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Chapter 4 Part 7
Life
Table and Survival Analysis
Survival
Analysis is used to Analyze the survival experience of a group of persons or
components. In medical research, survival analysis is helpful is studying the
survival of patients under one or more conditions. In industry, the survival may
be that of a component such as an electronic switch or a gear.
To
perform a survival analysis, the data must be in the following form:
1)
a TIME variable which contains a time (e.g., minutes, days, years, etc.)
in which the subject or component has been observed to be alive (not failed).
2)
a CENSOR variable which must take on the values 0 or 1,
where 1 means the subject has died (failed), and a 0 means the subject
was still alive (not failed) at the last available time period.
3)
optionally, a GROUPING variable which may have up to ten values (numeric
or character), i.e., the data may be in groups.
WINKS
allows you to choose from two types of life tables, Actuarial or Kaplan-Meier.
The Actuarial method uses fixed length intervals in the table, and the
Kaplan-Meier table uses intervals based on the data. Once the data are entered
into the program, a life table for each group is produced which includes, for
each time interval, the number entered, withdrawn, lost, dead, exposed, the
proportion dead, proportion surviving, cumulative proportion surviving, and
other information.
A
plot is given for the cumulative proportion surviving in the group(s) against
time. If more than one group is entered, a Mantel-Haenszel log-rank test is
performed to test the hypothesis of equal survival patterns for the groups. A
reference to how this test is developed is covered in Matthews and Farewell
(1988).
Actuarial
Life table analysis - Actuarial
The
data for this example are in the LIFE.DBF database on the WINKS disk. These data
are from Prentice (1973). To perform this analysis, follow these steps:
Step
1: Open the
database named LIFE.DBF.
Step
2: From the
Analyze menu, choose “Life Tables and Survival Analysis” then select
"Actuarial Life Table Analysis".
Step
3: Select
SURVIVAL and CENSOR fields (in that order), then select
GROUP
as the Group field. A portion of the LIFE database is shown here:
SURVIVAL
CENSOR GROUP
72
1
1
411
1
1
228
1
1
11
1
1
25
0
1
etc...
The
first column is the SURVIVAL field with entries of length of life, or length of
survival. The second column is the CENSOR field, an indicator of whether the
subject has failed (died) or not at the last observed time period. 1 means
failed, 0 means not failed (still alive). The third column contains a grouping
variable. In this case it is either 1 or 2. Group 1 may represent one treatment,
while group 2 represents another kind of treatment. The objective is to compute
survival curves to see if the treatments provide different average survival
distributions.
Step
4: Specify a
desired interval length or you can use the default length by simply pressing
Enter. For this example, press Enter to select the default length.
Step 5: WINKS will perform the calculations and display the results in the viewer.
---------------------------------------------------------------------------
Life Table and Survival Analysis C:\WINKS46P\LIFE.DBF
---------------------------------------------------------------------------
Actuarial Table Analysis
SURVIVAL GROUP:0
Interval Enter With- Dead Exposed Prop. Cumulative S.E.
Alive drawn Dead Alive Survival
0.0 99.0 38 2 22 37.00 0.5946 0.405 1.0000 0.0000
99.0 198.0 14 0 4 14.00 0.2857 0.714 0.4054 0.0807
198.0 297.0 10 1 3 9.50 0.3158 0.684 0.2896 0.0756
297.0 396.0 6 0 2 6.00 0.3333 0.667 0.1981 0.0677
etc...
95% confidence limits
Interval Exposed Cumulative Lower Upper Hazard
Survival Bound Bound Function
0.0 99.0 37.0 1.000 1.000 1.000 0.009
99.0 198.0 14.0 0.405 0.247 0.564 0.003
198.0 297.0 9.5 0.290 0.141 0.438 0.004
etc...
Summary Table
Total Dead Withdrawn Percent Censored
--------------------------------------------------
38 35 3 7.89%
etc...
(Continues for Group 1)
Mantel-Haenszel comparison of survival curves
-------------------------------------------------------
Chi-Square = .7472 with 1 D.F appx p = 0.388
The
first table includes the numbers of subjects
entered alive, withdrawn, dead, exposed, the proportion dead, proportion alive,
cumulative survival proportion and standard error for the first group. The
second table includes 95% confidence limits on the cumulative survival
proportion
From
the table, you can see that, in the first group, 22 of 37 exposed, or 59.5% died
in the first interval (0.0-99.0) and two were withdrawn. In the second group, 12
of 23.5 exposed (51.1%) died and one was withdrawn in the first interval. At the
end of the report, WINKS reports the results of the Mantel-Haenszel comparison
of the two curves. The hypotheses being tested are:
