p-value = extremal probability for a test statistic under the null
hypothesis, not accounting for multiple comparisons
BH p-value, pBH = extremal probability for the same, after accounting for
multiple comparisons to upper-bound the overall false positive rate at <= p
q-value = direct estimate of the FDR associated with pBH

see http://genomics.princeton.edu/storeylab/papers/directfdr.pdf for the
original, and quite well written paper, where on page 485,

The basic point that we make is that using the Benjamini and Hochberg
(1995) method to
control FDR at level á=đ0 is equivalent to (i.e. rejects the same p-values
as) using the proposed
method to control FDR at level á. The gain in power from our approach is
clear--we control
a smaller error rate (á á=đ0), yet reject the same number of tests.


q-values depend also on the estimated fraction of test p-values in the
chance or uniform component of the distribution at some pFDR p.
pi0 = estimated probability (overall) of a given result being truly null
(i.e., false positive) at p | FDR
q - value = BH p-value * pi0 (probability that test t incorrectly rejects
the null at pBH)

So q = pBH * pi0 (++) as can be verified from the output, and directly
estimates the pFDR for test t assuming independence among the tests.
The mathematical justification for this is given in the paper; the basic
machinery can be, and has been, extended to many other situations.

(++) If pi0 is estimated as at or very near 1.0, then pBH and q will be the
same for any given test t, to the limit of machine precision (see paper).

At least that's how it appears to be implemented last time I looked at the
code and the paper :-)



On Wed, Dec 19, 2012 at 7:22 AM, Jack Luo <jluo.rhelp@gmail.com> wrote:

> Hi,
>
> I am a bit confused about the concepts of the 3 things: FDR, FDR adjusted
> p-value and q-value, which I initially thought I was clear about.
>
> Are FDR adjusted p-value the same as q-value? (my understanding is that FDR
> adjusted p-value = original p-value * number of genes/rank of the gene, is
> that right?)
> When people say xxx genes are differentially expressed with an FDR cutoff
> of 0.05, does that mean xxx genes have an FDR adjusted p-value smaller than
> 0.05?
>
> Thanks,
>
> -Jack
>
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>
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-- 
*A model is a lie that helps you see the truth.*
*
*
Howard Skipper<http://cancerres.aacrjournals.org/content/31/9/1173.full.pdf>

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