Within-sample comparison of TMM normalized values?

Question

[Ekarl2]

I have the following RNA-seq set-up:

• 5 samples for comparison
• matrix with TMM-normalized FPKM values

Now, TMM-normalization allows comparison across samples, so I can compare gene X between samples 1-5. Can I also compare gene X with gene Y within, say, sample 2 or does the TMM-normalization make this inappropriate (e. g. using different scaling factors for each gene or anything like that)?

I have tried to read the TMM-normalization paper (cited below) and it seems that when there are more than two samples, it picks a reference sample and calculates a single scaling factor for each pairwise comparison between the reference and each non-reference sample. That would seem to suggest that the within-sample comparison like the one outlined above is possible. Is it?

Robinson, M. and A. Oshlack (2010). "A scaling normalization method for differential expression analysis of RNA-seq data." Genome Biology 11(3): R25.

Answer 1

[Devon Ryan]

TMM won't change the order of values, it's meant to adjust between samples only. So if you're asking, "Does gene A have a higher FPKM than gene B in sample 3", then you'll get the same answer with/without normalization (the exact size of the difference might differ, though).

[Ekarl2]

Would the exact size of the difference be different in percentage as well and can we say anything qualitatively about such difference? Would it be, on average, small, moderate, large, huge?

[Devon Ryan]

It'll depend on what you compute the percentage of. The normalized FPKMs will just be scaled by a constant, so the magnitude of the change will depend on what that constant is. How large the constant is will depend on the other samples. If the samples have similar depth and none of them are extreme outliers versus the others then the change will be moderate to small (in a well-behaved experiment, the normalization factors will be ~1).

[Ekarl2]

I was probably a bit unclear: so for a given sample, the relative proportions would still be the same since it is just scaled by a constant? In other words would the within-sample values for the ratio "non-TMM FPKM for gene X" / "non-TMM FPKM for gene Y" be the same as the value for the ratio "TMM-FPKM for gene X" / "TMM-FPKM for gene Y"?

[Devon Ryan]

Ah, you meant the ratio rather than some sort of percentage. Yes, the ratio will be the same, since the scaling factors should cancel out.

[Ekarl2]

Thanks! I will mark your answer as accepted.