An equivalence test between features lists, based on the Sorensen–Dice index and the joint frequencies of GO term enrichment

Table 5 Comparing the data structures to compute the goProfiles test and the one based on enrichment contingency tables.

	Non-enriched in both lists			Enriched only in list 1			Enriched only in list 2			Enriched in both lists
GO term number	1	\(\cdots\)	\(a = n_{00}\)	\(a + 1\)	\(\cdots\)	\(b = a + n_{10}\) \(= n_{.0}\)	\(b + 1\)	\(\cdots\)	\(c = b + n_{01}\)	\(c + 1\)	\(\cdots\)	\(c + n_{11}\) \(= n\)
Annotation frequency in gene list 1	\(F_{11}\)	\(\cdots\)	\(F_{1a}\)	\(F_{1(a + 1)}\)	\(\cdots\)	\(F_{1b}\)	\(F_{1(b+1)}\)	\(\cdots\)	\(F_{1c}\)	\(F_{1(c+1)}\)	\(\cdots\)	\(F_{1n}\)
Annotation frequency in gene list 2	\(F_{21}\)	\(\cdots\)	\(F_{2a}\)	\(F_{2(a + 1)}\)	\(\cdots\)	\(F_{2b}\)	\(F_{2(b+1)}\)	\(\cdots\)	\(F_{2c}\)	\(F_{2(c+1)}\)	\(\cdots\)	\(F_{2n}\)
Enrichment in list 1	0	\(\cdots\)	0	1	\(\cdots\)	1	0	\(\cdots\)	0	1	\(\cdots\)	1
Enrichment in list 2	0	\(\cdots\)	0	0	\(\cdots\)	0	1	\(\cdots\)	1	1	\(\cdots\)	1

In the latter test, the annotation frequencies are substituted by 0 and 1 (i.e., “non-enriched” and “enriched” GO term.) and if the test is based on the Sorensen–Dice similarity, the first set of GO terms (non-enriched in both lists) is ignored. The GO terms are arbitrarily ordered: from left to right, first there are all those non-enriched in both lists (\(n_{00}\) in total), next those enriched in the first list but not in the second one (\(n_{10}\)), then those enriched in the second list but not in the first (\(n_{01}\)) and finally those GO terms enriched in both lists (\(n_{11}\))

ISSN: 1471-2105