Introduction to Survival Analysis

Survival analysis is concerned with analyzing time-to-event data where the event of interest usually represents some type of “failure”. In clinical medicine, the event of interest may be e.g. death of a patient from well specified causes, autoimmune rejection of the graft by the transplant recipient or other type of graft failure in transplant studies. In certain situations, however, the true survival outcomes may not be observable, because we have observed a so called “censoring event” which prevented the event of interest from occurring. Such censoring event may represent, for instance, loss of a particular subject from follow-up, occurrence of administrative censoring, which typically takes place in clinical trials, or we may indeed observe other type of “failure”, e.g. death from fatal injuries rather than from cardiovascular causes which were of primary interest in a particular clinical trial. In this article we will stress the importance of a key assumption relating censoring process to survival outcomes and review principle univariate survival analysis methods for uncorrelated data. We will review popular models for analyzing univariate survival data, many of which enable us quantifying effect the prognostic variables independently exert on survival outcomes. Model examples will cover the classes of non-parametric, parametric and semi-parametric methods. We will also review underlying assumptions of individual models and stress the importance of using appropriate models in analyzing univariate time-to-event data