Summing the abundances of multiple peaks, and comparing the sum to another sample's sum I think this question may make sense here or in the chemistry exchange, but it is more statistics/chemometrics related so I am hoping you can help! 
I am working on a metabolomics dataset that produces area under peaks to represent the response of an instrument for a wide variety of metabolites. No metabolites identified have been quantified with an internal standard or calibration curve. 
However, the data has been normalized relative to the total ion current (TIC) for each sample, so each peak has been normalized to the entire area. 
I am trying to find a way to compare the total abundances of the lipids in one sample to the total abundances of lipids in another sample, essentially adding peak areas together. For example, Lipid A abundance + Lipid B abundance + Lipid C abundance, and compare these in say, Sample 1 vs Sample 2. Lipid A and Lipid B may have the same concentration, but different responses from the instrument and thus different areas under the curve. 
My question is - does this method of normalization create "units" that are essentially equal to each other in scale for the purposes of relative comparison (not quantitation)? My concern is that if Sample 1 has high lipid A, but low lipid B, and the opposite is true for Sample 2, I need to be sure that the samples' total lipid abundances are comparable.  
Long winded. Thanks in advance for your thoughts! 
 A: As @whuber already pointed out, the only way here lies in chemical assumptions.
You'd need two assumptions:


*

*Can you sensibly assume that all the lipid signals have the same  sensitivity (note that sensitivity implies a linear response in general).

*As you normalize your total counts over the whole spectrum, you also need to be sure that the matrix is either constant (exclude lipid signals from normalization) or again sensitivity across all species is constant.


If your knowledge about both your samples and the analytical process make these assumptions sensible, you can add the lipid signals. 
You do have a fundamental misunderstanding in thinking that only full quantitation needs linear relations or a calibration. Many semi-quantitative or qualitative questions also need calibration of your instrument response - though maybe not to absolute amounts of particular substances. The semi-quantitative approach you take needs the calibration across all substances in question to be known up to a constant factor. In other words, you need to know the relative sensitivities for the different lipids, and in addition you need to know either the relative sensitivities for the other signals or you need to be sure the relative composition of all other components of your sample is constant in order to be allowed to normalize in the way you propose.  
The response doesn't even need to be nonlinear, in your case already a linear response but varying sensitivities for the different lipids would make your approach wrong. Say lipid A has 2 counts / mol, lipid B 1 ct/ mol, C 3 ct/ mol. You observe 10 counts in total. Total lipids may be anywhere between 3,33 and 10 mol. This factor 3 in the range of possible values comes from the factor 3 in the assumed sensitivities. So if you can reasonably assume your lipid sensitivities to be within a factor x of each other, you can draw conclusions from total lipid counts up to a factor x. If that x is small enough compared to the observed differences, you may still be able to conclude something about your samples. 
