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Motivation Recent advances in DNA sequencing technologies have allowed the detailed characterization of genomes in large cohorts of tumors, highlighting their extreme heterogeneity, with no two tumors sharing the same complement of somatic mutations. Such heterogeneity hinders our ability to identify somatic mutations important for the disease, including mutations that determine clinically relevant phenotypes (e.g. cancer subtypes). Several tools have been developed to identify somatic mutations related to cancer phenotypes. However, such tools identify correlations between somatic mutations and cancer phenotypes, with no guarantee of highlighting causal relations. Results We describe ALLSTAR , a novel tool to infer reliable causal relations between somatic mutations and cancer phenotypes. ALLSTAR identifies reliable causal rules highlighting combinations of somatic mutations with the highest impact in terms of average effect on the phenotype. While we prove that the underlying computational problem is NP-hard, we develop a branch-and-bound approach that employs protein–protein interaction networks and novel bounds for pruning the search space, while properly correcting for multiple hypothesis testing. Our extensive experimental evaluation on synthetic data shows that our tool is able to identify reliable causal relations in large cancer cohorts. Moreover, the reliable causal rules identified by our tool in cancer data show that our approach identifies several somatic mutations known to be relevant for cancer phenotypes as well as novel biologically meaningful relations. Availability and implementation Code, data, and scripts to reproduce the experiments available at https://github.com/VandinLab/ALLSTAR. [ABSTRACT FROM AUTHOR]

Next-generation sequencing technologies allow to measure somatic mutations in a large number of patients from the same cancer type: one of the main goals in their analysis is the identification of mutations associated with clinical parameters. The identification of such relationships is hindered by extensive genetic heterogeneity in tumors, with different genes mutated in different patients, due, in part, to the fact that genes and mutations act in the context of pathways : it is therefore crucial to study mutations in the context of interactions among genes. In this work we study the problem of identifying subnetworks of a large gene-gene interaction network with mutations associated with survival time. We formally define the associated computational problem by using a score for subnetworks based on the log-rank statistical test to compare the survival of two given populations. We propose a novel approach, based on a new algorithm, called N etwork o f M utations A ssociated with S urvival (NoMAS) to find subnetworks of a large interaction network whose mutations are associated with survival time. NoMAS is based on the color-coding technique, that has been previously employed in other applications to find the highest scoring subnetwork with high probability when the subnetwork score is additive. In our case the score is not additive, so our algorithm cannot identify the optimal solution with the same guarantees associated to additive scores. Nonetheless, we prove that, under a reasonable model for mutations in cancer, NoMAS identifies the optimal solution with high probability. We also design a holdout approach to identify subnetworks significantly associated with survival time. We test NoMAS on simulated and cancer data, comparing it to approaches based on single gene tests and to various greedy approaches. We show that our method does indeed find the optimal solution and performs better than the other approaches. Moreover, on three cancer datasets our method identifies subnetworks with significant association to survival when none of the genes has significant association with survival when considered in isolation. [ABSTRACT FROM AUTHOR]

Advances in DNA sequencing technologies have enabled large cancer sequencing studies, collecting somatic mutation data from a large number of cancer patients. One of the main goals of these studies is the identification of all cancer genes-genes associated with cancer. Its achievement is complicated by the extensive mutational heterogeneity of cancer, due to the fact that important mutations in cancer target combinations of genes (i.e., pathways). Recently, the pattern of mutual exclusivity among mutations in a cancer pathway has been observed, and methods that find significant combinations of cancer genes by detecting mutual exclusivity have been proposed. A key question in the analysis of mutual exclusivity is the computation of the minimum number of samples required to reliably find a meaningful set of mutually exclusive mutations in the data, or conclude that there is no such set. In general, the problem of determining the sample complexity, or the number of samples required to identify significant combinations of features, of genomic problems is largely unexplored. 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. 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. [ABSTRACT FROM AUTHOR]

