On the sample complexity of cancer pathways identification

In this work we propose a framework to analyze the sample complexity of problems that arise in the study of genomic datasets. Our framework is based on tools from combinatorial analysis and statistical learning theory that have been used for the analysis of machine learning and probably approximately correct (PAC) learning. We use our framework to analyze the problem of the identification of cancer pathways through mutual exclusivity analysis of mutations from large cancer sequencing studies. We analytically derive matching upper and lower bounds on the sample complexity of the problem, showing that sample sizes much larger than currently available may be required to identify all the cancer genes in a pathway. We also provide two algorithms to find a cancer pathway from a large genomic dataset. On simulated and cancer data, we show that our algorithms can be used to identify cancer pathways from large genomic datasets.