I'm trying to compare the treatment effect on differentially expressed genes between control and diseased RNA-seq data. This question is based off another post I made where unfortunately the treatment was confounded with the batches.

It was suggested I used duplicateCorrelation() from the limma package to calculate the differentially expressed genes. More specifically, because the treatment was confounded with batches, I would have to do something like this to see what the treatment did:

(Treated Disease v. Untreated Disease) v. (Treated Control v. Untreated Control)

Again, the details of why I have to do this are in my last post

My question is really just about the specifics on how I would go about making this comparison and what the results mean. A commenter on the previous post states I'll be able to make inferences on how the treatment affects differentially expressed genes, but I'm having trouble working this out intuitively. If I separately did DEX analysis on: (TD v. UnTD) and then (TC v. UnTC), how would I compare the differentially expressed genes statistically. Any help would be great. Also if you have any thoughts about this whole thing in general, those would be appreciated!