properly. How is this done? Well, it’s not done by dividing the number of participants alive at a

certain time point in the study by the total number of participants in the study, because this fails to

account for censored observations.

Instead, think of the observation period in a study as a series of slices of time. Think about how each

time a participant survives a slice of time and encounters the next one, they have a certain probability

of surviving to the end of that slice and continuing on to encounter the next. The cumulative survival

probability can then be obtained by successively multiplying all these individual time-slice survival

probabilities together. For example, to survive three years, first the participant has to survive the first

slice (Year 1), then survive the second slice (Year 2), and then survive the third slice (Year 3). The

probability of surviving all three years is the product of the probabilities of surviving through Year 1,

Year 2, and Year 3.

These calculations can be laid out systematically in a life table, which is also called an actuarial life

table because of its early use by insurance companies. The calculations only involve addition,

subtraction, multiplication, and division, so they can be done manually. They are easy to set up in a

spreadsheet format, and there are many life-table templates available for Microsoft Excel and other

spreadsheet programs that you can use.

Making a life table

To create a life table from your survival data, you should first break the entire range of survival times

into convenient time slices. These can be months, quarters, or years, depending on the time scale of the

event you’re studying. Also, you have to consider the time increments in which you want to report your

results. You should arrange to have at least five slices or else your survival and hazard estimates will

be too coarse to show any useful features. Having many skinny slices doesn’t disturb the calculations,

but the life table will have many rows and may become unwieldy. For the survival times shown in

Figure 21-2, a natural choice would be to use seven 1-year time slices.

Next, count how many participants experienced the event during each slice, and how many were

censored, meaning they were last observed during this time slice and had not experienced the event.

From Figure 21-2, you see that

During the first year after surgery, one participant died (#1), and one participant was censored (#5,

who was LFU).

During the second year, no participants died or were censored.

During the third year, two participants died (#4 and #9), and none were censored.

Continue tabulating deaths and censored times for the fourth through seventh years, and enter these

counts into the appropriate cells of a spreadsheet like the one shown in Figure 21-3.