Basic Statistics

204 INTRODUCTION TO SURVIVAL ANALYSIS

Start of Observation

lost to follow-up

k-

Yr; alive

Year

Figure 14.2 Time to event with all patients starting at time 0

methods given in previous chapters and simply ignore the lost or withdrawn patients,
our results will be biased. These methods should not be used.
In Section 14.2 we present definitions and graphical descriptions of survival data.

14.2 SURVIVAL FUNCTIONS

In Section 4.2 we discussed displaying continuous data with histograms and distri-
bution curves. We also gave instructions for computing cumulative frequencies and
displaying the data given in Table 4.5. An example of a cumulative percent plot for
the normal distribution was given in Figure 6.1 1. In this section we present graphical
displays similar to those in Sections 4.2 and 6.1 and also present two somewhat dif-
ferent graphs commonly used in survival analysis. To simplify the presentation, we
initially ignore the topic of censored data.

14.2.1 The Death Density Function

We can imagine having data from a large number of patients who have died so that
a histogram of the time to death could be made with very narrow class intervals. A
frequency polygon could then be constructed similar to that given in Figure 4.3. The
vertical scale of the frequency polygon can be adjusted so that the total area under the
distribution curve is 1. Note that the total area under other distributions such as the
normal distribution is also 1. When we are plotting time to an event such as death,
this curve is called the death density function. An example of a death density function
is given in Figure 14.3, where the times until death range from 0 to approximately
3 years. The total area under the curve is 1. The death density function is helpful in
assessing the peak time of death. Also, the shape of the death density function is often