I will proceed to use JMP custom design. In many ways, this is an ordinary experiment with restrictions on the randomization. I am trying to keep the thought process and final design as straight-forward as possible. (It might need refinement - perhaps a lot of refinement!)
I used your definitions to make a design. Here are the salient points:
- All factors entered exactly as you defined them with two exceptions.
- Defined plasmid ratio as the log10 plasmid ratio for a low value of -3 and a high value of -1. Why? Because this factor represents your thinking about dilution steps and this transformation makes that change linear and simplify the modeling.
- I really don't like zero for the low value of a continuous factor. This definition essentially makes it a categorical factor: absent versus present. I actually left the low value for Serum Concentration at 0% but I recommend a low value like 1%: low but present.
- The number of levels for each factor is determined by the model. Including higher order terms will necessitate more factor levels. On the other hand, many levels are unnecessary (and inefficient - low information content - if the model is relatively simple.
- I don't think we need to explicitly treat the columns and the rows on the plate as blocking factors in the design.
- You prefer to work with half a plate at a time, subtracting out one column from each half for control runs.
- This choice defines the size of a whole plots in the design, 40 wells.
- The Cell Number should be the same for both cell types on a plate, so this factor is very hard to change.
- Cell Number becomes the whole plot factor.
- Its effects will be estimated with the lowest precision.
- This decision means that you cannot reduce the number of plates much. Four plates might be a practical minimum for the modeling.
- This design provides 80% power if the effect is at least 7X the standard deviation.
- The Cell Type and Serum Concentration should be the same for half the plate, so these factors are both hard to change.
- Cell Type and Serum Concentration become the sub-plot factors.
- Their effects will be estimated with the second lowest precision.
- This design provides the same 80% if their effects are at least 4X the standard deviation.
- It seems like you have a lot of replication but that is enjoyed only by the easy to change factors, Plasmid Ratio, Integration Time, and Time Post Transfection.
- I am not sure what replication and randomization mean for these factors because you will be presumably dealing with a plate or half-plate at a time here, too.
The following script will make the design I am talking about for your examination and consideration.
DOE(
Custom Design,
{Add Response( Maximize, "Dynamic Range", ., ., . ),
Add Factor( Continuous, 10000, 50000, "Cell Number", 2 ),
Add Factor( Continuous, -3, -1, "Log10 PLasmid Ratio", 0 ),
Add Factor( Continuous, 0, 4, "Serum Concentration", 1 ),
Add Factor( Categorical, {"HELA", "HEK293"}, "Cell Type", 1 ),
Add Factor( Continuous, 5000, 30000, "Integration Time", 0 ),
Add Factor( Discrete Numeric, {24, 48, 72}, "Time Post Transfection", 0 ),
Set Random Seed( 556681383 ), Number of Starts( 3 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
Add Term( {5, 1} ), Add Term( {6, 1} ), Add Potential Term( {6, 2} ),
Add Alias Term( {1, 1}, {2, 1} ), Add Alias Term( {1, 1}, {3, 1} ),
Add Alias Term( {1, 1}, {4, 1} ), Add Alias Term( {1, 1}, {5, 1} ),
Add Alias Term( {1, 1}, {6, 1} ), Add Alias Term( {2, 1}, {3, 1} ),
Add Alias Term( {2, 1}, {4, 1} ), Add Alias Term( {2, 1}, {5, 1} ),
Add Alias Term( {2, 1}, {6, 1} ), Add Alias Term( {3, 1}, {4, 1} ),
Add Alias Term( {3, 1}, {5, 1} ), Add Alias Term( {3, 1}, {6, 1} ),
Add Alias Term( {4, 1}, {5, 1} ), Add Alias Term( {4, 1}, {6, 1} ),
Add Alias Term( {5, 1}, {6, 1} ),
Set N Whole Plots( 4 ),
Set N Subplots( 8 ),
Set Sample Size( 320 ),
Make Design,
Change Anticipated Coefficients( [1 3.5 1 2 2 1 1 1] ),
Set RMSE( 1 ),
Set Run Order( Keep the Same )}
);
I expect that you will have issues with it, but I am doing the best that I can based on the information you have given me.
You can rename Whole Plots to Plate and Subplots to Half Plate if you like for clarity.
