I have the HTSeq counts for Gencode v19 protein-coding genes and long-noncoding RNAs separately. I normalized and performed a differential gene expression analysis on the two count data separately using VST (limma). My ultimate goal is to find whether there is any correlation between differentially expressed proteins and lncRNAs.
Now I think my approach has been incorrect altogether, and I should combine the counts from the two datasets and normalize them together. This is because the expression levels of protein coding genes and non-coding RNAs vary a lot. But I am still unsure which approach is correct. What do you guys think? What is advisable? To perform the normalization+differential gene expression analysis on lncRNA and protein coding genes separately or together? And why?