probability of observing overlap between sets of genes

Question

[grant.hovhannisyan]

Imagine there are two species, A and B. A has 560 genes and B has 101 genes. 66 genes are in common between two species. After doing differential expression analysis we observed that there 18 DE genes for species A and 5 DE genes for species B, and 2 DE genes are in common between species. Our question is whether this overlap of two genes is more than expected by chance or not (does it make sense)?

What I do is to calculate the probability of getting overlap of 2 or more when randomly selecting 18 and 5 elements from two lists with 560 and 101 elements. In R it is :

library(lattice)

simulate_de_rate<-function(n_iter){
  result_vector<-NULL
  for(n in c(1:1000)){
    n_matched<-0
    i<-1
    while (i<=n_iter){
      a<-sample(c(1:560),18)
      b<-sample(c(-45:66),5)
      if (length(intersect(a,b))>=2){
        n_matched<-n_matched+1
      }
      i<-i+1
    }
    rate<<-n_matched/n_iter*100
    result_vector<-c(result_vector,rate)
  }
  print(result_vector)
  histogram(result_vector)
}

simulate_de_rate(1000)

So the probability of getting this overlap is very low, ~0.3%. Is it valid to say that the result that we see is not by chance? Can you suggest a statistically more rigorous way of calculation?Thanks

[Benn]

You probably want to take a look at the geneOverlap package.

[zx8754]

Related, possible duplicate post:

• Comparing gene expression overlap with hypergeometric distribution
• Hypergeometric Test On Gene Set
• Probability of gene list overlap
• Hypergeometric test for overlapped genes
• etc

[grant.hovhannisyan]

Thanks, more than enough to figure out how to do it correctly :)