Hi,

I have a representative data like this. the first column is control and second is treated

df<- structure(list(col1A = c(1.64, 0.03, 0, 4.202, 2.981, 0.055, 
0, 0.002, 0.005, 0, 0.002, 0.649, 2.55, 2.762, 6.402, 0.91, 0.037, 
0, 5.757, 3.916, 0.022, 0, 0, 0.003, 0, 0.262, 0.136, 2.874, 
3.466, 5.003), col2A = c(2.635, 0.019, 0, 5.638, 3.542, 0.793, 
0.259, 0, 0.046, 0.004, 0.017, 0.971, 3.81, 3.104, 5.849, 1.027, 
0.021, 0, 4.697, 2.832, 0.038, 0.032, 0.001, 0.003, 0, 0, 0.317, 
2.743, 3.187, 6.455)), row.names = c("A", "AA", "AAA", "Aab", 
"buy", "yuyn", "gff", "fgd", "kil", "lilk", "hhk", "lolo", "fdd", 
"vgfh", "nghg", "gdtd", "ayad", "terer", "quwte", "nshdg", "ahaf", 
"eqew", "tars", "nshdt", "andydv", "oalkd", "jayqgd", "nahdgd", 
"nagdd", "hdydy"), class = "data.frame")


group<-factor(c("C","T"))
design<-model.matrix(~group)
data<-DGEList(counts=df,group=group)
data<-estimateGLMCommonDisp(d,design,method="deviance",robust="TRUE",subset=NULL)
data$common.dispersion=0.4
res <- exactTest(data)

I am wondering if this is correct? can I reply somehow on the p value and FDR? let me know where I am making mistake or if there is other package that can be better ?

I assume you've read the relevant section of the edgeR user's guide (i.e., Section 2.11). If you don't have replicates, there is very little that you can do. This is a fundamental theoretical limitation that cannot be overcome. The p-values and FDR resulting from any analysis without replication should not be trusted. Also, the estimateGLMCommonDisp call above will fail for various reasons (no residual d.f., run on d instead of data, robust should be a logical scalar).

You see to be trying to use a suggestion from Section 2.11 of the edgeR User's Guide, but your analysis is nevertheless still nonsense at the moment because edgeR is not designed to work with arbitrary "normalized expression values".

Trying to use permutation with only 2 samples also makes no sense. No informative permutations are possible with only 2 observations.

If you can obtain raw data in the form of meaningful counts, and you really want FDR values, then the two possible approaches are suggestions 2 and 3 in the edgeR User's Guide section on What to do if you have n replicates.

Suggestion 2 from the User's Guide is to use pre-specified dispersion value. For example you might use

group <- factor(c("C","T"))
d <- DGEList(counts=df, group=group)
keep <- filterByExpr(d)
d <- d[keep,,keep.lib.sizes=FALSE]
d <- calcNormFactors(d, method="TMMwzp")
res <- exactTest(d, dispersion=0.2)
topTags(res)

This analysis without replicates isn't ideal, but nevertheless is vastly better than the method proposed in the Chen et al (2011) paper that you cite, which fails to take biological variation into account at all. You not need to use estimateDisp, or any of its variants, which are only for replicated data.

The dispersion value of 0.4 that you use in your code is higher than I have ever seen for published mRNA-seq data, although a high value like that could perhaps be appropriate for single cell RNA-seq. The example in Section 2.11 of the edgeR User's uses dispersion = 0.4^2 = 0.16, which is a typical sort of value for independent human samples in my experience.

Suggestion 3 from the edgeR User's Guide suggests a rough way of trying to conservatively estimate the dispersion. That would go like this:

group <- factor(c("C","T"))
d <- DGEList(counts=df, group=group)
keep <- filterByExpr(d)
d <- d[keep,,keep.lib.sizes=FALSE]
d <- calcNormFactors(d, method="TMMwzp")
d <- estimateGLMCommonDisp(d, method="deviance", robust=TRUE, subset=NULL)
res <- exactTest(d)
topTags(res)

This method uses estimateGLMCommonDisp to fit a single-group model to both libraries, and to estimate the dispersion allow for a few genes to be outliers. This method does however need a large number of genes to work with, which you don't seem to have