chi-square test to identify significantly mutated genes

Question

[nhaus]

We performed WES for a couple of mouse biopsies. I want to identify genes that are more frequently mutated than one might expect based on the average mutation frequency and the gene length. For this I intend to use the χ2 test.

I was wondering if you guys think that this is a valid approach and also how I might be able to determine the average mutation frequency in order to ultimately determine the expected number of mutations per gene.

Any input is greatly appreciated!