Enrichment pathways comparison between conditions

Question

[judhenaosa]

Hi.

I have the pathways obtained from an enrichment analysis for five conditions (Condition_A, Condition_B, Condition_C, and Condition_D). With the pathways lists, I made an intersection set (vennDiagram), and I obtained the number of common pathways for every possible combination just the next table shows:

Comparison	Common_path_Number
Condition_A vs Condition_B vs Condition_C vs Condition_D vs Condition_E	13
Condition_B vs Condition_C vs Condition_D vs Condition_E	1
Condition_A vs Condition_C vs Condition_D vs Condition_E	1
Condition_C vs Condition_D vs Condition_E	2
Condition_A vs Condition_B vs Condition_D vs Condition_E	0
Condition_B vs Condition_D vs Condition_E	0
Condition_A vs Condition_D vs Condition_E	1
Condition_D vs Condition_E	3
Condition_A vs Condition_B vs Condition_C vs Condition_E	0
Condition_B vs Condition_C vs Condition_E	0
Condition_A vs Condition_C vs Condition_E	0
Condition_C vs Condition_E	0
Condition_A vs Condition_B vs Condition_E	0
Condition_B vs Condition_E	0
Condition_A vs Condition_E	3
Condition_E	4
Condition_A vs Condition_B vs Condition_C vs Condition_D	20
Condition_B vs Condition_C vs Condition_D	3
Condition_A vs Condition_C vs Condition_D	4
Condition_C vs Condition_D	9
Condition_A vs Condition_B vs Condition_D	0
Condition_B vs Condition_D	0
Condition_A vs Condition_D	0
Condition_D	18
Condition_A vs Condition_B vs Condition_C	3
Condition_B vs Condition_C	1
Condition_A vs Condition_C	0
Condition_C	12
Condition_A vs Condition_B	1
Condition_B	2
Condition_A	3

Now, I need to establish if they are significantly intersected. I guess the best way is using a Fisher test. If so, What is the correct form to create the contingency table?

If you have any tips to resolve this task. I will appreciate it.

Kind regards,

Juan

[egeulgen]

oh, also see How To Determine The Statistical Significance Of Overlap (Intersect) Between Three Sets

Answer 1

[egeulgen]

Initially, I thought you could try a multivariate hypergeometric distribution based test, implemented as MultiHypergeometric in the CRAN package extraDistr.

After searching a while, however, this article also looks very promising:

... developed a theoretical framework for computing the statistical distributions of multi-set intersections based upon combinatorial theory, and then accordingly designed a procedure to efficiently calculate the exact probabilities of multi-set intersections.

Bonus:

We further developed multiple efficient and scalable techniques to visualize multi-set intersections and the corresponding intersection statistics.

The method is available as an R package: SuperExactTest

Hope this helps, -E