R Programming for Actuarial Science

20 The Kaplan-Meier Estimator

Peter McQuire

library(survival)

20.1 Introduction

In 1958 Edward Kaplan and Paul Meier published their paper “Nonparametric estimation from incomplete observations” which set out details of their famous non-parametric survival model. Their paper remains one of the most cited in medical survival research.

The objective of the model is to produce a non-parametric distribution of the survival function. An example of a typical survival function that may be obtained from a Kaplan-Meier (“K-M”) analysis is shown in Figure 20.1 (left); the plot shows the survival distribution obtained from a study of lung cancer patients, together with 95% confidence limits.

Figure 20.1 K-M survival function of lung cancer patients.

Based on the results from a K-M analysis we can make estimates about the probability that a life will survive for a period of time. For example, from Figure 20.1 (left) we may estimate that a patient, with a particular set of characteristics, has a 41% probability of surviving one year. We may also wish to compare the survival probabilities of two or more groups of lives, such as male/female, or where one group may have been administered with a recently developed medicine. Analysing two K-M curves can help us do this (see Figure 20.1 (right)). We will return to Figure 20.1 later in the chapter.

Remark 20.1 The simple plot function is used ...