Question: BH vs BY in p.adjust

0

lemerle@embl.de •

**50**wrote:Quoting Wolfgang Huber <huber at="" ebi.ac.uk="">:
> Hi Caroline,
>
> what does
>
> hist(fit2$p.value[,1], breaks=100, col="orange")
>
> look like?
hi wolfgang,
well.... not at all uniform:
> x <- hist(fit2$p.value[,1], breaks=30,
> col="orange",main="distribution of raw p-values",labels=T)
> cbind(x$mids,x$counts)
[,1] [,2]
[1,] 0.025 1891
[2,] 0.075 270
[3,] 0.125 209
[4,] 0.175 123
[5,] 0.225 100
[6,] 0.275 101
[7,] 0.325 79
[8,] 0.375 79
[9,] 0.425 85
[10,] 0.475 57 .....
but from here on, the distribution is uniform (around 50 in every bin
until
p-val=1). so there are a lot of differential probesets in this
contrast. but
between 519 and 1032 as estimated from BY and BH adjustments with 1%
FDR,
there's quite a difference.... or can i estimate it directly from this
histogram .....substracting the baseline gives me 2439 probesets,
almost 70% of
the whole set:
> baseline <- mean(x$counts[11:20])
> sum(x$counts-baseline)
[1] 2439
how safe is this ?
Assuming that the p-values are uniform distributed under
> the null hypothesis (which they should be if they are worth their
> name), then the shape of this distribution can give you an idea of
> the proportion of differential vs non-differential probesets.
by the way, in cases that it's not uniformly distributed, from the
range values
of the over-represented bins on the histogram, can we not get an idea
of the
effect size associated with the differential probesets responsible for
this
non-uniformity ?
or the other way around, if i happened to know that there were
differential
probesets but all of only moderate effect size, i might expect a bulge
at
moderate p-values, while lower ones could well instead be uniformly
distributed, right?
but then if that were the case, could it also be that if all
differential
probesets had similar p-values, say 0.2, they could more easily be
discovered
than the same number associated to a lower but wider ranger of
p-values, only
because they would add significance to each other?
this doesn't quite sound right if it's true that the adjustment
procedure
preserves the rank that the genes have from the p-value.
thanks for the help and comments
caroline
>
> Best wishes
> Wolfgang
>
> --
> ------------------------------------------------------------------
> Wolfgang Huber EBI/EMBL Cambridge UK http://www.ebi.ac.uk/huber
>
>> 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
>> contrast:
>>
>>> 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
>>
>
>
--
Caroline Lemerle
PhD student, lab of Luis Serrano
Structural Biology and Biocomputing Dept
tel 00-49-6221-387-8335
--

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modified 13.2 years ago
by
Wolfgang Huber ♦

**13k**• written 13.2 years ago by lemerle@embl.de •**50**