Applied Statistics Using SPSS, STATISTICA, MATLAB and R

362 9 Survival Analysis
A: The Heart Valve Survival datasheet contains the computed final date
for the study (variable DATE_STOP). This is the date of the first occurring event,
if it did occur, or otherwise, the last date the patient was known to be alive and
well. The survivor function estimate shown in Figure 9.4 is obtained by using
STATISTICA with DATE_OP and DATE_STOP as initial and final dates, and
variable EVENT as censored data indicator. From this figure, one can estimate that
about 85% of patients survive five years (1825 days) without any event occurring.
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
S(t)
Complete Censored
t (days)
0 1000 2000 3000 4000 5000 6000 7000 8000
Figure 9.4. Kaplan-Meier estimate of the survivor function for the event-free
survival of patients with heart valve implant, obtained with STATISTICA.
9.2.3 Statistics for Non-Parametric Analysis
The following statistics are often needed when analysing survival data:
1. Confidence intervals for S(t).
For the Kaplan-Meier estimate, the confidence interval is computed assuming that
the estimate Sˆ ( t)
is normally distributed (say for a number of intervals above 30),
with mean S(t) and standard error given by the Greenwood’s formula:
[ Sˆ
( t)
]
2
ˆ ⎪⎧
k d j ⎪⎫
s ≈ S(
t)
⎨∑
j=
1 ⎬ , for tk ≤ t < tk+1. 9.13
⎪⎩
n j ( n j − d j ) ⎪⎭