Associating somatic mutation with clinical outcomes through kernel regression and optimal transport

Somatic mutations in cancer patients are inherently sparse and potentially high dimensional. Cancer patients may share the same set of deregulated biological processes perturbed by different sets of somatically mutated genes. Therefore, when assessing the associations between somatic mutations and clinical outcomes, gene-by-gene analysis is often under-powered because it does not capture the complex disease mechanisms shared across cancer patients. Rather than testing genes one by one, an intuitive approach is to aggregate somatic mutation data of multiple genes to assess their joint association with clinical outcomes. The challenge is how to aggregate such information. Building on the optimal transport method, we propose a principled approach to estimate the similarity of somatic mutation profiles of multiple genes between tumor samples, while accounting for gene-gene similarities defined by gene annotations or empirical mutational patterns. Using such similarities, we can assess the associations between somatic mutations and clinical outcomes by kernel regression. We have applied our method to analyze somatic mutation data of 17 cancer types and identified at least five cancer types, where somatic mutations are associated with overall survival, progression-free interval, or cytolytic activity.