[BioC] Limma contrasts questions

[Gordon Smyth]

At 08:00 PM 31/05/2006, bioconductor-request at stat.math.ethz.ch wrote:
>Date: Tue, 30 May 2006 14:13:04 -0400
>From: "James W. MacDonald" <jmacdon at med.umich.edu>
>Subject: Re: [BioC] Limma contrasts questions
>To: Sean Davis <sdavis2 at mail.nih.gov>
>Cc: Bioconductor <bioconductor at stat.math.ethz.ch>
>
>Hi Sean,
>
>Sean Davis wrote:
> > Just ANOTHER limma contrast matrix question:
> >
> > I am trying to compute some contrasts of interest and have three factors:
> >
> >  Treatment (Hypoxic,Norm)
> >  Tissue (4 levels)
> >  Genotype (WT,KO)
> >
> > I chose a parameterization like this for the design matrix:
> >
> >
> >>colnames(design)
> >
> >  [1] "TSBrain.Hypoxic.KO"  "TSBrain.Hypoxic.WT"  "TSBrain.Norm.KO"
> >  [4] "TSBrain.Norm.WT"     "TSHLM.Hypoxic.KO"    "TSHLM.Hypoxic.WT"
> >  [7] "TSHLM.Norm.KO"       "TSHLM.Norm.WT"       "TSKidney.Hypoxic.KO"
> > [10] "TSKidney.Hypoxic.WT" "TSKidney.Norm.KO"    "TSKidney.Norm.WT"
> > [13] "TSLiver.Hypoxic.KO"  "TSLiver.Hypoxic.WT"  "TSLiver.Norm.KO"
> > [16] "TSLiver.Norm.WT"
> >
> > I would like to determine the effect of the KO as compared to the WT.  What
> > might a contrast matrix look like?  How about Kidney versus liver?  And the
> > effect of the KO as compared to WT in liver?  I have looked at the limma
> > guide and thought I had the idea, but this is slightly more 
> complicated than
> > the limma example given.
>
>Getting out the main effects with this design matrix will be a pain. If
>I am not mistaken, your contrasts matrix should look like this (colnames
>omitted for clarity - they are in the same order as you mention).
>
>0.125   0       0
>-0.125  0       0
>0.125   0       0
>-0.125  0       0
>0.125   0       0
>-0.125  0       0
>0.125   0       0
>-0.125  0       0
>0.125   0.25    0
>-0.125  0.25    0
>0.125   0.25    0
>-0.125  0.25    0
>0.125   -0.25   0.5
>-0.125  -0.25   -0.5
>0.125   -0.25   0.5
>-0.125  -0.25   -0.5
>
>Remember that a contrast is simply adding/subtracting coefficients with
>the constraints that the coefficients on each side of the comparison sum
>to one, and overall sum to zero. Hence, in the first case we are adding
>and subtracting 1/8, the second 1/4, and the third 1/2.
>
>Best,
>
>Jim
>
> > Thanks,
> > Sean

Dear Sean (and Jim),

I feel I should jump in here with a couple of comments. Firstly, the 
design matrix you've used is intended to focus on interactions and 
condition-specific effects rather than on main effects. This form of 
design matrix makes it easy to extract condition-specific contrasts. 
If you really want the factorial anova -style main effect for 
Genotype then it would be easier to use the factorial style 
parametrization. To do this, make factors for Tissue, Treatment and 
Genotype and construct the design matrix using the usual sort of 
anova formula like

    design <- model.matrix(~ Genotype*Treatment*Tissue)

Then the main effect will be one of the coefficients in your fitted model.

But the deeper question which always worries me here is: what exactly 
do you mean by "the effect of the KO as compared to the WT"? Is there 
any such thing? The experimental design you've chosen suggests that 
you expect interactions between the different factors. I don't think 
that you can usefully interpret the main effect if interactions are 
present. Wouldn't it be better to dissect the genotype effect in 
different cases? Do you want to test for interaction effects? What 
will you do if they are present?

Best wishes
Gordon