# [BioC] Limma design and contrast matrix question.

James W. MacDonald jmacdon at uw.edu
Fri Jan 24 16:07:41 CET 2014

```Hi Matt,

On 1/23/2014 7:13 PM, Thornton, Matthew wrote:
> Hello,
>
> I am analysing microarray data collected with Affymetrix MouseGene 2.0 ST chips.  I have a few questions about properly using limma. I have four groups with three replicates.  The groups are Control, Treatment #1 & #2, Treatment #1, and Treatment #2. I may not have the proper design matrix. I am not familiar with their use in linear regression. Currently, my design matrix is set up like this:
>
> # Design matrix for Limma
> design <- model.matrix(~ 0+factor(c(1,1,1,2,2,2,3,3,3,4,4,4)))
> colnames(design) <- c("Control", "Group1", "Group2", "Group3")
>
>> design
>     Control Group1 Group2 Group3
> 1        1      0      0      0
> 2        1      0      0      0
> 3        1      0      0      0
> 4        0      1      0      0
> 5        0      1      0      0
> 6        0      1      0      0
> 7        0      0      1      0
> 8        0      0      1      0
> 9        0      0      1      0
> 10       0      0      0      1
> 11       0      0      0      1
> 12       0      0      0      1
> attr(,"assign")
> [1] 1 1 1 1
> attr(,"contrasts")
> attr(,"contrasts")\$`factor(c(1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4))`
> [1] "contr.treatment"
>
> This was modified directly from the limma users guide page 36. Should the control group be all 1's? and should Group1 (treatment 1 & 2) be 1's from row 7:12? I would like to find genes different from control and I would like to find genes differentially expressed between the combination of treatments versus each treatment alone.

You could parameterize your model that way, but I would personally keep
it the way you have it. This parameterization (a cell means model)
simply computes the mean expression for each group, and then you have to
make all contrasts explicitly. The model with all 1's in the first
column has an implicit contrast (everything is a comparison to control),
so you have to make contrasts for some comparisons, but not for others.

Either way you will get the same exact results - the only difference is
the interpretation of the coefficients.

>
> My Contrasts matrix is set up like this:
>
> # Limma contrast matrix more than 5, no Venn diagrams.
> contrast.matrix <- makeContrasts(Group1-Control, Group2-Control, Group3-Control, Group3-Group2, Group3-Group1, Group2-Group1, levels=design)
>
>> contrast.matrix
>           Contrasts
> Levels    Group1 - Control Group2 - Control Group3 - Control Group3 - Group2
>    Control               -1               -1               -1               0
>    Group1                 1                0                0               0
>    Group2                 0                1                0              -1
>    Group3                 0                0                1               1
>           Contrasts
> Levels    Group3 - Group1 Group2 - Group1
>    Control               0               0
>    Group1               -1              -1
>    Group2                0               1
>    Group3                1               0
>
> Is there a better way to relate the fact that Group 2 is a combination of treatment 1 and treatment 2?

Not really. This is the point at which I start the experimental design
grilling session. Why did you do the combination treatment? What did you
expect to see (e.g., what is your hypothesis that you are testing)?

Do you expect synergistic effects? If so, by how much? You could use
treat() to see if you reliably get a particular fold change increase in
group 2 versus both group 3 and group 4 (or the mean expression of those
two treatments). But how you analyze that combination treatment is
dependent on the hypothesis you are testing.

Best,

Jim

>
> Thanks!
>
> Matt
> Matthew E. Thornton
>
> Research Lab Specialist
> Saban Research Institute
>
> USC/Children’s Hospital Los Angeles
> 513X,  Mail Stop 35
> 4661 W. Sunset Blvd.
> Los Angeles, CA 90027-6020
>
> matthew.thornton at med.usc.edu
>
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--
James W. MacDonald, M.S.
Biostatistician
University of Washington
Environmental and Occupational Health Sciences
4225 Roosevelt Way NE, # 100
Seattle WA 98105-6099

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