The R Book, 3rd Edition

15Survival Analysis

A great many studies in statistics deal with deaths or with failures of components: they involve the numbers of deaths, the timing of death, or the risks of death to which different classes of individuals are exposed. The analysis of survival data is a major focus of the statistics business (see Kalbfleisch and Prentice, 2002; Miller et al., 1998; Fleming and Harrington, 2011), for which supports a wide range of tools. The main theme of this chapter is the analysis of data that take the form of measurements of the time to death, or the time to failure of a component. Up to now, we have dealt with mortality data by considering the proportion of individuals that were dead at a given time. In this chapter, each individual is followed until it dies, then the time of death is recorded (this will be the response variable). Individuals that survive to the end of the experiment will die at an unknown time in the future; they are said to be censored (as explained below).

15.1 Handling survival data

Since everything dies eventually, it is often not interesting to analyse the results of survival experiments in terms of the proportion that were killed; in due course, they all die. We'll use the package survival (Therneau and Grambsch, 2000) to handle survival analyses in this chapter which offers a range of functions for graphical representations, hypothesis testing, ...