The Cumulative Survival probability, in Column H, is the probability of surviving from the start

date through to the end of the interval. It has no units, and it can be expressed as a fraction or as a

percentage. The value for any time slice applies to the moment in time at the end of the interval.

The cumulative survival probability is always 1.0 (or 100 percent) at time 0, whenever you

designate that time 0 is (in the example, date of surgery), but it’s not included in the table.

The cumulative survival function decreases only at the end of an interval that has at least one

observed death, because censored observations don’t cause a decrease in the estimated survival.

Censored observations however influence the size of the decreases when subsequent events occur.

This is because censoring reduces the number at risk, which is used in the denominator in the

calculation of the death and survival probabilities.

If an interval contains no events and no censoring, like in the 1–2 years row in the table in Figure

21-4, it has no impact on the calculations. Notice how all subsequent values for Column B and for

Columns E through H would remain identical if that row were removed.

Graphing hazard rates and survival probabilities from a life table

Graphs of hazard rates and cumulative survival probabilities (Columns F and H from Figure 21-4,

respectively) can be prepared from life-table results using Microsoft Excel or another spreadsheet or

statistical program with graphing capabilities. Figure 21-5 illustrates the way these results are

typically presented.

Figure 21-5a is a graph of hazard rates. Hazard rates are often graphed as bar charts, because

each time slice has its own hazard rate in a life table.

Figure 21-5b is a graph of cumulative survival probabilities, also known as the survival

function. Survival values are usually graphed as stepped line charts, 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.

© John Wiley & Sons, Inc.

FIGURE 21-5: Hazard function (a) and survival function (b) results from life-table calculations.