An exact method to compute a $p$-value for the beyond-pairwise correlations among cancer gene mutations

The increasing observation of mutual exclusivity correlations among cancer gene mutations is a key component for identifying driver events or pathways in cancer genome analysis. Here we report a rigorous statistical method to compute an exact $p$-value for the beyond-pairwise mutual exclusivity or co-occurrence relationships among cancer gene mutations by enumerating a null distribution of overlapping mutations across more than two genes. The validity and the advantage of our method is explicitly demonstrated in both cancer gene mutations and simulation data through the comparison to the permutation test.