You are asking about an interaction term, which is (drug-continued - control1) - (drug-withdrawed - control2), which assumes that there are actual differences between the two control samples. If the two controls are essentially the same thing, they cancel out and then it's just drug-continued - drug-withdrawed.

There's probably a more automatic way of doing this, but I don't totally get how `DESeq2`

does the contrasts, so I do it the dumb direct way. As a fake example

```
> dds <- makeExampleDESeqDataSet()
> design(dds)
~condition
> colData(dds)
DataFrame with 12 rows and 1 column
condition
<factor>
sample1 A
sample2 A
sample3 A
sample4 A
sample5 A
... ...
sample8 B
sample9 B
sample10 B
sample11 B
sample12 B
## change this to have four levels
> colData(dds) <- DataFrame(condition = factor(rep(LETTERS[1:4], each = 3)))
> colData(dds)
DataFrame with 12 rows and 1 column
condition
<factor>
1 A
2 A
3 A
4 B
5 B
... ...
8 C
9 C
10 D
11 D
12 D
## and change to a cell means model, which isn't totally necessary, but maybe easier to understand
> design(dds) <- ~ 0 + condition
> design(dds)
~0 + condition
> dds <- DESeq(dds)
estimating size factors
estimating dispersions
gene-wise dispersion estimates
mean-dispersion relationship
final dispersion estimates
fitting model and testing
## the signs in the interaction term I described above, after
## distributing into the parentheses are 1, -1, -1, 1
## so we use that as the contrast
> results(dds, c(1, -1, -1, 1))
log2 fold change (MLE): +1,-1,-1,+1
Wald test p-value: +1,-1,-1,+1
DataFrame with 1000 rows and 6 columns
baseMean log2FoldChange
<numeric> <numeric>
gene1 88.17007 0.895912
gene2 11.37401 0.267528
gene3 10.31525 -3.993132
gene4 2.00921 0.069651
gene5 18.40443 -0.322246
... ... ...
gene996 13.0700 1.448528
gene997 14.3798 0.200951
gene998 79.2857 -0.550139
gene999 16.5750 -0.014954
gene1000 14.8213 -2.309181
lfcSE stat
<numeric> <numeric>
gene1 0.592058 1.5132152
gene2 1.463057 0.1828555
gene3 1.442082 -2.7690057
gene4 2.609663 0.0266897
gene5 1.069997 -0.3011655
... ... ...
gene996 0.992003 1.4602058
gene997 1.149728 0.1747813
gene998 0.633383 -0.8685729
gene999 1.124772 -0.0132952
gene1000 1.049954 -2.1993176
pvalue padj
<numeric> <numeric>
gene1 0.13022500 0.852226
gene2 0.85491143 0.998859
gene3 0.00562277 0.763831
gene4 0.97870726 0.998859
gene5 0.76328833 0.998859
... ... ...
gene996 0.1442335 0.852768
gene997 0.8612515 0.998859
gene998 0.3850808 0.979411
gene999 0.9893923 0.998859
gene1000 0.0278553 0.763831
```

Thanks a lot.