CHAPTER 21 Summarizing and Graphing Survival Data 307

Looking at the Life-Table Method

To estimate survival and hazard rates in a population from a set of observed sur-

vival times, some of which are censored, you must combine the information from

censored and uncensored observations 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 sur-

vival probabilities together. For example, to survive three years, first the partici-

pant 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 calcula-

tions 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, quar-

ters, 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.