[BioC] Calculation of t-tests for factorial design

[James W. MacDonald]

Hi Pascal,

On 9/10/2010 10:04 AM, Pascal Gellert wrote:
> Hi all,
>
> Unfortunately I cannot find out how limma calculates t-tests for my
> factorial design of micrarrays, but let's begin from the start:
>
> I have the following microarray experiment:
>
> WT Knock-Out
> Treated 2 2
> Untreated 2 2
>
> This way I can make the following comparisons:
>
> WT Treated / WT Untreated: This shows me, what the effect of the
> treatment itself is.
> Knock-out Treated / Knock-out Untreated: To see what effect the
> treatment has on Knock out animals.
> (Knock-out Treated / Knock-out Untreated) / (WT Treated / WT Untreated):
> The effect of treatment to Knock-Out animals under consideration of
> changes of gene expression due to treatment in WT animals.
>
> So my main interest lies in the last comparison. I did this with the
> following code:
>
> targets <-read.table(file="Targets.csv", sep="\t", header=T,
> row.names=1, as.is=T)
> TS <- paste(targets$Strain, targets$Treatment, sep=".")
> TS <- factor(TS, levels=c("wt.non","ko.non","wt.treat","ko.treat"))
>
> design <- model.matrix(~0+TS)
> colnames(design) <- levels(TS)
> fit <- lmFit(eset, design)
>
> cont.matrix <- makeContrasts(
> WT.nonVStreat =wt.non-wt.treat,
> KO.nonVStreat=ko.non-ko.treat,
> Diff=(ko.non-ko.treat)-(wt.non-wt.treat),
> levels=design)
> fit2 <- contrasts.fit(fit, cont.matrix)
> fit2 <- eBayes(fit2)
>
> eset contains my expression values in log2 scale.
> The contrast are calculated by
> wt.non-wt.treat
> ko.non-ko.treat
> (ko.non-ko.treat)-(wt.non-wt.treat)
> as I described above. For all 3 comparisons, eBayes calculates t-tests,
> but for the last comparison, which values are used for the t-test?
> All signals of ko.non and ko.treat compared to wt.non and wt.treat? I
> think it's calculated in a completely different way, does anyone know how?

It's not calculated in a completely different way. The contrasts you are 
computing are just the numerator for the t-statistic. So for the first 
two contrasts, the numerator is simply the difference between the means 
of two groups. In the third case, the numerator is the difference 
between the differences (e.g., is calculated exactly as you have specified).

Best,

Jim


>
> Best regards,
>
> Pascal
>
> _______________________________________________
> Bioconductor mailing list
> Bioconductor at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/bioconductor
> Search the archives:
> http://news.gmane.org/gmane.science.biology.informatics.conductor

-- 
James W. MacDonald, M.S.
Biostatistician
Douglas Lab
University of Michigan
Department of Human Genetics
5912 Buhl
1241 E. Catherine St.
Ann Arbor MI 48109-5618
734-615-7826
**********************************************************
Electronic Mail is not secure, may not be read every day, and should not be used for urgent or sensitive issues