I have been reading a lot about within-sample and between-sample RNA-seq normalization but I still haven't found an answer for my question.
My data consists of an RNA-seq matrix with Transcripts-Per-Million (TPM) values, so it is within-sample normalized. I want to compare the expression of two genes within a sample (expression gene 1 / expression gene 2), and then compare the resulting ratio between samples (from the same group, I do not have different conditions or experiments, this is not my purpose). My guess is that, as I am comparing relative abundances between genes within a sample, I can compare these ratios between samples without a between-sample normalization (like DESeq2 or TMM). But I am not 100% sure. Do I need this normalization or I can compare samples directly with TPM in this particular case?