Hi Patrick,
fgsea is not our software and we don't provide support for it, my understanding is that they take several algorithmic shortcuts that result in them being able to produce significance statistics without actually generating the full null distribution as we do in the full original GSEA implementation.
The FDR produced by GSEA is a global false discovery statistic using the information from the distributions of all analyzed gene sets to produce an estimate of false discovery rate given the input collection of gene sets. I don’t believe fgsea produces an equivalent statistic, it's padj is based on mathematical correction of the pval not an analysis of the true global distributions. The NOM p-value, in contrast represents the significance statistic of a gene set just compared to its own null distribution, since fgsea isn't generating all the null distributions as we do, I can't speak to the accuracy of their statistics.
As for significance cutoffs, since GSEA Preranked runs in gene set permutation mode and not phenotype permutation mode, the standard statistical cutoffs of p<0.05, FDR<0.05 are generally reasonable.
Sorry I couldn't be of more help here, if you want to dig into the mathematical assumtions of fgsea, the method is available as a preprint here: https://www.biorxiv.org/content/10.1101/060012v3.full
And we rehost the publication for the original GSEA method here: https://www.gsea-msigdb.org/gsea/doc/subramanian_tamayo_gsea_pnas.pdf (along with the GSEA User guide: https://software.broadinstitute.org/gsea/doc/GSEAUserGuideFrame.html)
-Anthony
Anthony S. Castanza, PhD
Curator, Molecular Signatures Database
Mesirov Lab, Department of Medicine
University of California, San Diego
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