COMPUTING ESTIMATES OF f(t), S(t), AND h(t)^209Meier method does not require the data to be grouped. These two descriptive methods
are often used to obtain graphs of survival data.14.3.1 Clinical LifeTablesWe now demonstrate the method for computing clinical life tables using the data
presented in Table 14.1. The data in Table 14.1 are a sample taken from the same
distribution as that used to draw Figures 14.3-14.6; the distribution is called a Weibull
distribution, a distribution widely used in survival analysis.
The sample size is 40. In the first column of Table 14.1 are listed the patient
numbers. In the second column are listed the known days the patients lived after
entering the study. In the third column, the last known status of the patient is given.
This same pattern is repeated in the next two sets of three columns. The last known
status has been coded 1 if the patient died, 2 if the patient was lost to follow-up, or 3
if the patient was withdrawn alive. For example, patient 1 died at 21 days and patient
5 was lost to follow-up at 141 days. Patients 20 and 37 were withdrawn alive.
In making a clinical life table, we must first decide on the number of intervals we
want to display. With too many intervals, each has very few individuals in it, and
with too few intervals, we lose information due to the coarse grouping.
Here we choose intervals of .5 year, which will result in five intervals. At the start
of the first interval, 40 patients are entered in the study. The first interval goes from 1
to 182 days or up to .5 year and is written as .O to < .5 year. In computing clinical life
tables no distinction is made between lost or withdrawn; their sum will be labeled c for
censored. During the first interval eight patients die and one is censored (patient 5).
The second interval is .5 to < 1.0 year or 183-365 days. During this time period,
15 patients died (2 were lost and 1 was withdrawn alive or 3 censored). The next
interval is 1 .O to < 1.5 years and has 8 patients who die and 1 who was censored. The
next interval, 1.5 to 2.0, has 1 who died and 1 censored, and the last interval has 2
patients who died.
The results are summarized in Table 14.2. The first column describes the intervals;
note that the width of the interval is w = .5 year. The second column, labeled nent,
gives the number of patients entering each interval. The third column, labeled c,
includes a count of the patients who are censored. The fifth column lists the number
of patients who die in each interval and is labeled d. This set of columns displays the
information given in Table 14.1.
Before discussing the remaining columns of Table 14.2, we show how to compute
the number of patients entering each interval (nent). For the first interval it is the
sample size, here 40. For the second interval we begin with the Rent for the first
interval and subtract from it both the number dying and the number censored during
the first interval. That is, we take 40 - 1 - 8 = 31 starting the second interval. For
the start of the third interval, we take 31 - 3 - 15 = 13. The numbers entering
the fourth and fifth intervals are computed in the same fashion. In general, from the
second interval on, the number at the outset of the interval is the number available at
the outset of the previous interval minus the number who are censored or die during
the previous interval.