Supporting Text for “Accurate Computation of Survival Statistics in Genome-wide Studies”

Model Suppose a set G of genes was sequenced in a collection P of patients, all of whom have the same disease. Each sequenced gene2 g ∈ G partitions the set of patients into two subsets: the P(g), with patients with a mutation in g, and the P̄(g), with patients with no mutation in g. The goal is to identify genes whose mutational status is highly correlated with the survival time, in the sense that the survival distribution of patients in P(g) is different from the survival distribution of patients in P̄(g). A key challenge in survival analysis is dealing with censored patients whose exact survival time is unknown. Censoring occurs for a variety of reasons, but the most common is that the study only lasts for a finite amount of time, and some fraction of patients remain alive at the conclusion of the study. In addition, during the course of the study patients may leave the study for a variety of reasons, that are unrelated to their treatment or disease state. The censored survival time is the last time the patient was observed in the study, which is a lower bound for the patient’s survival time3. Survival analysis assumes that censoring is non informative, i.e. the event that a patient is censored is independent of the patient’s survival beyond the censoring time. The log-rank test [1] (or family of tests) is the most commonly used non-parametric test for comparing the survival distribution of two or more populations with data subject to censoring. The advantage of this test is that it includes the censored data in its statistic, rather then removing it from the data. Since a large fraction of patients may be censored (e.g., up to 94% in the data below), it is not desirable to remove this “missing data” from consideration. In the section below, we describe two different versions of the log-rank test, the conditional log-rank and the permutational log-rank test.