[BioC] Question: How does limma derives its logFC value in two colored arrays?

[Gordon K Smyth]

Dear Sunny,

> Date: Mon, 27 Sep 2010 03:14:01 -0400
> From: Sunny Srivastava <research.baba at gmail.com>
> To: bioconductor <bioconductor at stat.math.ethz.ch>
> Subject: [BioC] Question: How does limma derives its logFC value in
> 	two	colored arrays?
>
> Hello Bioconductor Gurus,
>
>
> I have the a data about gene expression from TWO COLORED Agilent array. I
> wanted to check differential expression between p3 and wild strain of yeast.
> In one array p3 is colored with Cy5 and wild is colored with Cy3 and in the
> second array the dyes are swapped. Assuming I have normalized my data using
> VSN and obtained M values for the two arrays, I now want to use limma to
> derive the differentially expressed genes.
>
> My model matrix (say design) in this case will be
>
> p3
> 1
> -1
>
> if wild type is the reference.
>
> If my understanding is correct about how limma analyzes differential
> expression, then M value is the dependent variable, sample annotation
> (whether p3 or wild, provided by design) is the independent (explanatory)
> variable, and a linear model is fit per gene using the following equation.
>
>
> lmFit( M , design)

This is all correct.

> As the data per gene is small, it is better to use eBayes method to obtain
> genewise p-value. But the object obtained from eBayes (say fit3) doesn't
> contain the value *logFC*.

Yes it does--the logFC is fit3$coefficients.  This terminology is because 
the logFCs are estimated as the coefficients of the linear model.

Best wishes
Gordon

> When I use topTable to order the genes, then
> logFC appears.
>
> The concept of logFC is clear to me in case of a Affy single colored array
> (ie log (Int_trt/ Int_control) ), but somehow I am still confused how to
> interpret this in two colored arrays.
>
> In my opinion M value (for each array) should represent logFC if color bias
> is ignored. How does limma derives its logFC value in two colored arrays? Is
> it based on the B statistics? Please enlighten me !
>
> Thanks in advance for any help.
>
> Best Regards,
> S.

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