I have a gene expression data set with the following features:
1) mutation status (binary variable: mutant vs. WT)
2) Grouping (Group1, Group 2)
The question is whether the mutation leads to an increase in difference in gene expression between patients in Group 2 vs. Group 1.
I have thought about doing t-tests. In a clear example, mutant-Group1 vs. mutant-Group2 would be significant and WT-Group1 vs WT-Group2 shouldn't not be significant. However, I can think of examples that would be problematic (marginally not significant results, two significant results with very different p-values, etc.).
I have thought about simulating a null distribution for the difference between 2 pairs of random data sets, but is there a more straightforward method for analysis? For example, does the difference between t-test statistics also follow a normal distribution (it seems like that could prioritize genes of interest)? Likewise, is there a single test that can be used (instead of two separate tests)?