Basic Statistics

SURVIVAL ANALYSIS DATA 203

Start of Study End of Study

(^4) lost
to follow-up
withdrawn alive
5

• Year
  1995 2000 2003

Figure 14.1 Example of measuring time to an event for five patients.

Patients also leave the study. This can occur because the patient died or was lost
to follow-up or perhaps because the patient deliberately left the study. Some patients
are not followed until death because the study ends in 2003.
Typical examples for five patients are shown in Figure 14.1 to illustrate these
possibilities. Patient 1 started in 1995 and died 2years later. Patient 2 entered in
1996 and died 3 years later. Patient 3 entered in 2001 and died 1 year later. Patient
4 entered in 1999 and was lost to follow-up after 2.5 years. At the time of the end of
the study, it was not known what happened to this patient. Patient 5 entered in 1997
and was still alive at the end of the study. When this happens to a patient, the patient
is said to be withdrawn alive.
The same data are shown in Figure 14.2 using the start of observation for each
patient as the starting point. Here the results are shown as if all the patients entered at
the same time. In pretending that all the patients entered at the same time, we assume
that there were no changes over time either in the treatment or in the type of patient
enrolled that would affect the time to death. Note that in Figure 14.2 it is easier to
compare the times to an event than in Figure 14.1.
In this example, the known dead are three. Further, we know that patient 4 lived
at least 2.5 years and that patient 5 lived at least 6 years. These last two patients’
observations are said to be censored. With censored data we know something about
the survival time but we do not know the actual survival time.
One reason for examining the survival data from the five patients was to see why
survival analysis is different from the methods already covered in this book for con-
tinuous (interval or ratio) data. If we have measurements of data such as heights, we
do not have censored observations. Survival analysis enables us to use all the avail-
able data, including the data on the patients who were lost to follow-up or withdrawn
due to the study ending but whose actual time of death is unknown. If we use the