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An innovative form of Fisher ratio (F-ratio) analysis (FRA) is developed for use with comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry (GC × GC−TOFMS) data and applied to the investigation of the changes in the metabolome in human plasma for patients with injury to their anterior cruciate ligament (ACL). Specifically, FRA provides a supervised discovery of metabolites that express a statistically significant variance in a two-sample class comparison: patients and healthy controls. The standard F-ratio utilizes the between-class variance relative to the pooled within-class variance. Because standard FRA is adversely impacted by metabolites expressed with a large within-class variance in the patient class, "control-normalized FRA" has been developed to provide complementary information, by normalizing the between-class variance to the variance of the control class only. Thirty plasma samples from patients who recently suffered from an ACL injury, along with matched controls, were subjected to GC × GC−TOFMS analysis. Following both standard and control-normalized FRA, the concentration ratio for the top 30 "hits" in each comparison was obtained and then t-tested for statistical significance. Twenty four out of 30 metabolites plus the therapeutic agent, naproxen (24/30), passed the t-test for the control-normalized FRA, which included 8/24 unique to control-normalized FRA and 16/24 in common with the standard FRA. Likewise, standard FRA provided 21/30 metabolites passing the t-test, with 5/21 undiscovered by control-normalized FRA. The complementary information obtained by both F-ratio analyses demonstrates the general utility of the new approach for a variety of applications.

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