[BioC] Limma analyses;paired and/or factorial design?

Gordon K Smyth smyth at wehi.EDU.AU
Fri May 4 07:07:22 CEST 2012

Hi Naomi and John,

True enough.  Obviously I don't read carefully enough.

If each mouse gets both treatments, then it's a paired (or split-plot or 
repeated measures or multilevel) design.  If all the mice were the same 
genotype and sex, then the design would be simply:

   design <- model.matrix(~mouse+treatment)

as in Section 8.3 of the limma User's Guide.

However, with sex and genotype differences it can be complicated, 
depending on what John wants to test, as the experiment has multiple 
levels of variation (mouse and array).  If John simply wants to test for a 
treatment effect within each genotype, then the design might be:

   design <- model.matrix(~mouse+treatmentA+treatmentB)

where treatmentA=1 for genotype A mice receiving treatment and zero 
otherwise, and similarly for treatmentB.  This assumes no interaction 
between treatment and sex.

If however John wants to test for baseline differences between genotypes 
or between sexes, then it is necesssary to recover information from the 
between-mice strata, so mouse needs to be entered as a random blocking 

Best wishes

On Thu, 3 May 2012, Naomi Altman wrote:

> If each mouse receives both treatments, this is a split plot design with 
> genotype:gender as the whole plot factor and treatment as the subplot 
> treatment.  You need to have a block effect for mouse.  Since these are 1 
> color arrays, you can simply put in mouse as block.
> --Naomi
> At 08:00 PM 5/3/2012, Gordon K Smyth wrote:
>> Dear John,
>> If all the mice were the same sex, then it would be a 2x2 factorial.
>> Having both male and female, you have some difficult choices to make, 
>> depending on whether the treatment or the KO can have sex-linked effects. 
>> In the simplest case that the answer is no in both cases, then you might 
>> make a design matrix from
>>    design <- model.matrix(~sex+genotype+genotype:treatment)
>> in order to test for treatment effects within each genotype.
>> In any case, designing an analysis depends on the questions you want to 
>> answer as well as the treatments you have.
>> Best wishes
>> Gordon
>>> Date: Wed, 2 May 2012 15:34:46 +0100
>>> From: john herbert <arraystruggles at gmail.com>
>>> To: <bioconductor at stat.math.ethz.ch>
>>> Subject: [BioC] Limma analyses;paired and/or factorial design?
>>> Dear Bioconductors,
>>> Please can anyone advise on this?
>>> One colour array; I have 8 mice. Each mouse can have a genotype of WT or 
>>> KO.
>>> For each mouse, there are 2 samples, one with treatment and one control.
>>> Is this a combined paired and factorial design and if so, how can I
>>> construct a design matrix?
>>> There is also Male and Female (half mice of each group).
>>> Thank you for any advice on this.
>>> Kind regards,
>>> John.

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