[BioC] ANOVA analysis using edgeR

[Gordon K Smyth]

Dear Yogender Gowtham,

The edgeR user guide tells you how to do the anova test, as you have 
already noted for yourself.

It really is as simple as the user's guide says.  What you are not 
understanding is that if B-A, C-A, D-A and E-A are all zero, then it 
follows that the gene must have the same expression level in all 5 
conditions, and hence all the other possible comparisons (B-C, D-E etc 
etc) must be zero as well.

In fact any four contrasts between the five conditions are sufficient. 
If any four contrasts are zero, then all must be zero.  This is why the 
anova test for five conditions is on 4 degrees of freedom.

edgeR will return you the same correct F test whichever set of 4 contrasts 
you ask it to test.  This means you will get the same test results from 
testing B-A, C-A, D-A and E-A simultaneously as you would from E-D, D-C, 
C-B and B-A, or indeed from any other set of four independent contrasts.

By the way, it is not true that performing pairwise t-tests will 
necessarily give liberal FDR values.  If the FDR is controlled correctly 
for each individual comparison, then it is automatically controlled for 
the whole set of tests.  You may be thinking of p-values and type I error 
rates, but FDRs scale up differently to type I error rates.  There is 
actually little to be gained in the genomic context from doing an anova 
test if you are going to follow it up by posthoc t-tests.

Best wishes
Gordon

> On Aug 1, 2014, at 12:52 AM, Yogender Gowtham <ygowtha at g.clemson.edu> wrote:
>
> Hello All:
>
> I am Yogender Gowtham, a graduate student from Clemson University. We 
> are using RNA-Seq to investigate the transcriptional changes of Chinese 
> Hamster Ovary (CHO) cells during serum-free adaptation. Our experiment 
> has two cell lines, say Y and Z, under 3 different serum concentrations, 
> say, 10%, 5% and 0%. Cell line Z could not be adapted to 0% serum 
> condition and hence we have unbalanced set of conditions. For clarity, 
> the conditions are listed below
>
> A - Y at 0%                 D - Z at 5%
> B - Y at 5%                 E - Z at 10%
> C - Y at 10%
>
> We have come up with 9 different pairwise comparisons based on the 
> scientific questions we want to answer. But performing so many pairwise 
> comparisons will lead to more liberal FDR values. Hence we want to 
> perform ANOVA analysis on all the five conditions.
>
> Based on section 3.2.6 which explains how to perform ANOVA-like 
> analysis. From what I understand, it contrasts each column with 
> intercept and will list any differences that are non-zero (B-A, C-A, 
> D-A, E-A). But ideally we want B-A, B-C, B-D, E-B, C-A, D-C, E-C, D-A, 
> or E-A comparisons in an ANOVA test.
>
> If anyone can suggest a method on edgeR to perform ANOVA tests, that 
> will be perfect. If not, can someone suggest other possible packages 
> that could help me do an ANOVA analysis on multiple groups.
>
> Regards
>
>
> Yogender Kumar Gowtham
> Graduate Research Assistant
> Clemson University
> Department of Bioengineering
> 202 Biosystems Research Complex
> Clemson, SC
> (864)650-7451

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