A major goal of cancer sequencing projects is to identify genetic alterations that determine clinical phenotypes, such as survival time or drug response. Somatic mutations in cancer are typically very diverse, and are found in different sets of genes in different patients. This mutational heterogeneity complicates the discovery of associations between individual mutations and a clinical phenotype. This mutational heterogeneity is explained in part by the fact that driver mutations, the somatic mutations that drive cancer development, target genes in cellular pathways, and only a subset of pathway genes is mutated in a given patient. Thus, pathway-based analysis of associations between mutations and phenotype are warranted. Here, we introduce an algorithm to find groups of genes, or pathways, whose mutational status is associated to a clinical phenotype without prior definition of the pathways. Rather, we find subnetworks of genes in an gene interaction network with the property that the mutational status of the genes in the subnetwork are significantly associated with a clinical phenotype. This new algorithm is built upon HotNet, an algorithm that finds groups of mutated genes using a heat diffusion model and a two-stage statistical test. We focus here on discovery of statistically significant correlations between mutated subnetworks and patient survival data. A similar approach can be used for correlations with other types of clinical data, through use of an appropriate statistical test. We apply our method to simulated data as well as to mutation and survival data from ovarian cancer samples from The Cancer Genome Atlas. In the TCGA data, we discover nine subnetworks containing genes whose mutational status is correlated with survival. Genes in four of these subnetworks overlap known pathways, including the focal adhesion and cell adhesion pathways, while other subnetworks are novel.