[BioC] limma and 2way anova

[James W. MacDonald]

Hi Lisa,

Lisa Luo wrote:
> Hi List, I have a questions regarding Limma and 2way ANOVA.  I have a
> data set containing 2 cell lines and a gene knockout.  So in the
> design file, I have cell1.KO, cell1.WT, cell2.KO and cell2.WT.  I
> want to get the differentially expressed genes between KO and WT.  Is
> the contrast (0.5*(cell1.KO-cell1.WT+cell2.KO-cell2.WT)) right?  Is
> this the same as looking knockout effect in 2way anova? When I take a
> look at the heatmap, the genes identified seemed to be differentially
> expressed in either one of the comparison?

This is not the same as a conventional main effect in a two-way ANOVA, 
but it _does_ measure the difference between KO and WT. Just not the way 
that you might think.

Note that the statistic you are constructing has the average difference 
between KO and WT in the numerator, and a moderated measure of the 
standard error associated with each coefficient in the denominator.

What this means is you will select those genes where the average 
difference between KO and WT is 'large' and the variability of each 
group (cell1.KO, cell2.KO, cell1.WT, cell2.WT) is low. Because of this, 
you can get a significant contrast if e.g., cell1.KO - cell1.WT is large 
(but cell2.KO - cell2.WT is very small), if the variance estimate for 
each term is small, which is what I think you are seeing.

If you are really looking for a standard main effect (i.e., KO vs WT 
ignoring cell type) then you can do one of two things. First, you can 
set your parameterization up so you are explicitly fitting a model with 
main effects, or you can fit a simpler model where you are just doing a 
t-test comparing KO vs WT and pooling the cell types.

As an example, let's say you have two replicates of each sample, and the 
replicates look like this:

 > rep(c("cell1.KO","cell1.WT","cell2.KO","cell2.WT"), each=2)
[1] "cell1.KO" "cell1.KO" "cell1.WT" "cell1.WT" "cell2.KO" "cell2.KO" 
"cell2.WT" "cell2.WT"

Now you can set up your model like this:

 > KO <- factor(rep(1:2, each = 2, times = 2))
 > KO
[1] 1 1 2 2 1 1 2 2
Levels: 1 2
 > CELL <- factor(rep(1:2, each = 4))
 > CELL
[1] 1 1 1 1 2 2 2 2
Levels: 1 2
 > design <- model.matrix(~KO + CELL)
 > design
   (Intercept) KO2 CELL2
1           1   0     0
2           1   0     0
3           1   1     0
4           1   1     0
5           1   0     1
6           1   0     1
7           1   1     1
8           1   1     1
attr(,"assign")
[1] 0 1 2
attr(,"contrasts")
attr(,"contrasts")$KO
[1] "contr.treatment"

attr(,"contrasts")$CELL
[1] "contr.treatment"

Now your second coefficient measures the difference between KO and WT 
while ignoring cell type, just like in a conventional two-way ANOVA.

HTH,

Jim


> 
> Thanks,
> 
> Lisa
> 
>  ---------------------------------
> 
> 
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> 
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-- 
James W. MacDonald, M.S.
Biostatistician
Affymetrix and cDNA Microarray Core
University of Michigan Cancer Center
1500 E. Medical Center Drive
7410 CCGC
Ann Arbor MI 48109
734-647-5623


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