Basic Statistics

202 INTRODUCTION TO SURVIVAL ANALYSIS

describe when each is useful. In Section 14.5 we briefly describe other analyzes
performed using survival analysis.

14.1 SURVIVAL ANALYSIS DATA

14.1.1 Describing Time to an Event

In order to determine the time until an event, we need to define both a starting and
an ending time. It is the starting time that usually presents more difficulties. Ideally,
we want the starting time for all patients in the study to be the same in terms of
their course of diseuse. If the starting time for patient A is early in the course of the
disease due to a sensitive screening program and if, for patient B, the starting time is
after the patient has had the disease for a long time and after treatment is in progress,
then obviously their starting times are not comparable. With data of this type, the
results are difficult if not impossible to evaluate. Both in planning a study and in
reporting the results, a clear statement of starting times is essential.
The event defining the end of the length of time is usually better known. Death
certificates and hospital records provide clear statements of time of death. Precise
time to an event such as remission may be more difficult to obtain, for even the patient
may be somewhat unsure when it has occurred. Usually, however, the event is clearly
defined and its time accurately known.
For small samples, the time until an event occurs can be determined by counting
the number of days or whatever unit of time is used from the starting time to the ending
time for each patient by hand. But for large samples, especially when the time periods
are long, computer programs are generally used. Statistical programs that compute
the length of time from starting to ending dates and also perform the analysis are
ideal. For example, Stata converts dates to times so that the duration between two
dates can be obtained. When this option is not available, some of the more complete
spreadsheet programs will compute time periods between dates and the time periods
can then be entered into statistical programs. Alternatively, the calculations can be
performed using the options in the spreadsheet program.

14.1.2 Example of Measuring Time to an Event

We begin with a small hypothetical study to show how time to an event is measured.
In this example, the event is death. In a typical survival study, the study starts at
a particular point in time. Here, it will be assumed that the study starts enrolling
patients at the beginning of 1995. Baseline data are collected on each patient at the
time of enrollment. Then, treatment and follow-up start and information is collected
on the status of each patient. The study continues until terminated at the beginning
of 2003. Between 1995 and 2003, the starting time when each patient enters the
study is considered to be when his or her disease condition is diagnosed. Note that
researchers seldom have a large enough sample of patients immediately available and
need to enter patients over time.