title: Accurate computation of survival statistics in genome-wide studies.
abstract: 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.
authors.affiliation: Department of Mathematics and Computer Science, University of Southern Denmark, Funen, Denmark; Department of Computer Science, Brown University, Providence, Rhode Island, United States of America; Center for Computational Molecular Biology, Brown University, Providence, Rhode Island, United States of America.
authors.forename: Fabio
authors.initials: F
authors.lastname: Vandin
authors.affiliation: Department of Computer Science, Brown University, Providence, Rhode Island, United States of America; Center for Computational Molecular Biology, Brown University, Providence, Rhode Island, United States of America.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Papoutsaki
authors.affiliation: Department of Computer Science, Brown University, Providence, Rhode Island, United States of America; Center for Computational Molecular Biology, Brown University, Providence, Rhode Island, United States of America.
authors.forename: Benjamin J
authors.initials: BJ
authors.lastname: Raphael
authors.affiliation: Department of Computer Science, Brown University, Providence, Rhode Island, United States of America.
authors.forename: Eli
authors.initials: E
authors.lastname: Upfal
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D030541:Databases, Genetic / Q000706:statistics & numerical data; D005260:Female; D014644:Genetic Variation; D055106:Genome-Wide Association Study / Q000706:statistics & numerical data*; D023281:Genomics / Q000706:statistics & numerical data; D059014:High-Throughput Nucleotide Sequencing / Q000706:statistics & numerical data; D006801:Humans; D008297:Male; D015233:Models, Statistical; D009154:Mutation; D009369:Neoplasms / Q000235:genetics / Q000401:mortality; D016019:Survival Analysis