1.1 Time-to-event data
A survival study needs three things to be defined clearly:
- a time origin, the moment from which time is measured: the date of diagnosis, of randomisation in a trial, of installation of a machine, of birth;
- an event, sometimes called a failure: death, relapse, breakdown, finding a job;
- a time scale: days, months, years, or another measure such as hours of operation or kilometres driven.
The survival time \(T\) of a subject is the time from the origin to the event. It is a non-negative random variable, usually with a skewed distribution: many subjects have short times and a few very long ones, so the normal distribution is rarely appropriate.
Example 1.1.1. The lung data in R come from a study of \(228\) patients with advanced lung cancer by the North Central Cancer Treatment Group. For each patient we know the number of days from enrolment to death or to the end of follow-up, whether the patient died, and covariates such as age, sex and a performance score measuring how well the patient could carry out ordinary tasks. Of the \(228\) patients, \(165\) died during the study and \(63\) were still alive when they were last seen (Software 1.5.1).
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