I am using DESeq2 for RNAseq analysis. I have 3 conditions (Control, Treatment 1, and Treatment 2). I gave the design matrix formula as ~  replicate + condition. And I get two sets of results as

res1 <- results(dds, contrast=c('condition','control','t1'))
res2 <- results(dds, contrast=c('condition','control','t2'))

Now, I am interested in genes that are only regulated in treatment 1 but not in treatment 2. I simply selected genes with res1$padj<0.05 and res2$padj>0.05.

1. Is there a systematic way to do this? One way would be to rename treatment 2 also as control. But then, we are only selecting genes DE in treatment 1 compared to the combined  condition of control and treatment 2. This doesn't really solve the same problem. Does it? Is there a different way to write a fancy contrast condition to do this?

2. If we simply use the (adjusted) p-values of the two results obtained separately, what would be the way to formulate the test and arrive at a significance level? If I use res1$padj<0.05 and res2$padj>0.05 what is the effective significance of this test? Does it depend on how many genes are found significant in treatment 1 and 2 respectively?

3. Any other ideas? A different package that can handle this?

4.  

Update

I can eliminate trying to select for the null by modifying the way I frame the test (and slightly modifying the problem), either by using the results with altHypothesis="lessAbs" or by testing DE between treatments 1 and 2, and selecting genes that show say, signficant but opposite DE from Control to Treatment 1, and 1 to 2. So now, I have two tests that share a condition (or samples), and I want to select genes that are significant in both tests. But these tests are correlated (I think).

Absence of evidence is not evidence of absence. If you want to test for equivalent expression between two groups, you cannot use the p-values from a test of differential expression. You must conduct a different statistical test, which DESeq2 also provides. To conduct an equivalence test, you must use altHypothesis="lessAbs" when calling "results", and you must also make several of other adjustments, which you should read about in the help page for "results" as well as the DESeq2 manual, before you try to do this kind of test. Also note that unless you have very many samples, equivalence testing often has very low statistical power for genomics data.