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12.8 SURVIVAL ANALYSIS 651
technique, of which the Kaplan–Meier procedure is one. Nonparametric techniques are
defined and discussed in detail in Chapter 13.
Calculations for the Kaplan–Meier Procedure
n =
p 1 =
p 2 =
We let
the number of subjects whose survival times are available
the proportion of subjects surviving at least the first time period
(day, month, year, etc.)
the proportion of subjects surviving the second time period
after having survived the first time period
p 3 = the proportion of subjects surviving the third time period
after having survived the second time period
.
p k = the proportion of subjects surviving the kth time period
after having survived the 1k - 12th time period
We use these proportions, which we may relabel pN 1 , pN 2 , pN 3 , . . . , pN k as estimates of
the probability that a subject from the population represented by the sample will survive
time periods 1, 2, 3, . . . , k, respectively.
For any time period, t11 … t … k2, we estimate the probability of surviving the
tth time period, p t , as follows:
pN t =
number of subjects surviving at least 1t - 12 time periods
who also survive the tth period
number of subjects alive at end of time period 1t - 12
(12.8.1)
The probability of surviving to time t, S1t2, is estimated by
S N 1t2 = pN 1 * pN 2 * . . . * pN t
(12.8.2)
We illustrate the use of the Kaplan–Meier procedure with the following example.
EXAMPLE 12.8.1
To assess results and identify predictors of survival, Martini et al. (A-23) reviewed
their total experience with primary malignant tumors of the sternum. They classified
patients as having either low-grade (25 patients) or high-grade (14 patients) tumors.
The event (status), time to event (months), and tumor grade for each patient are shown
in Table 12.8.1. We wish to compare the 5-year survival experience of these two groups
by means of the Kaplan–Meier procedure.
Solution: The data arrangement and necessary calculations are shown in Table 12.8.2.
The entries for the table are obtained as follows.
1. We begin by listing the observed times in order from smallest to largest
in Column 1.