Introductory Biostatistics

to obtainSS^ðtÞ, multiply all values in column (4) up to and includingt. From
Table 11.1, we have, for example:

7-week survival rate is 80:67%

22-week survival rate is 53:78%

and a 95% confidence interval forSð 7 Þis (.6531, .9964).
Note:An SAS program would include these instructions:

PROC LIFETEST METHOD = KM;

TIME WEEKS*RELAPSE(0);

where WEEKS is the variable name for duration time, RELAPSE the variable
name for survival status, ‘‘0’’ is the coding for censoring, and KM stands for
the Kaplan–Meier method.

11.2.2 Comparison of Survival Distributions

Suppose that there aren 1 andn 2 subjects, corresponding to treatment groups 1
and 2, respectively. The study provides two samples of survival data:

fðt 1 i;d 1 iÞg i¼ 1 ; 2 ;...;n 1

and

fðt 2 j;d 2 jÞg j¼ 1 ; 2 ;...;n 2

In the presence of censored observations, tests of significance can be con-
structed as follows:

TABLE 11.1

(1) (2) (3) (4) (5)

ti ni di 1 
di
ni
SS^ðtiÞ

6 21 3 0.8571 0.8571
7 17 1 0.9412 0.8067
10 15 1 0.9333 0.7529
13 12 1 0.9167 0.6902
16 11 1 0.9091 0.6275
22 7 1 0.8571 0.5378
23 6 1 0.8333 0.4482

386 ANALYSIS OF SURVIVAL DATA