[BioC] adjusted p values of the genes in the intersection of Venn

[Gordon Smyth]

Dear Marg,

I understand the question that you're asking but, unfortunately, it 
is a question that doesn't have an answer at this time.  I've given 
it some thought over the last few years, and I don't believe that 
current statistical theory provides a way to compute the FDR for an 
intersection of tests.

Here's a summary of the situation.  Suppose you do a limma analysis 
(say) with contrasts AvsB and CvsD.  You select genes which are DE 
for AvsB controlling the FDR at 0.01, and similarly for CvsD.  Now 
you want to look at genes the intersection, i.e., genes which are DE 
for both AvsB and CvsD.

Unfortunately there is no way to compute the FDR for the genes in the 
intersection.  (A very simple Bayesian analysis suggests that the 
intersection FDR should be about 0.02=1-0.99^2 if the two contrasts 
are independent.  But the two contrasts are not usually independent, 
and this is only an approximate calculation anyway.)

Similarly, there is no way to choose the FDR for the separate 
contrasts AvsB and CvsD so as to control the FDR for the intersection 
to be a given value.

In technical terms, the problem is that your question has a composite 
null hypothesis and classical statistical theory is not very good at 
testing composite null hypotheses.  (It is composite because you are 
considering A=B,C=D; A=B,C!=D; A!=B,C=D all to be part of the null.)

Best wishes
Gordon

>BioC] adjusted p values of the genes in the intersection of Venn
>Margaret Gardiner-Garden m.gardiner-garden at garvan.org.au
>Wed Nov 15 06:06:52 CET 2006
>
>Hi,  We have two lists of genes (one regulated by treatment A and the other
>regulated by treatment B ).  Each list contains genes with a BY adjusted p
>value (or FDR) <0.01.  As we expected from the biology, when we do a Venn
>diagram many of the genes that are affected by treatment A are also affected
>by treatment B ie lie in the intersection.  We are wondering how to
>calculate the FDR of the intersection set.  If the gene belongs to both
>sets, does this mean that its FDR is now less than 0.01? And does this then
>mean that the genes that are not in the intersection set (ie are exclusive
>to treatment A or treatment B) have a FDR more than 0.01?
>
>We would really appreciate any advice that people can give...
>
>Thanks in advance,
>Marg
>
>
>Dr Margaret Gardiner-Garden
>Garvan Institute of Medical Research
>384 Victoria Street
>Darlinghurst Sydney
>NSW 2010 Australia
>
>Phone: 61 2 9295 8348
>Fax: 61 2 9295 8321
>