First of all, I am a biologist not a mathematician. Please let me know if you need more details to be able to answer my question. Also, I apologize in advance for the, likely many, math-illiterate mistakes I may make.
GO terms are used to annotate protein function, each term describes a specific function that can be carried out by a protein in a given cell. I have calculated the probability of association for each possible pair of GO terms, based on how often a given protein is annotated to both terms.
Now, I am using this probability to find interactions between proteins annotated to "dissimilar" GO terms. Since I am dealing with very large data sets, I need to apply a multiple testing correction to my probabilities.
A colleague suggested that I should multiply my p-value by the number of tests performed to obtain a corrected e-value:
e-val=p-val x #Tests
My method consists of taking a protein-protein interaction network (for the purposes of this question, this is just a normal, albeit relatively sparse, unweighted graph) and partitioning it into overlapping classes (see disclaimer). I then look for i) nodes that are found at the intersection (i.e. belonging to both) of dissimilarly annotated classes or ii) nodes that, while belonging to neither, connect these classes (ie have edges connecting them to nodes of each class).
My problem is that method i) involves orders of magnitude more tests than method ii):
- i : 46,568,354 tests
- ii: 102,911 tests
Since I am using the same uncorrected p-values for each method, applying this multiple testing correction (multiplying the p-value by the number of tests performed) will give me completely different e-values for the same pair of GO terms, making it impossible to compare the results of these methods to one another.
So, how can I get a comparable e-value?
DISCLAIMER: Yes, I do know that, by definition, a graph partition consists of disjoint classes but my math vocabulary fails me. If someone has a term for a graph "partition" with overlapping classes I would very much like to hear it.