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Calculating FC on probabilistic quotient normalization (PQN) data

I am working with publicly available metabolomics data that has been probabilistic quotient normalized (PQN). I am interested in calculating the fold changes (FC) between case/control. Some of the normalized values are negative so I am unsure if I am capturing the true differences between samples when I apply more traditional FC calculations. Is there an approach you have used to calculate fold changes on these types of normalized data?

fold change statistics normalization

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