Survival analysis and Cox regression

Abstract

The data provided by clinical trials are often expressed in terms of survival. The analysis of survival comprises a series of statistical analytical techniques in which the measurements analysed represent the time elapsed between a given exposure and the outcome of a certain event. Despite the name of these techniques, the outcome in question does not necessarily have to be either survival or death, and may be healing versus no healing, relief versus pain, complication versus no complication, relapse versus no relapse, etc. The present article describes the analysis of survival from both a descriptive perspective, based on the Kaplan-Meier estimation method, and in terms of bivariate comparisons using the log-rank statistic. Likewise, a description is provided of the Cox regression models for the study of risk factors or covariables associated to the probability of survival. These models are defined in both simple and multiple forms, and a description is provided of how they are calculated and how the postulates for application are checked - accompanied by illustrating examples with the shareware application R.