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Mar 17, 2017 5:11 AM
(3148 views)

Hi,

I have been thinking about possible ways to create this experimental design and would appreciate any input.

What we are doing is putting together genetic elements in certain ways. We drive gene expression with a promoter, and stop it with a terminator. These elements have measurable stregths and we sometimes use them as discrete numeric factors. So an experiment we would like do would have 3 genes in 3 positions with a set of promoters and terminators. It would look something like this:

Pos1

Promoter/Gene/Terminator

Pos2

Promoter/Gene/Terminator

Pos3

Promoter/Gene/Terminator

The problem I have is this, if i have a set of promoters (6), genes (3), terminators (6) these can go in any combination in any position - but they can ONLY be used once due to the way the organims works. So if i choose for position 1 promoter 4, then I cannot use it again for the rest of the design. I imagine this is some kind of mixture but I am not sure how I capture that accross my positional charactaritics expecially with all the interactions that might be important. I am stuck so any help appreciated! I normally use custom designer to do this kind of work.

8 REPLIES

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Mar 17, 2017 8:46 AM
(3129 views)

Hi,

Just to be clear: does that mean you have 9 factors? i.e.

Pos1 Promoter

Pos1 Gene

Pos1 Terminator

Pos2 Promoter

.

.

.

.

Pos3 Terminator

And

Promoter factors are 6-level categorical

Gene factors are 3-level categorical

Terminator factors are 6-level categorical

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Mar 17, 2017 9:23 AM
(3125 views)

Hi,

Yest that is one way I have explored designing the experiment.

If I seperate out all the positional elements to a set of categorical factors, then I worry that I am not capturing the fact that they are related (in that they are the same sets in different positions and if one is used in one position it can't be reused) and how those interactions map across the positional elements.

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Mar 20, 2017 2:17 PM
(3082 views)

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Mar 23, 2017 9:31 AM
(3041 views)

Hi,

Only the 4th run in the design I have attatched is valid in this exprement. The factors can't be repeated in a design, even though they come from the same set, if it is used once the other postional factors cannot contain it.

Dave

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Mar 27, 2017 5:04 AM
(2953 views)

Hi Dave,

That explains your problem nicely.

I think the Disallowed Combinations feature in Custom Design might be the solution.

I started a design with 3 factors, all discrete numeric, with levels 1, 4, 6:

P_PW1_P1,

P_PW1_P2,

P_PW1_P3

Then I "Use Disallowed Combinations Script" and add the following as the expression:

P_PW1_P1 == P_PW1_P2 |

P_PW1_P1 == P_PW1_P3 |

P_PW1_P2 == P_PW1_P3

Basically, we are defining factor X1 level = factor X2 level as a combination that is not allowed. And the same for X1/X3 and X2/X3.

" | " is the symobol for Or , which is how we combine multiple combinations that are disallowed, such as these.

I think this gives a design that would work for you.

(full script below)

@ryan_lekivetz has some good examples of using the disallowed combinations filter and/or script in his blog posts.

https://community.jmp.com/t5/JMP-Blog/Using-the-Disallowed-Combinations-Filter-in-JMP-12/ba-p/30588

Regards,

Phil

DOE(

Custom Design,

{Add Response( Maximize, "Y", ., ., . ),

Add Factor( Discrete Numeric, {1, 4, 6}, "P_PW1_P1", 0 ),

Add Factor( Discrete Numeric, {1, 4, 6}, "P_PW1_P2", 0 ),

Add Factor( Discrete Numeric, {1, 4, 6}, "P_PW1_P3", 0 ),

Set Random Seed( 1489472428 ), Number of Starts( 89357 ), Add Term( {1, 0} ),

Add Term( {1, 1} ), Add Potential Term( {1, 2} ), Add Term( {2, 1} ),

Add Potential Term( {2, 2} ), Add Term( {3, 1} ), Add Potential Term( {3, 2} ),

Add Alias Term( {1, 1}, {2, 1} ), Add Alias Term( {1, 1}, {3, 1} ),

Add Alias Term( {2, 1}, {3, 1} ), Set Sample Size( 6 ),

Disallowed Combinations(

P_PW1_P1 == P_PW1_P2 | P_PW1_P1 == P_PW1_P3 | P_PW1_P2 == P_PW1_P3

)}

);

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Mar 29, 2017 4:39 AM
(2930 views)

That is great. I think that works!

Are these disallowed combinations being accounted for in finding the optimal model in custom designer or just broadly exculded? Will this affect interpritaiton of any interaction terms?

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Mar 29, 2017 5:32 AM
(2918 views)

Custom design is finding the optimal design given the disallowed combinations.

However, in this example you end up with a very constrained system. So I don't think the experiment will actually be very useful. I think you were probably right in the first instance that a mixture design is required here.

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Apr 3, 2017 7:47 AM
(2848 views)

Hi Dave,

I think the above is a unique situation where #factors = #factorlevels and is a unique problem. I think where #factor levels > #factors the experiment is no longer so constrained and the model will be estimable. See example below, where each of the 3 factors is now 6-level.

Regards,

Phil

DOE(

Custom Design,

{Add Response( Maximize, "Y", ., ., . ),

Add Factor( Discrete Numeric, {1, 2, 3, 4, 5, 6}, "P_PW1_P1", 0 ),

Add Factor( Discrete Numeric, {1, 2, 3, 4, 5, 6}, "P_PW1_P2", 0 ),

Add Factor( Discrete Numeric, {1, 2, 3, 4, 5, 6}, "P_PW1_P3", 0 ),

Set Random Seed( 1073470905 ), Number of Starts( 4060 ), Add Term( {1, 0} ),

Add Term( {1, 1} ), Add Potential Term( {1, 2} ), Add Potential Term( {1, 3} ),

Add Potential Term( {1, 4} ), Add Potential Term( {1, 5} ), Add Term( {2, 1} ),

Add Potential Term( {2, 2} ), Add Potential Term( {2, 3} ),

Add Potential Term( {2, 4} ), Add Potential Term( {2, 5} ), Add Term( {3, 1} ),

Add Potential Term( {3, 2} ), Add Potential Term( {3, 3} ),

Add Potential Term( {3, 4} ), Add Potential Term( {3, 5} ),

Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),

Add Term( {2, 1}, {3, 1} ), Set Sample Size( 13 ),

Disallowed Combinations(

P_PW1_P1 == P_PW1_P2 | P_PW1_P1 == P_PW1_P3 | P_PW1_P2 == P_PW1_P3

), Optimality Criterion( 2 ), Simulate Responses( 1 ), Make Design,

Set Run Order( Randomize ), Make Table}

);