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12.8 SURVIVAL ANALYSIS 649
(3) the condition of being alive at the time the investigator decides to terminate the
study.
For each patient in the study, the investigator records the amount of time (in
months, days, years, or some other measures of time) elapsing between the point at which
the patient entered the study and the point at which he or she experienced one of the
terminating events. The time elapsing between enrollment in the study and the experiencing
of one of the events is referred to as the patient’s survival time. The set of such
survival times recorded during the course of a study is referred to as survival data.
Suppose we have the following information on three of the patients in the study
involving heart-attack patients. Patient A entered the study on January 1, 2002, and had
a myocardial infarction on December 31, 2003. Patient A’s survival time is 24 months.
Patient B entered the study on July 1, 2002, and moved out of state on December 31,
2002. Patient B’s survival time is 6 months. Patient C entered the study on August 1,
2002, and was still alive when the study was terminated on December 31, 2004. Patient
C’s survival time is 29 months. The survival time for patient B is called a censored survival
time, since the terminating event was loss to follow-up rather than the event of
interest. Similarly, since the terminating event for patient C was being alive at the end
of the study, this patient’s survival time is also called a censored survival time. The survival
times for patient B and patient C are called censored data. The experiences of these
three patients may be represented graphically as shown in Figure 12.8.1.
Censored data can arise in a variety of ways. In singly censored data, a fixed number
of subjects enter into a study at the same time and remain in the study until one of
two things occur. First, at the conclusion of the study, not all of the subjects may have
experienced a given condition or endpoint of interest, and therefore their survival times are
not known exactly. This is called type I censoring. Second, the study may be ended after
a certain proportion of subjects have experienced a given condition. Those that did not
experience the condition would not have a known survival time. This is called type II censoring.
A third type of censoring leads to progressively censored data. In this type of censoring,
the period of the study is fixed, but subjects may enter the experiment at different
times. (For example, in a clinical study, patients can enter the study at any time after diagnosis.)
Patients may then experience, or not experience, a condition by the end of the study.
Those who did not experience the condition do not have known survival times. This is
called type III censoring. Clearly the details surrounding censored data are complex and
A
Patient
B
C
Jan.1
2002
July 1
2002
Jan. 1
2003
Jan. 1
2004
Dec. 31
2004
FIGURE 12.8.1 Patients entering a study at different times with
known ( )
and censored ( ) survival times.