Recent cancer sequencing studies provide a wealth of somatic mutation data from a large number of patients. One of the most intriguing and challenging questions arising from this data is to determine whether the temporal order of somatic mutations in a cancer follows any common progression. Since we usually obtain only one sample from a patient, such inferences are commonly made from cross-sectional data from different patients. This analysis is complicated by the extensive variation in the somatic mutations across different patients, variation that is reduced by examining combinations of mutations in various pathways. Thus far, methods to reconstruct tumor progression at the pathway level have restricted attention to known, a priori defined pathways. In this work we show how to simultaneously infer pathways and the temporal order of their mutations from cross-sectional data, leveraging on the exclusivity property of driver mutations within a pathway. We define the pathway linear progression model, and derive a combinatorial formulation for the problem of finding the optimal model from mutation data. We show that with enough samples the optimal solution to this problem uniquely identifies the correct model with high probability even when errors are present in the mutation data. We then formulate the problem as an integer linear program (ILP), which allows the analysis of datasets from recent studies with large numbers of samples. We use our algorithm to analyze somatic mutation data from three cancer studies, including two studies from The Cancer Genome Atlas (TCGA) on large number of samples on colorectal cancer and glioblastoma. The models reconstructed with our method capture most of the current knowledge of the progression of somatic mutations in these cancer types, while also providing new insights on the tumor progression at the pathway level. [ABSTRACT FROM AUTHOR]

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations. [ABSTRACT FROM AUTHOR]

Background: Cancer sequencing projects are now measuring somatic mutations in large numbers of cancer genomes. A key challenge in interpreting these data is to distinguish driver mutations, mutations important for cancer development, from passenger mutations that have accumulated in somatic cells but without functional consequences. A common approach to identify genes harboring driver mutations is a single gene test that identifies individual genes that are recurrently mutated in a significant number of cancer genomes. However, the power of this test is reduced by: (1) the necessity of estimating the background mutation rate (BMR) for each gene; (2) the mutational heterogeneity in most cancers meaning that groups of genes (e.g. pathways), rather than single genes, are the primary target of mutations. Results: We investigate the problem of discovering driver pathways, groups of genes containing driver mutations, directly from cancer mutation data and without prior knowledge of pathways or other interactions between genes. We introduce two generative models of somatic mutations in cancer and study the algorithmic complexity of discovering driver pathways in both models. We show that a single gene test for driver genes is highly sensitive to the estimate of the BMR. In contrast, we show that an algorithmic approach that maximizes a straightforward measure of the mutational properties of a driver pathway successfully discovers these groups of genes without an estimate of the BMR. Moreover, this approach is also successful in the case when the observed frequencies of passenger and driver mutations are indistinguishable, a situation where single gene tests fail. Conclusions: Accurate estimation of the BMR is a challenging task. Thus, methods that do not require an estimate of the BMR, such as the ones we provide here, can give increased power for the discovery of driver genes. [ABSTRACT FROM AUTHOR]

Problem: We study the problem of identifying differentially mutated subnetworks of a large gene–gene interaction network, that is, subnetworks that display a significant difference in mutation frequency in two sets of cancer samples. We formally define the associated computational problem and show that the problem is NP-hard. Algorithm: We propose a novel and efficient algorithm, called DAMOKLE, to identify differentially mutated subnetworks given genome-wide mutation data for two sets of cancer samples. We prove that DAMOKLE identifies subnetworks with statistically significant difference in mutation frequency when the data comes from a reasonable generative model, provided enough samples are available. Experimental results: We test DAMOKLE on simulated and real data, showing that DAMOKLE does indeed find subnetworks with significant differences in mutation frequency and that it provides novel insights into the molecular mechanisms of the disease not revealed by standard methods. [ABSTRACT FROM AUTHOR]

Next-generation DNA sequencing technologies are enabling genome-wide measurements of somatic mutations in large numbers of cancer patients. A major challenge in the interpretation of these data is to distinguish functional "driver mutations" important for cancer development from random "passenger mutations." A common approach for identifying driver mutations is to find genes that are mutated at significant frequency in a large cohort of cancer genomes. This approach is confounded by the observation that driver mutations target multiple cellular signaling and regulatory pathways. Thus, each cancer patient may exhibit a different combination of mutations that are sufficient to perturb these pathways. This mutational heterogeneity presents a problem for predicting driver mutations solely from their frequency of occurrence. We introduce two combinatorial properties, coverage and exclusivity, that distinguish driver pathways, or groups of genes containing driver mutations, from groups of genes with passenger mutations. We derive two algorithms, called Dendrix, to find driver pathways de novo from somatic mutation data. We apply Dendrix to analyze somatic mutation data from 623 genes in 188 lung adenocarcinoma patients, 601 genes in 84 glioblastoma patients, and 238 known mutations in 1000 patients with various cancers. In all data sets, we find groups of genes that are mutated in large subsets of patients and whose mutations are approximately exclusive. Our Dendrix algorithms scale to whole-genome analysis of thousands of patients and thus will prove useful for larger data sets to come from The Cancer Genome Atlas (TCGA) and other large-scale cancer genome sequencing projects. [ABSTRACT FROM AUTHOR]