[BioC] normalization and analysis of connected designs

[Gordon Smyth]

At 10:06 PM 3/07/2003, Ramon Diaz-Uriarte wrote:
>Dear Gordon,
>
>Thank you very much for your comments and discussion of Wolfgang's message,
>and for clarifying some issues (about Wolfinger's and Churchill's approaches)
>which I though I understood, but I didn't. Thanks a lot for the reference,
>too.
>
>Interesting about Churchill's approach, though, is that his paper in Nature
>Genetics (2002, 32: 490-495) makes all comparisons either within-array or
>using connected designs and, for example one of his papers with K. Kerr (Kerr
>& Churchill, 2001, Biostatistics, 2: 183-201) says explicitly that "in order
>to fit models such as (4.1), (4.2) and (4.3) a design should be connected"
>(p. 8 of the technical report; 4.1 to 4.3 are the usual ANOVA models of the
>Churchill group).

Well, I think Gary's Nature Genetics paper was purely on design and didn't 
actually discuss analysis. I think he made the important point that you 
should arrange that comparisons you are most interested in should be 
arranged so that they made as directly as possible, either on the same 
arrays or via as few an intermediaries as possible. In the Biostatistics 
paper, they said that you need a connected design in order to be able to 
estimate gene x array interactions, and this is very true. Allowing gene x 
array interactions pretty much implies that whatever analysis you do will 
be equivalent to analysing the log-ratios. I think one of the strengths of 
Gary's work is that he has made a lot of issues explicit by writing them 
down in models and amongst other things this goes a long way towards 
clarifying the relationship between single-channel analysis and analysis of 
log-ratios. It's not for me to interpret Gary's papers though, he can do it 
far better himself!

I think we'll see more single-channel analyses in the future but it does 
require more care and employs more complex statistical models than analysis 
of log-ratios. The paired structure introduced by the competitive 
hybridization (in classical statistical design terms it's like a split plot 
design) does make the analysis of cDNA arrays more complex than that of 
one-channel or affy arrays.

Regards
Gordon

>I'll have to do some more reading. This is getting a lot more messy than I
>thought.
>
>Best,
>
>Ramón