Hello.

I intend to perform three contrasts including: i) mock.24h vs mock.4h; ii) S2.24h vs S2.4h and iii) the difference between these two comparisons (S2.24h vs S2.4h) - (mock.24h vs mock.4h). The design of my colData is as follows

condition            time           group
S2                    4h            S2.4h
S2                    4h            S2.4h
S2                    24h           S2.24h
S2                    24h           S2.24h
mock                  4h            mock.4h
mock                  4h            mock.4h
mock                  24h           mock.24h
mock                  24h           mock.24h

To address this, I have provided the following design, but I am not sure if these are correct.

design(dds) <- ~ group
dds <- DESeq(dds)
resultsNames(dds)
# e.g. for group mock.24h vs mock.4h
results(dds, contrast = c("group", "mock.24h", "mock.4h")) 
# e.g. for group S2.24h vs S2.4h
results(dds, contrast = c("group", "S2.24h", "S2.4h"))
# e.g. for difference group (S2.24h vs S2.4h) - (mock.24h vs mock.4h)
results(dds, contrast = c("group", c("S2.24h",  "S2.4h") - ("mock.24h", "mock.4h")))

What would be the most correct way to make this kind of contrasts? I look forward to reading your answers.

Your first two are fine. The usual way for the last question is to make a new design ~ condition + time + condition:time, and instead of contrasts, there should be an element in reusltNames like conditionS2.time24hr, and you use that.

It's always wise to do a reality check of your results by taking the normalized counts, working out the averages of the different groups, and the fold changes you get that way should be pretty close to what DESeq tells you.