I understand that negative z-score in pathway analysis of differentially expressed genes means stability between conditions. In other words the list of submitted genes contains less than expected genes belonging to that pathway.
I submitted to Enrichr an artificial list of 10 genes belonging to the Hippo signalling pathway (DCHS1, DCHS2, FAT1, FAT2, FAT3, FAT4, WWC1, NF2, MST1, MST2). Under KEGG 2016 analysis, Hippo signalling is the sole one identified but features a negative z-score.
How should this negative score be interpreted?
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jomo018
1 answer
It reflects a 'deviation from the expected rank' of the gene. The 'expected rank' is computed by using a random input of genes for the given gene-set. For each of your genes, their respective Z-scores are then obtained via the standard deviation by comparing the actual to the expected ranks.
We first compute enrichment using the Fisher exact test for many random input gene lists in order to compute a mean rank and standard deviation from the expected rank for each term in each gene-set library. Then, using a lookup table of expected ranks with their variances, we compute a z-score for deviation from this expected rank, this can be a new corrected score for ranking terms.
[source: https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-14-128]
With a negative value, it indicates that it's rank is 'below' that expected. I think that any deviation (positive or negative) should be interpreted generally in the same way. The larger the absolute Z-score, the larger the deviation from the expected value.
I put 'below' in apostrophes because, mathematically, a lower numerical value actually reflects a higher rank (e.g. 1 is a higher rank than 3, but 1 is less than 3 numerically). I don't know exactly how the authors encoded it.
Kevin
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