[BioC] normalization and analysis of connected designs

[Gordon Smyth]

Dear Ramon,

I am with you. The direct comparison design you describe is a very sensible 
type of design which is intended to compare RNA samples using within-spot 
comparisons, i.e., log-ratios or M-values. The limma package in 
Bioconductor is specifically designed to analyse experiments of this type. 
You're quite correct that you do need a connect design in order to compare 
all the RNA types in this way.

Wolfgang is arguing for what in my lab we call a 'single-channel analysis'. 
The main proponents of single-channel analysis in the literature are Rus 
Wolfinger at SAS and Gary Churchhill at the Jax lab. As far as I am aware 
there is no software in Bioconductor designed to do single-channel analysis 
of cDNA arrays. We (I mean here Jean, Sandrine who wrote the marray 
packages and I) don't yet provide single-channel software because we 
consider it to be an experimental methodology whose validity is still be 
established. Normalization of single-channel data in particular is 
something that we are still trying to do a satisfactory job of. The only 
discussion of single-channel normalization for cDNA data that I am aware of 
in the literature is Yang and Thorne, see below.

Wolfinger and Churchhill fit mixed linear models in which a spot is a 
random effect. One then has multiple error strata corresponding to spots, 
to individual channel intensities within spots and perhaps to arrays as 
well. There are certainly cases where one can get more information out of 
this approach than analysing arrays entirely using log-ratios. 
Statistically, the method consists of using random effects to recover 
information from the between-spot error strata. The real problem is to know 
when it is valid to take this approach and when it is not.

I may have misinterpreted Wolfgang, but he does seem to be proposing a even 
more radical approach in which the spot error strata is ignored entirely. 
(I think that is only way one could get the calculation that the D-A 
variance is reduced by a third.) This is more radical than anything I've 
seen in the literature, and I don't personally think it would be a good 
approach for cDNA microarray data.

Regards
Gordon

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.

At 03:27 AM 3/07/2003, w.huber at dkfz-heidelberg.de wrote:
>Hi Ramon,
>
>What makes the difference between D and A hybridized on the same array,
>and on different arrays? It is (a) the between-array variation (e.g.
>because each time the spotter puts down a drop of DNA it is a a little bit
>different, or because the arrays had different surface treatments, etc.),
>and (b) the between-hybridization variation (e.g. different temperatures,
>different volumes of the reaction chamber). These two sources of variation
>need to be compared to others sources, e.g. (c) between-RNA-extraction,
>(d) between-reverse-transcription, (e) between-labeling, (f) between-dyes.
>(c)-(f) are present no matter whether you D and A are on one array or on
>different ones.
>
>That it is possible to make (a) and (b) small is shown by the fact that
>useful results have been obtained through single-color arrays such as Affy
>or Nylon membranes. Whether in your experiment (a) and (b) are small
>compared to (c)-(f) depends on your particular experiment. If they are,
>you are better of with h_3G - h_1R than with the full chain of summands. I
>have seen examples where this seemed to be the case.
>
>Anyone else?
>
>Best regards
>   Wolfgang
>
>
>On Wed, 2 Jul 2003, Ramon Diaz-Uriarte wrote:
>... [SNIP]
> > I am not sure I follow this. I understand that, __if__ D and A had been
> > hybridized in the same array, then the variance of their comparison 
> would be
> > a third of the variance of the comparison having to use the (two-step)
> > connectiion between A and D. But I am not sure I see how we can directly do
> > h_3G - h_1R
> > (if this were possible, then, there would be no need to use connected
> > designs.)
> >
> > ... [SNIP] ...
> >
> > So either way, I don't get to see how we can directly do
> > h_3G - h_1R
> >
> > But then, maybe I am missing something obvious again...
>
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