[BioC] normalization and analysis of connected designs

[w.huber at dkfz-heidelberg.de]

Hi Ramon,

the package "vsn" has implemented single-channel normalization for cDNA
microarrays since the end of 2001 and was published at ISMB 2002. We have
run considerable comparison studies on data to validate it, where it
compared favorably with log-ratio based methods. One of these comparisons
is reported in that paper.

The importance of spot-to-spot variation (relative to other kinds of
varation) needs to be carefully considered. As a first approximation, the
following calculation was pointed out to me by Gordon Smyth:

Assume you have n arrays, with red and green values R1, G1, R2, .., Rn, Gn
on the logarithmic scale. Assume var(Rk) = var(Gk) = sigma^2,
corr(Gk,Rk)=rho and corr(Gk, Rj)=0 if j!=k. Then compare
(1) var(R1-Gn) = 2 * sigma^2
(2) var{ (R1-G1) - (R2-G2) - ... (Rn-Gn) } = 2n * (1-rho) sigma^2

Whether (1) is larger than (2) or the other way round depends on n and the
size of rho.

Best regards

-------------------------------------
Wolfgang Huber
Division of Molecular Genome Analysis
German Cancer Research Center
Heidelberg, Germany
Phone: +49 6221 424709
Fax:   +49 6221 42524709
Http:  www.dkfz.de/mga/whuber
-------------------------------------


On Fri, 25 Jul 2003, Ramon Diaz-Uriarte wrote:

> Dear Xavi,
>
> Thanks for your last two emails. I see your point, but it is my understanding
> (which has improved a lot thanks to comments from Gordon Smith) that one of
> the important reasons for dealing with ratios in cDNA arrays is controlling
> spot-to-spot variation. In fact, this is mentioned explictly in several
> papers (e.g., Yang & Thorne, 2003, p. 405). So, regardless of the importance
> of competitive hybridization, spot-to-spot variation is always there.
> I am not that familiar with Affy, but I think that, because their setup is
> very different (e.g., multiple probes per clone), the direct analogy "if we
> do it with Affy we ought to be able to do it with cDNA" does not really hold
> just like that.
>
> By the way, the paper of Yang & Thorne, which Gordon Smith mentioned in a
> previous email, contains discussion of single-channel normalization for cDNA,
> and Natalie Thorne presented a very interested talk at the last RSS meetings
> dealing with single-channel normalization. However, if I understand
> correctly, there are still some issues that need to be investigated more
> fully for single channel normalization and they are working on it.
>
> Yang, Y. H., and Thorne, N. P. (2003). Normalization for two-color cDNA
> microarray data. In: D. R. Goldstein (ed.), Science and Statistics: A
> Festschrift for Terry Speed, IMS Lecture Notes - Monograph Series, Volume
> 40, pp. 403-418.
>
>
> Best,
>
> Ramón