Certain amount of material is injected in animals, say proteinA, proteinB .... proteinZ, and measurements were made on the corresponding amount recovered. Would have been nice to inject equal amounts and do stats on how much was recovered, increase/decrease etc. and corresponding effect sizes. But that is not possible given experimental constraints, so proteins A, B, C, D all had different original amounts, different by several orders of magnitudes, say 1 unit, 100 unit or 10000 unit.
Eventually need to compare the proteins with each other, which has best performance in the experiment, i.e. best recovery compared to injected amount. Currently using log2FC, and getting a single value for each protein, say 5-fold protein A, 10 fold protein B, -2 fold protein C, so on and so forth. this gives some qualitative assessment of which are doing best compared to others. Using MA plots to factor in amount of material as well.
But I now need to compare between the proteins, to say something like how much better (or worse) proteinA is compared to proteinZ. Taking ratios of Log2FC, is that fair? Any stats anyone can recommend?
Granted it is not ideal scenario, but need to provide some inference based on the the measurements so any suggestions are welcome.
This seems like a poor (fatal) experimental design at first glance. Since protein and injection amount are perfectly correlated, you won't be able to deconvolute the effect of protein from injection amount. What was the reasoning behind injecting different amounts?
Different amounts is because of biological constraints which we have no control over. Think of it as a protein library with different members in unequal amounts.
What are the components of your current logFC ratio? log2(amount injected/amount recovered) ? If so, does -2 fold mean you recover more than you inject? What does it mean to do "better" or "worse"?
Yes, your interpretation of log2ratio is correct. And yes we can recover both more or less than injected. More is better and less is worse. Both increase and decrease can be several orders of magnitude, So log scale seems appropriate for visualization such as MA plot. The comparison between different entities is where I am running into issues.