[BioC] BH vs BY in p.adjust + FDR interpretation

lemerle at embl.de lemerle at embl.de
Sat Jul 29 00:08:32 CEST 2006

dear list,

i am analysing a set of affymetrix chips using limma to get lists of
differentially expressed probesets.
concerning BH and BY, the two methods available with p.adjust that adjust
p-values controlling for the false discovery rate, i was surprised to find a
large discrepancy in the number of differentially expressed genes in the case
of one contrast of interest:

> fit <- lmFit(eset.f,design)
> fit2 <- contrasts.fit(fit,c.matn)
> fit2 <- eBayes(fit2)

# adjustment for multiple testing of the set of p-values derived from the first

> p.value <- fit2$p.value[,1]
> bh <- p.adjust(p.value, method = "BH")
> by <- p.adjust(p.value, method = "BY")

# number of differentially expressed genes below the cutoff value of 0.01 for
the 2 methods

> length(which(bh<0.01))

[1] 1032

> length(which(by<0.01))

[1] 519

# size of the original set: 3549 probesets (with 15 observations for each)

> dim(exprs(eset.f))

[1] 3549   15

i don't think there is a bug anywhere (but i'd gladly send you my data to
reproduce this), i'm more inclined to think that i know too little to make
sense of this at this stage....

could this difference be due to the fact that these numbers correspond to a
large fraction of the whole set tested and that the two methods behave
differently with respect to this?

if estimates of false positives at this cutoff were reliable with both methods,
wouldn't this imply that BH gives a far better coverage of the set of truly
differentially expressed genes than BY (TP/(TP+FN)), for the same control over
false discovery (here, 1%)?

i've seen mentioned but only vaguely that the magnitude of change is an issue.
that the methods work best when it is low.... if you think that may be it,
could you point me to something i might read to understand this better?

a related question i have is about the interpretation of FDR values close to 1,
in such cases where there are many changes, ie when the fraction of
non-differentially expressed genes in the whole set is far below 1...

i've come to understand that methods controlling fdr substitute the p-value of
each gene for a value that corresponds to the minimum cut-off to apply in order
for that gene to be called positive, with the added info that such a set
obtained by applying this minimum cutoff can be expected to contain that
percentage of false positives.
but as the fdr rate ranges from 0 to 1, the chosen cutoff can fall above the
true percentage of non-differentially expressed sets and i don't see how such
an estimate can still be reliable up to 1 if the true number of false positives
is  far lower.... unless it represents only an upper bound of how many false
positives to expect... is this the case ?

thanks for any comment, i'm confused about this....


Caroline Lemerle
PhD student, lab of Luis Serrano
Structural Biology and Biocomputing Dept
EMBL, Heidelberg, Germany
tel 00-49-6221-387-8335

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