Example 37.2: Life Table Estimates for Males with Angina Pectoris
The data in this example come from Lee (1992, p. 91) and
represent the survival rate of males with angina pectoris.
Survival time is measured as years from the time of diagnosis.
The data are read as number of events and
number of withdrawals in each oneyear time interval for 16 intervals.
Three variables are constructed from the data: Years (an artificial
time variable with values that are the midpoints of the time intervals),
Censored (a censoring indicator variable with value 1
indicating censored
observations and value 0 indicating event observations), and
Freq (the
frequency variable).
Two observations are created for
each interval, one representing the event observations
and the other representing the censored observations.
title 'Survival of Males with Angina Pectoris';
data males;
keep Freq Years Censored;
retain Years .5;
input fail withdraw @@;
Years + 1;
Censored=0;
Freq=fail;
output;
Censored=1;
Freq=withdraw;
output;
datalines;
456 0 226 39 152 22 171 23 135 24 125 107
83 133 74 102 51 68 42 64 43 45 34 53
18 33 9 27 6 23 0 30
;
PROC LIFETEST is invoked to compute the various life table
survival estimates, the median residual time, and their standard errors.
The life table method of computing estimates is requested by specifying
METHOD=LT. The intervals are specified by the INTERVAL= option.
Graphs of the life table estimate, log of the estimate,
negative loglog of the estimate, estimated density function, and estimated
hazard function are requested by the PLOTS= option.
No tests for homogeneity are carried
out because the data are not stratified.
symbol1 c=blue;
proc lifetest data=males method=lt intervals=(0 to 15 by 1)
plots=(s,ls,lls,h,p);
time Years*Censored(1);
freq Freq;
run;
Output 37.2.1: Life Table Survival Estimates
Survival of Males with Angina Pectoris 
Life Table Survival Estimates 
Interval 
Number Failed 
Number Censored 
Effective Sample Size 
Conditional Probability of Failure 
Conditional Probability Standard Error 
Survival 
Failure 
Survival Standard Error 
Median Residual Lifetime 
Median Standard Error 
Evaluated at the Midpoint of the Interval 
[Lower, 
Upper) 
PDF 
PDF Standard Error 
Hazard 
Hazard Standard Error 
0 
1 
456 
0 
2418.0 
0.1886 
0.00796 
1.0000 
0 
0 
5.3313 
0.1749 
0.1886 
0.00796 
0.208219 
0.009698 
1 
2 
226 
39 
1942.5 
0.1163 
0.00728 
0.8114 
0.1886 
0.00796 
6.2499 
0.2001 
0.0944 
0.00598 
0.123531 
0.008201 
2 
3 
152 
22 
1686.0 
0.0902 
0.00698 
0.7170 
0.2830 
0.00918 
6.3432 
0.2361 
0.0646 
0.00507 
0.09441 
0.007649 
3 
4 
171 
23 
1511.5 
0.1131 
0.00815 
0.6524 
0.3476 
0.00973 
6.2262 
0.2361 
0.0738 
0.00543 
0.119916 
0.009154 
4 
5 
135 
24 
1317.0 
0.1025 
0.00836 
0.5786 
0.4214 
0.0101 
6.2185 
0.1853 
0.0593 
0.00495 
0.108043 
0.009285 
5 
6 
125 
107 
1116.5 
0.1120 
0.00944 
0.5193 
0.4807 
0.0103 
5.9077 
0.1806 
0.0581 
0.00503 
0.118596 
0.010589 
6 
7 
83 
133 
871.5 
0.0952 
0.00994 
0.4611 
0.5389 
0.0104 
5.5962 
0.1855 
0.0439 
0.00469 
0.1 
0.010963 
7 
8 
74 
102 
671.0 
0.1103 
0.0121 
0.4172 
0.5828 
0.0105 
5.1671 
0.2713 
0.0460 
0.00518 
0.116719 
0.013545 
8 
9 
51 
68 
512.0 
0.0996 
0.0132 
0.3712 
0.6288 
0.0106 
4.9421 
0.2763 
0.0370 
0.00502 
0.10483 
0.014659 
9 
10 
42 
64 
395.0 
0.1063 
0.0155 
0.3342 
0.6658 
0.0107 
4.8258 
0.4141 
0.0355 
0.00531 
0.112299 
0.017301 
10 
11 
43 
45 
298.5 
0.1441 
0.0203 
0.2987 
0.7013 
0.0109 
4.6888 
0.4183 
0.0430 
0.00627 
0.155235 
0.023602 
11 
12 
34 
53 
206.5 
0.1646 
0.0258 
0.2557 
0.7443 
0.0111 
. 
. 
0.0421 
0.00685 
0.17942 
0.030646 
12 
13 
18 
33 
129.5 
0.1390 
0.0304 
0.2136 
0.7864 
0.0114 
. 
. 
0.0297 
0.00668 
0.149378 
0.03511 
13 
14 
9 
27 
81.5 
0.1104 
0.0347 
0.1839 
0.8161 
0.0118 
. 
. 
0.0203 
0.00651 
0.116883 
0.038894 
14 
15 
6 
23 
47.5 
0.1263 
0.0482 
0.1636 
0.8364 
0.0123 
. 
. 
0.0207 
0.00804 
0.134831 
0.054919 
15 
. 
0 
30 
15.0 
0 
0 
0.1429 
0.8571 
0.0133 
. 
. 
. 
. 
. 
. 

Results of the life table estimation are shown in Output 37.2.1.
The fiveyear survival rate is 0.5193 with a standard error of 0.0103.
The estimated
median residual lifetime, which is 5.33 years initially, has reached
a maximum of 6.34 years at the beginning of the second year and decreases
gradually to a value lower than the initial 5.33 years at the beginning of
the seventh year.
Output 37.2.2: Summary of Censored and Event Observations
Summary of the Number of Censored and Uncensored Values 
Total 
Failed 
Censored 
Percent Censored 
2418 
1625 
793 
32.80 
NOTE: 
There were 2 observations with missing values, negative time values or frequency values less than 1. 


Output 37.2.2 shows the number of event and censored observations.
The percentage of the patients
that have withdrawn from the study is 32.8%.
Output 37.2.3: Life Table Survivor Function Estimate
Output 37.2.4: Log of Survivor Function Estimate
Output 37.2.5: Log of Negative Log of Survivor Function Estimate
Output 37.2.6: Hazard Function Estimate
Output 37.2.7: Density Function Estimate
Output 37.2.3 displays the graph of the life table survivor function
estimates versus years after diagnosis. The median survival time,
read from the survivor function curve, is
5.33 years, and the 25th and 75th percentiles are 1.04 and 11.13 years,
respectively.
As discussed in Lee (1992), the graph of the estimated hazard function
(Output 37.2.6) shows
that the death rate is highest in the first year of diagnosis. From
the end of the first year to the end of the tenth year, the death
rate remains relatively constant, fluctuating between 0.09 and 0.12.
The death rate is generally higher after the tenth year.
This could indicate
that a patient who has survived the first year has a
better chance than a patient who has just been diagnosed. The profile of
the median residual lifetimes also supports this interpretation.
An exponential model may be appropriate for the survival of these male
patients with angina pectoris since
the curve of the log of the survivor function estimate versus years of
diagnosis
(Output 37.2.4) approximates a straight line through the origin.
Visually,
the density estimate (Output 37.2.7) resembles that of an exponential
distribution.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.