Analyzing conditions that are not completely independent

Question

Hello,

I am trying to characterize a biological manufacturing process near the end of our process (during harvest). I am looking at 3 continuous factors: Cell Time in Media 1, Cell Time in Media 2, and Cell Time in Media 3. These factors occur in chronological order during the process. I am interested in MEs and the interaction effects between these 3 factors. The tricky part is Cell Time in Media 1 and 2 are hard to change since we need more volume. After those two steps we can split off into multiple smaller conditions for Media 3. However, lets say we have 3 conditions, then for the first two steps (Media 1 and 2) the cells are actually in the same tube together, and we are only creating 3 conditions on the third factor (we now split off into 3 vials). I am not sure on how to account for this during analysis since technically these aren't independent conditions. JMP puts out a split plot design when I make the DoE (5 whole plots with 3 conditions each), which makes sense to me, but I think there is still an assumption that each condition is independent. In our case they are not completely independent since for each whole plot the 3 conditions are actually one condition for the first two factors and only become 3 conditions during the last step.

My question is what do I need to do differently during the Fit Model analysis to account for this? Is there even a way? It seems JMP adds a whole plot random effect to the model automatically when you create the split plot design but I don't think this addresses the issue above.

Thank you!

Edit: To clarify, I used custom design and specified the first two factors as very hard to change. The third factor I did easy to change.

statman · Answer

I suggest you read Box and Jones "Split-plot designs for robust product experimentation".  I use this approach quite often as it is extremely efficient.  Unfortunately the analysis can not be done by JMP without some intervention.  You will need to analyze the Whole plot separately from the subplot.  I do this by first analyzing the entire data set with a saturated model.  Turn the parameter estimates table into a new table and create normal & Pareto plots for each Plot (WP and SP).

ted_ellefson · Answer

At the 2019 Discovery Summit there was a presentation => The Design and Analysis of Experiments With “Order” Factors (2019-US-30MP-200)

If I understand your question perhaps this presentation would be of interest.

Biotech27 · Answer

Basically we grow cells in flasks, then at the end of the process we "harvest" them, meaning spinning them down and resuspending them in different formulations of media so we can freeze them down.

But I think you answered my question. I'm struggling a bit to wrap my head around why the Whole Plot random effect accounts for the dependence but it's reassuring to hear that it does.