[Rd] RE: [BioC] limma, FDR, and p.adjust

[Kimpel, Mark W]

Marcus, Gordon, and R developers,

Thanks to you both for kind and useful replies. Gordon you are correct,
I did post this question once before but, as I approach publication of a
rapid communication paper, wanted to make absolutely sure that I was
correct in assuming that the p values of p.adjust were the same as the q
values published in the FDR literature that I am familiar with.

If I seem a bit stubborn in pursuing this once again, it is because I
have spent a fair amount of time trying to explain the idea of FDR to my
lab-mates and how it differs from the concept of FWER. All of the
previous p adjust functions, to my knowledge, correct for FWER; the
authors of many of the FDR papers have gone to great lengths to distance
themselves from some of the terminology associated with FWER so that the
FDR methods are not confused with them.

My point to the R and BioC communities was that, if I was correct that
p.adjust was somehow adjusting the p values using different FDR
methodologies, that this should not be confused with how FDR is
discussed in the original papers. I have seen a recent post on BioC
where the originator asked at what FDR level the p values were being
adjusted to (still thinking, I believe, about the p value threshold
concept), so I don't think I am the only one who has confused by this.

As I pointed out, I do see the utility for developers, such as Gordon,
for the ability to call just one function when dealing with adjusting p
values. Given the proliferation of FDR methods, however, and to allow
for implementation of many of them in the future, I would propose that
the R-developers use a function architecture such as this:

p.adjust (method = c("bonferronni, ...., fdr(method))), where fdr called
a function fdr(method = "B&H, "B&Y",....). In the help section of fdr
the method for turning q values into p values could be explained for
each of the differing fdr methodologies.

Gordon, limma is a wonderful package and I will be publishing some very
exciting findings using (and citing) it. Might I suggest adding a
paragraph to the user's guide about fdr and p values? Having raised this
issue, I would be more than happy to contribute a first draft that you
could use or not use as you see fit.

Marcus, thank you so much for you code. This is an fdr implementation
that I think is clearer and more functional than available under
p.adjust but I couldn't get my code to make it work.

Thank you both for your help to me and support of the BioC community.

Mark W. Kimpel MD

 

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-----Original Message-----
From: Marcus Davy [mailto:MDavy at hortresearch.co.nz] 
Sent: Monday, December 20, 2004 12:15 AM
To: Kimpel, Mark W; bioconductor at stat.math.ethz.ch;
r-help at stat.math.ethz.ch
Subject: Re: [BioC] limma, FDR, and p.adjust


Mark,
there is a fdr website link via Yoav Benjamini's homepage which is:
http://www.math.tau.ac.il/%7Eroee/index.htm
On it you can download an S-Plus function (under the downloads link)
which calculates the false discovery rate threshold alpha level using
stepup, stepdown, dependence methods etc. 
Some changes are required to the plotting code when porting it to R. I
removed the xaxs="s" arguement on line 80. The fdr function requires a
list of p-values as input, a Q-value (*expected* false discovery rate
control at level Q) and a required method of fdr controlling procedure.

> As you can see after running the code, the p values are truly being
> adjusted, but for what FDR? If I set my p value at 0.05, does that
mean
> my FDR is 5%? I have been told by someone that is the case but,
> normally, when discussing FDR, q values are reported or just one p
value
> is reported--the threshold for a set FDR. The p.adjust documentation
is
> unclear.

The p.adjust function appears to be using the "stepup" fdr controlling
procedure when method="fdr" is specified. It adjusts the 
p-values so that FDR control is at the desired level alpha over the
entire range (0,1), which gives the same result as specifying a 
Q-value in the fdr function itself calculating a false discovery rate
threshold alpha level so that FDR<=Q.

So it adjusts for all FDR desired levels. If your p-value threhold is
0.05 then the expected proportion of false discoveries is 5%.

e.g.

n   <- 1000
pi0 <- 0.5
x <- rnorm(n, mean=c(rep(0, each=n*pi0), rep(3, each=n - (n*pi0))))
p <- 2*pnorm( -abs(x))
p <- sort(round(p,3))

p.adjusted <- p.adjust(p, method="fdr")

# Controlling fdr at Q, and p.adjust at level alpha
Qvalue <- alpha <- 0.05
  
threshold <- fdr(p, Q=Qvalue, method="stepup")     # fdr function
available from the website link above
threshold

plot(p, p.adjusted)
abline(v=threshold, lty=2)
abline(h=alpha, lty=2)

> # Stepup FDR control at Q=0.05
> sum(p <= threshold)
[1] 372
> 
> # p.adjust(ed) p-values at level alpha=0.05
> sum(p.adjusted <= alpha)
[1] 372

Simultaneously modifying Qvalue, and alpha above to a different expected
proportion of false discoveries should still produce identically sized
rejected lists.

Hope that helps.

marcus



>>> "Kimpel, Mark W" <mkimpel at iupui.edu> 20/12/2004 3:57:43 AM >>>
I am posting this to both R and BioC communities because I believe there
is a lot of confusion on this topic in both communities (having searched
the mail archives of both) and I am hoping that someone will have
information that can be shared with both communities.

I have seen countless questions on the BioC list regarding limma
(Bioconductor) and its calculation of FDR. Some of them involved
misunderstandings or confusions regarding across which tests the FDR
"correction" is being applied. My question is more fundamental and
involves how the FDR method is implemented at the level of "p.adjust"
(package: stats).

I have reread the paper by Benjamini and Hochberg (1995) and nowhere in
their paper do they actually "adjust" p values; rather, they develop
criteria by which an appropriate p value maximum is chosen such that FDR
is expected to be below a certain threshold. 

To try to get a better handle on this, I wrote the following simple
script to generate a list of random p values, and view it before and
after apply p.adjust (method=fdr). 
 
rn<-abs(rnorm(100, 0.5, 0.33))
rn<-rn[order(rn)]
rn<-rn[1:80]
rn
p.adj<-p.adjust(rn, method="fdr")
p.adj

As you can see after running the code, the p values are truly being
adjusted, but for what FDR? If I set my p value at 0.05, does that mean
my FDR is 5%? I have been told by someone that is the case but,
normally, when discussing FDR, q values are reported or just one p value
is reported--the threshold for a set FDR. The p.adjust documentation is
unclear.

For the R developers, I can understand how one would want to include FDR
procedures in p.adjust, but I wonder, given the numerous FDR algorithms
now available, if it would be best to formulate an FDR.select function
that would be option to p.adjust and itself incorporate more recent FDR
procedures than the one proposed by Benjamini and Hochberg in 1995.
(Benjamini himself has a newer one). Some of these may currently be
available as add-on packages but they are not standardized regarding I&O
and this makes it difficult for developers to incorporate them into
packages such as limma.

So those are my questions and suggestions, 

Thanks,

Mark W. Kimpel MD

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