I am wondering about the proper way to control for gene-specific differences in the background mutation rate when using Genome MuSiC PathScan.

From what I understand from the documentation, PathScan assumes a uniform background mutation rate for all genes that enter the analysis. I think this assumption is wrong and I am thus worried about its consequences in terms of pathways that are erroneously identified as significantly mutated.

Is there any way to deal with this? Is it for example a viable strategy to first identify significantly mutated genes with Genome MuSiC SMG (which considers gene-specific differences in the background mutation rate) and let only the significantly mutated genes enter the pathway analysis? But I assume that this would result in a loss of power, because we are no longer looking at all mutations affecting a particular pathway at once.

Are there maybe alternative tools that consider gene-specific mutation rates for pathway enrichment analysis in cancer?