[BioC] library size and fold changes

[Gordon K Smyth]

Dear Bogdan,

Give that library size may affect FDR, but will not affect FC (even might 
increase it slightly), it would seem to me more natural to relax the FDR 
cutoff rather than the FC cutoff.  I would use the same FC cutoff 
regardless of library size.

This is especially so because, once counts get to a certain size, the 
p-value under the negative binomial model depends only on the fold change, 
further increases in count size making little or no difference.  This is 
because the sequencing variability become negligible for large counts, 
after which biological inter-library variability is the only soure of 
variation.

What is a sensible analysis for your current data might of course depend 
on many things, which we don't know from your email

Best wishes
Gordon

---------------------------------------------
Professor Gordon K Smyth,
Bioinformatics Division,
Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Vic 3052, Australia.
Tel: (03) 9345 2326, Fax (03) 9347 0852,
smyth at wehi.edu.au
http://www.wehi.edu.au
http://www.statsci.org/smyth

On Tue, 6 Dec 2011, Bogdan Tanasa wrote:

> Dear Mark, Gordon,
>
> probably a naive statistical question on edgeR : considering 3 samples of
> 3 library sizes : a) 10 mil reads, b) 30 mil reads, and c) 12 mil reads.
>
> after applying edgeR, I do obtain 1) > 2000 genes differentially expressed
> between a) and b) (FDR< 0.01, FC > 2), and 2) only ~ 200 genes
> differentially expressed between a) and c) (FDR < 0.01, FC >2).
>
> my question would be : given the fact that the number of differentially
> expressed genes is dependent on the library size, would it be valid to
> compare and contrast the set 1) of 2000 differentially expressed genes (FDR
> < 0.01, FC >2), with an expanded set 2) of 200+800 differentially expressed
> genes (FDR < 0.01, BUT FC > 1.2).
>
> thanks a lot,
>
> Bogdan
>

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