Genome-Wide Survival Analysis of Somatic Mutations in Cancer

Deriving clinical utility from large genomic datasets requires the identification of statistically significant associations between genomic measurements and a clinical phenotype. An important instance of this problem is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. The most widely used statistical test for comparing the survival time of two (or more) classes of samples is the nonparametric log-rank test. Nearly all implementations of the log-rank test rely on the asymptotic normality of the test statistic. However, this approximation gives poor results in many high-throughput genomics applications where: (i) the populations are unbalanced; i.e. the population containing a given variant is significantly smaller than the population without that variant; (ii) one tests many possible variants and is interested in those variants with very small p-values that remain significant after multi-hypothesis correction. Our contributions are: (1) We show empirically that the inaccuracy of the asymptotic approximation for the log-rank test results in a large number of false positives in cancer genomics applications due to unbalanced populations, and that among the two exact distributions (permutational and conditional) proposed in the literature, the permutational distribution provides a more accurate approximation of the true p-values. (2) We develop and analyze a novel fully polynomial time approximation scheme (FPTAS) for computing the p-value of the log-rank statistic for any range of population sizes under the exact permutational distribution. (3) We demonstrate the practicality and accuracy of our approach by testing the algorithm on somatic mutation data from The Cancer Genome Atlas (TCGA).