[BioC] limma and minimum fold change

[Wolfgang Huber]

Hi Eva

in the ordinary t-test, the t-statistic is proportional to the ratio of 
fold change 'fc' and estimated within-group standard deviation 's'; and 
the p-value depends on that through a monotonous transformation, ie. 
setting a p-value cutoff is equivalent to setting a cutoff on |t|. 
s_gene is simply, for each gene separately, the empirical standard 
deviation.

With limma/eBayes, you replace s by a cleverly calibrated compromise 
s_limma between s_gene and an overall pooled s_tot (across all genes). 
With a small number of replicates, that compromise is close to s_tot; 
with many replicates, close to s_gene; and somewhere inbetween in 
intermediate cases. Now, if (eBayes decides that) you have few 
replicates, then s_gene ~ s_tot is always the same for all genes, and 
your p-value cutoff is directly equivalent to a cutoff on fc. This, it 
appears, is what you see.

Have a look, in your 'eb' object, at the slots 'df.prior' and 
'df.residual'. The manual page of eBayes says: "s2.post is the weighted 
average of s2.prior and sigma^2 with weights proportional to df.prior 
and df.residual respectively."

	Best wishes
	Wolfgang


Il Nov/13/10 10:44 PM, Sean Davis ha scritto:
> On Sat, Nov 13, 2010 at 1:56 PM, Eva Benito Garagorri<ebenito at umh.es>wrote:
>
>> Dear list,
>>
>> I have been working with some microarray data where I make simple
>> comparisons between a control and a treatment group. I used vsn to normalize
>> and limma to find differentially expressed genes. I used "topTable" with
>> number=Inf and p.value=0.05 to get all significant genes for a given
>> condition, regardless of their fold change. I seem to be getting significant
>> genes with a fold change systematically bigger than 1.3 (linear scale), both
>> up and downregulated. I was wondering whether this can happen and why or
>> whether I am missing something or making a mistake in the analysis. I guess
>> I expected that some genes would be significant even with a very small fold
>> change. I tried the same analysis with the ALL dataset and I found that
>> genes were significant with a fold change above ~1.1. Below is the code I
>> used for the analysis of the ALL dataset, which is essentially the same I
>> used for my own analysis. Thanks in advance!
>>
>>
> Hi, Eva.  I think what you are saying is that you are seeing genes that
> change by 30% and that you are concerned that you should see genes with a
> smaller fold change being significant?  The fold change that is significant
> will be dependent on a number of factors, but sample size and biologic
> factors such as the amount of heterogeneity in the two conditions are strong
> contributors.  I wouldn't say that there is anything wrong with your
> results, at least without knowing more detail.
>
> Sean
>
>
>
>>   Eva
>>
>>
>> library(ALL)
>> data(ALL)
>> library(limma)
>>
>>
>> f = ALL$mol.biol
>>
>> mat = model.matrix(~f, ALL)
>> lm = lmFit(ALL, mat)
>> eb = eBayes(lm)
>>
>> sign = topTable(eb, coef=2,number=Inf,p.value=0.05)
>> dim(sign)
>>
>> sort(2^sign$logFC)
>>
>>
>>
>>
>>
>>> sessionInfo()
>> R version 2.11.1 (2010-05-31)
>> x86_64-apple-darwin9.8.0
>>
>> locale:
>> [1] es_ES.UTF-8/es_ES.UTF-8/C/C/es_ES.UTF-8/es_ES.UTF-8
>>
>> attached base packages:
>> [1] stats     graphics  grDevices utils     datasets  methods   base
>>
>> other attached packages:
>> [1] limma_3.4.4   ALL_1.4.7     Biobase_2.8.0
>>
>> loaded via a namespace (and not attached):
>> [1] tools_2.11.1
>>
>>
>>
>>
>>
>>
>>
>>
>> ----------
>> Eva Benito Garagorri
>> PhD program in Neurosciences
>> Institute for Neurosciences in Alicante
>> UMH-CSIC
>> San Juan de Alicante
>> 03550
>> Spain
>> ebenito at umh.es
>> (34) 965 91 92 33
>>
>>
>>
>>
>>
>>         [[alternative HTML version deleted]]
>>
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