CHAPTER 21 Summarizing and Graphing Survival Data 313

where a horizontal line represents the cumulative survival probability during

each time slice. The cumulative survival for the Year 0 to 1 time slice is 1.0

(100 percent), so the horizontal line stays at y = 1.0. But between Year 1 and

Year 3, the cumulative survival probability drops to 0.895, so a vertical line is

dropped from 1.0 to y = 0.895 at the time the Year 1 to Year 2 interval starts.

It goes across both that interval and the next one because there are no deaths

in these intervals. This stepped line continues downstairs and finally ends at

the end of the last interval where the cumulative survival probability is 0.128.

Digging Deeper with the

Kaplan-Meier Method

Using very narrow time slices doesn’t hurt life-table calculations. In fact, you can

define slices so narrow that each participant’s survival time falls within its own

private little slice. Imagine you had N participants. Your life table would have N

rows with data from one participant each. You could theoretically add all rest of

the rows to fill out the rest of the time slices. These would not have any data in

them, and since empty rows don’t affect the life-table calculations, you could just

stick with your life table where each row has one participant’s data. And if you

happen to have two or more participants with exactly the same survival or censor-

ing time, it’s okay to put each one in their own row.

The life-table calculations work fine with only one participant per row and pro-

duce what’s called Kaplan-Meier (K-M) survival estimates. You can think of the K-M

method as a very fine-grained life table. Or, you can see a life table as a grouped

K-M calculation.

A K-M worksheet for the survival times is shown in Figure 21-6. It is based on the

one-participant-per-row idea and is laid out much like the usual life-table

FIGURE 21-5:

Hazard function

(a) and survival

function (b)

results from

life-table

calculations.

© John Wiley & Sons, Inc.