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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.

Recent large cancer studies have measured somatic alterations in an unprecedented number of tumours. These large datasets allow the identification of cancer-related sets of genetic alterations by identifying relevant combinatorial patterns. Among such patterns, mutual exclusivity has been employed by several recent methods that have shown its effectiveness in characterizing gene sets associated to cancer. Mutual exclusivity arises because of the complementarity, at the functional level, of alterations in genes which are part of a group (e.g., a pathway) performing a given function. The availability of quantitative target profiles, from genetic perturbations or from clinical phenotypes, provides additional information that can be leveraged to improve the identification of cancer related gene sets by discovering groups with complementary functional associations with such targets. In this work we study the problem of finding groups of mutually exclusive alterations associated with a quantitative (functional) target. We propose a combinatorial formulation for the problem, and prove that the associated computational problem is computationally hard. We design two algorithms to solve the problem and implement them in our tool UNCOVER. We provide analytic evidence of the effectiveness of UNCOVER in finding high-quality solutions and show experimentally that UNCOVER finds sets of alterations significantly associated with functional targets in a variety of scenarios. In particular, we show that our algorithms find sets which are better than the ones obtained by the state-of-the-art method, even when sets are evaluated using the statistical score employed by the latter. In addition, our algorithms are much faster than the state-of-the-art, allowing the analysis of large datasets of thousands of target profiles from cancer cell lines. We show that on two such datasets, one from project Achilles and one from the Genomics of Drug Sensitivity in Cancer project, UNCOVER identifies several significant gene sets with complementary functional associations with targets. Software available at: https://github.com/VandinLab/UNCOVER.

Recent large cancer studies have measured somatic alterations in an unprecedented number of tumours. These large datasets allow the identification of cancer-related sets of genetic alterations by identifying relevant combinatorial patterns. Among such patterns, mutual exclusivity has been employed by several recent methods that have shown its effectiveness in characterizing gene sets associated to cancer. Mutual exclusivity arises because of the complementarity, at the functional level, of alterations in genes which are part of a group (e.g., a pathway) performing a given function. The availability of quantitative target profiles, from genetic perturbations or from clinical phenotypes, provides additional information that can be leveraged to improve the identification of cancer related gene sets by discovering groups with complementary functional associations with such targets. In this work we study the problem of finding groups of mutually exclusive alterations associated with a quantitative (functional) target. We propose a combinatorial formulation for the problem, and prove that the associated computational problem is computationally hard. We design two algorithms to solve the problem and implement them in our tool UNCOVER. We provide analytic evidence of the effectiveness of UNCOVER in finding high-quality solutions and show experimentally that UNCOVER finds sets of alterations significantly associated with functional targets in a variety of scenarios. In particular, we show that our algorithms find sets which are better than the ones obtained by the state-of-the-art method, even when sets are evaluated using the statistical score employed by the latter. In addition, our algorithms are much faster than the state-of-the-art, allowing the analysis of large datasets of thousands of target profiles from cancer cell lines. We show that on two such datasets, one from project Achilles and one from the Genomics of Drug Sensitivity in Cancer project, UNCOVER identifies several significant gene sets with complementary functional associations with targets. Software available at: https://github.com/ VandinLab/UNCOVER.

Genome-wide association studies with moderate sample sizes are underpowered, especially when testing SNP alleles with low allele counts, a situation that may lead to high frequency of false-positive results and lack of replication in independent studies. Related individuals, such as twin pairs concordant for a disease, should confer increased power in genetic association analysis because of their genetic relatedness. We conducted a computer simulation study to explore the power advantage of the disease-concordant twin design, which uses singletons from disease-concordant twin pairs as cases and ordinary healthy samples as controls. We examined the power gain of the twin-based design for various scenarios (i.e., cases from monozygotic and dizygotic twin pairs concordant for a disease) and compared the power with the ordinary case-control design with cases collected from the unrelated patient population. Simulation was done by assigning various allele frequencies and allelic relative risks for different mode of genetic inheritance. In general, for achieving a power estimate of 80%, the sample sizes needed for dizygotic and monozygotic twin cases were one half and one fourth of the sample size of an ordinary case-control design, with variations depending on genetic mode. Importantly, the enriched power for dizygotic twins also applies to disease-concordant sibling pairs, which largely extends the application of the concordant twin design. Overall, our simulation revealed a high value of disease-concordant twins in genetic association studies and encourages the use of genetically related individuals for highly efficiently identifying both common and rare genetic variants underlying human complex diseases without increasing laboratory cost. [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]

Two proposed algorithms predict which combinations of mutations in cancer genomes are priorities for experimental study. One relies on interaction network data to identify recurrently mutated sets of genes, while the other searches for groups of mutations that exhibit specific combinatorial properties. [ABSTRACT FROM AUTHOR]