I have a expression data from a small cohort of samples taken at baseline and after 2 independent treatments. I can do differential expression contrasting T1 and T2 or I can contrast T1 vs baseline and T2 vs baseline and look at the differences. What is the difference between these two analyses? Are they both valid? If so what inferences can be drawn from each?
If you're interested in looking at the differences between two treatments then you'll end up wanting to do both a direct contrast as well as the individual comparisons to baseline.
The direct contrast will give you the genes actually differentially expressed between the two conditions. In practice, you may want to filter this a bit so you only have genes differentially expressed vs. baseline in at least one condition (e.g., to get rid of genes only slightly higher due to T1 and slightly lower in T2, but not different enough in either case to be DE). Use a pretty lax p-value threshold (e.g., 0.1 or 0.2) for this.
Depending upon the type of treatment used the set of DEGs will change.If the treatments have similar kind of effect you will get a small list (less variable genes will have higher p-val) using a cutoff of p<0.05. So, it's better to start with control vs treated comparisons then T1 vs T2.
Compare the lists form CTRL vs T1 and CTRL vs T2 you will get the genes that are expressed in both conditions as well as unique to individual treatments.