Benjamin J. Raphael

Motivation: The somatic mutations in the pathways that drive cancer development tend to be mutually exclusive across tumors, providing a signal for distinguishing driver mutations from a larger number of random passenger mutations. This mutual exclusivity signal can be confounded by high and highly variable mutation rates across a cohort of samples. Current statistical tests for exclusivity that incorporate both per-gene and per-sample mutational frequencies are computationally expensive and have limited precision. Results: We formulate a weighted exact test for assessing the significance of mutual exclusivity in an arbitrary number of mutational events. Our test conditions on the number of samples with a mutation as well as per-event, per-sample mutation probabilities. We provide a recursive formula to compute P -values for the weighted test exactly as well as a highly accurate and efficient saddlepoint approximation of the test. We use our test to approximate a commonly used permutation test for exclusivity that conditions on per-event, per-sample mutation frequencies. However, our test is more efficient and it recovers more significant results than the permutation test. We use our Weighted Exclusivity Test (WExT) software to analyze hundreds of colorectal and endometrial samples from The Cancer Genome Atlas, which are two cancer types that often have extremely high mutation rates. On both cancer types, the weighted test identifies sets of mutually exclusive mutations in cancer genes with fewer false positives than earlier approaches. Availability and Implementation: See http://compbio.cs.brown.edu/projects/wext for software. Contact:braphael@cs.brown.edu Supplementary information:Supplementary data are available at Bioinformatics online.

The somatic mutations in the pathways that drive cancer development tend to be mutually exclusive across tumors, providing a signal for distinguishing driver mutations from a larger number of random passenger mutations. This mutual exclusivity signal can be confounded by high and highly variable mutation rates across a cohort of samples. Current statistical tests for exclusivity that incorporate both per-gene and per-sample mutational frequencies are computationally expensive and have limited precision. We formulate a weighted exact test for assessing the significance of mutational exclusivity in an arbitrary number of mutational events. Our test conditions on the number of samples with a mutation as well as per-event, per-sample mutation probabilities. We provide a recursive formula to compute $p$-values for the weighted test exactly as well as a highly accurate and efficient saddlepoint approximation of the test. We use our test to approximate a commonly used permutation test for exclusivity that conditions on per-event, per-sample mutation frequencies. However, our test is more efficient and it recovers more significant results than the permutation test. We use our Weighted Exclusivity Test (WExT) software to analyze hundreds of colorectal and endometrial samples from The Cancer Genome Atlas, which are two cancer types that often have extremely high mutation rates. On both cancer types, the weighted test identifies sets of mutually exclusive mutations in cancer genes with fewer false positives than earlier approaches.

Motivation: The three-dimensional structure of the genome is an important regulator of many cellular processes including differentiation and gene regulation. Recently, technologies such as Hi-C that combine proximity ligation with high-throughput sequencing have revealed domains of self-interacting chromatin, called topologically associating domains (TADs), in many organisms. Current methods for identifying TADs using Hi-C data assume that TADs are non-overlapping, despite evidence for a nested structure in which TADs and sub-TADs form a complex hierarchy. Results: We introduce a model for decomposition of contact frequencies into a hierarchy of nested TADs. This model is based on empirical distributions of contact frequencies within TADs, where positions that are far apart have a greater enrichment of contacts than positions that are close together. We find that the increase in contact enrichment with distance is stronger for the inner TAD than for the outer TAD in a TAD/sub-TAD pair. Using this model, we develop the TADtree algorithm for detecting hierarchies of nested TADs. TADtree compares favorably with previous methods, finding TADs with a greater enrichment of chromatin marks such as CTCF at their boundaries. Availability and implementation: A python implementation of TADtree is available at http://compbio.cs.brown.edu/software/ Contact:braphael@cs.brown.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Cancer is a heterogeneous disease with different combinations of genetic alterations driving its development in different individuals. We introduce CoMEt, an algorithm to identify combinations of alterations that exhibit a pattern of mutual exclusivity across individuals, often observed for alterations in the same pathway. CoMEt includes an exact statistical test for mutual exclusivity and techniques to perform simultaneous analysis of multiple sets of mutually exclusive and subtype-specific alterations. We demonstrate that CoMEt outperforms existing approaches on simulated and real data. We apply CoMEt to five different cancer types, identifying both known cancer genes and pathways, and novel putative cancer genes.

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. The identification of genetic variants associated with survival time is crucial in genomic studies. To this end, a number of methods have been proposed to computing a p-value that summarized the difference in survival time of two or more population. The most widely used method among these is the log-rank test. Widely used implementations of the log-rank test present a systematic error that emerges in most genome-wide applications, where the two populations have very different sizes, and the accurate computation of very small p-values is required due to the evaluation of a number of candidate variants. Considering cancer genomic applications, we show that the systematic error leads to many false positive associations of somatic variants and survival time. We present and analyze a new algorithm, ExaLT that accurately computes the p-value for the log-rank test under a distribution that is appropriate for the parameters found in genomics. Unlike previous approaches, ExaLT allows to control the accuracy of the computation. We use ExaLT to analyze cancer genomics data from The Cancer Genome Atlas (TCGA), identifying several novel associations in addition to well known associations. In contrast, the standard implementations of the log-rank test report a huge number of presumably false positive associations.