Column H shows the cumulative probability of surviving from the time of surgery all the way through

the end of this time slice. To survive from the start time through the end of any given year (year N), the

participant must survive each of the years from Year 1 through Year N. Because surviving each year is

an independent accomplishment, the probability of surviving all N of the years is the product of the

individual years’ probabilities. So Column H is a running product of Column G. In other words, the

value of Column H for Year N is the product of the first N values in Column G.

Here’s to fill in Figure 22-3 (with the results shown in Figure 22-4):

For Year 1, H is the same as G: a 0.895 probability of surviving one year.

For Year 2, H is the product of G for Year 1 times G for Year 2; that is, 0.895 × 1.000, or 0.895.

For Year 3, H is the product of the Gs for Years 1, 2, and 3; that is, 0.895 × 1.000 × 0.750, or

0.671.

Calculations continue in the same way for the remaining years.

Putting everything together

Figure 21-4 shows the spreadsheet with the results of all the preceding calculations.

© John Wiley & Sons, Inc.

FIGURE 21-4: Completed life table to analyze the survival times shown in Figure 22-2.

Interpreting a life table

Figure 21-4 contains the hazard rates (in Column F) and the cumulative survival probabilities

(in Column H) for each year following surgery, based on your sample of ten participants. Keep in

mind these life-table features:

The hazard and survival values obtained from this life table are estimates from a sample of the true

population hazard and survival functions (in this case, using one-year intervals).

The intervals are often the same size for all the rows in a life table like in the example, but they

don’t have to be. You may choose these on the basis of the probabilities in your data.

The hazard rate obtained from a life table for each time slice is equal to the Probability of Dying

(Column F) divided by the width of the slice. Therefore, the hazard rate for the first year would be

expressed as 0.105 per year, or 10.5 percent per year.