE files), it is possible to have only five subplots per whole plot (and six total whole plots) and still achieve decent power for all model terms.

Does combining the species into a single design inherently require a larger number of unique subplots per whole plot, or is there a way to preserve that smaller structure while keeping the three-species labeling?

Thanks again — this is getting very close to exactly what I need!

[#9]

Hi @BenoitM,

Yes, I have understood (wrongly apparently) that the triplicates were used to allocate each treatment to each species, so that the comparison could be easier (and visualizations too). It seems you want in each whole plot same treatment combinations for each of the 3 species, as well as triplicates for each treatment combinations.

If yes, that means you would have only maximum 5 unique treatments of the 4 factors per whole plots, that would then be done for each of the three species (so 3x5 = 15 runs), which then would be triplicated (so ending at 15x3 = 45 runs). There won't be enough runs available to fit a RSM for the 4 easy-to-change factors in each whole plot, as a minimum of 15 unique treatment combinations would be needed.

One strategy would be to simplify the assumed model in each whole plot, so that it fit your requirements.

Another possibility is to use 2 whole plots to fit the RSM (since each level of Temperature is "seen" for 2 whole plots).
To do this, you need to create an I-optimal design with 4 continous factors and a blocking factor (5 runs per block, to allow triplicates for the 3 species), specify a RSM model, adjust the complexity of the model (you need a minimum of 20 runs with this blocking factor and full RSM model for the 4 continuous factors) by removing some terms or changing the estimability to "If Possible", and finally allocate the runs of the first block to the first whole plot of the same temperature, and the runs of the second block to the second whole plot of the same temperature. Then, you can multiply these 5 runs per block by 9, to get your 45 runs per whole plots, and having triplicates of the treatment combinations for each of the three species.  

I put an example I have created of these 2 whole plots used to fit a Bayesian I-optimal design for the 4 factors. These 2 whole plots correspond to the same level of temperature, so the procedure would need to be done 2 more times to have the other "parts" of this design (for the 2 remaining Temperature levels).

A little visualization to appreciate the setting of this first part of the design:

Of course the runs need to be randomized inside each whole plot, I just let the order of the construction to facilitate the visualization.

Hope I did understand your needs correctly,

[#10]

Hi @Victor_G  quick follow-up:

If I just want to fit one RSM for the four continuous factors combined across all whole plots (and temperature included in the model, meaning five total factors) instead of a full RSM for every whole plot, would that be a sensible approach?

If yes, would it then be feasible using the 5 subplots per whole plot scheme I described earlier?

Thanks again for your guidance,

Benoît