Two blocking variables for DSD to integrate replicates and multiple sampling points?

[#1]

Hello,

I'm setting up an experiment where I measure changes in cell numbers in response to the concentration of 8 different cell culture media ingredients (i.e. continuous factors). A DSD with 8 extra runs gives me a 29 run experiment for this. Since the main time sink of this experiment is making up the different media mixes, I'm planning to run 3 exact replicates, preferrably blocked since the replicates will be in different 96-well plates, and differences in handling (e.g. time not spent in the incubator, etc) may lead to differential growth. All easy enough to set up by augmenting the DSD.

Run	Media Mix	Block	Response
1	1	1	?
...	...	...	...
28	28	1	?
29	29	1	?
30	1	2	?

However, I'm also gathering data over several days (non-invasively measuring cell numbers) of these runs, up to 7 times. I'm expecting the difference between treatments to increase due to exponential growth of the cells up to a point, then decrease again as they run out of space. I could fit models to the data from the individual days and use the one with the best PValues, but it seems like a waste of data not to integrate it all into a single model.

However, the way I understand it, if I just used one blocking variable and put all replicate/day combinations into seperate blocks (see below), I would be aliasing the variability in response due to different days and different replicas.

Run	Media Mix	Day	Block	Response
1	1	1	1	?
...	...	...	...	...
28	28	1	1	?
29	29	1	1	?
30	1	1	2	?
...	...	...	...	...
87	29	1	3	?
88	1	2	4	?

Is it possible to use two blocking variables to get around this problem?

Run	Media Mix	Day	Block A	Block B	Response
1	1	1	1	1	?
...	...	...	...	...	...
28	28	1	1	1	?
29	29	1	1	1	?
30	1	1	2	1	?
...	...	...	...	...	...
87	29	1	3	1	?
88	1	2	1	2	?

I hope what I'm asking makes sense. I think I could alternatively put the day as a categorical factor, but I don't want any model to include it, so it feels unnecessary.

[#2]

Correction, it's 10 factors, obviously.

I've been thinking: Would it be advantageous to instead just include the measurements on different days as their own responses?

Run	Media Mix	Day	Block	Response Day 1	Response Day 2	...	Response Day 7
1	1	1	1	?	?	...	?
...	...	...	...	...	...	...	...
28	28	1	1	?	?	...	?
29	29	1	1	?	?	...	?
30	1	1	2	?	?	...	?
...	...	...	...	...	...	...	...
87	29	1	3	?	?	...	?
88	1	2	4	?	?	...	?

[#3 · Accepted solution]

Hi @Snail2212,

I'm sorry, but I don't understand very well your need and use of two blocking.

If I understand well, one of the blocking was about day variability measurement. Concerning the measurement over 7 days, are you able to measure for each day each experimental run ?

• If yes, then as you suggest you can create different response columns for each day, and do an analysis by day, or stack your data and then use a curve analysis approach (FDE with JMP Pro, Fit Curve or Nonlinear with JMP).
• If no, then you might use a block to take into account the fact that the measurement you're doing are depending on the day, which is a source of variability not taken into account in the factors in your experimental design.

The second blocking factor you're investigating is about the use of different 96-well plates for your experiments ?
As you mention, you can then create a block when creating the design (or when augmenting it) to represent the fact that experiments will be on different plates, and the use of this blocking factor in the design will take care that the blocks are the most similar to each others. Or simply create the original DSD, and then copy-paste the design 3 times and add a block column with the relevant column properties : Value Order (for the ordering of the blocks), Runs per Block, Design Role (= Blocking) and Factor Changes (Easy ?).

I hope this first answer will help you,

[#4 · Accepted solution]

Thank you Victor, this was really helpful. I can indeed measure all conditions and all replications on all days, which gives me an abundance of data that I did not want to throw away. I found a lecture online titled "JMP Academic: Analyzing Function (aka Curve) Data with JMP Pro" based on your suggestions, and I'm stoked at the possibilities. This tool would allow me to analyze my media constituents not only for a single outcome like the growth in cell number, but super valuable data on all phases of growth ( initial lag phase, growth rate during exponential phase, maximum cell density at stationary phase, etc), given my data is of high-enough quality and dense enough. Probably more useful once I'm building a RSM as opposed to the screening phase, but it's exciting!

Also, thank you for your practical tips on how to actually use JMP to do what I want. As someone with only google to teach me, pointers that may seem obvious to experienced users are very much appreciated.

[#5]

The definitive screening designs benefit from the fold-over structure, but this structure imposes some rigid rules. Designing the experiment you want with Custom Design might be easier. The DSD is s special case of a custom design using the alias-optimal criterion. 

[#6]

Thank you, Mark. I am doing a screening experiment where I expect at least a few factors to be irrelevant, so I wanted to use the DSD for it's ability to collapse into something more meaningful for few active effects. I realize the solution I proposed of turning the days into a multi-level categorical factor would have precluded me from using it, it was not a very clever idea.