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 censoring 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 produce 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 worksheet shown in Figure 22-4, but with a

few differences in the raw data cells and minor differences in the calculations:

Instead of a column identifying the time slices, there are two columns identifying the individual

participant (Column A) and their survival or censoring time (Column B). The table is ordered from

the shortest time to the longest.

Instead of two columns containing the number who died and were censored in each interval, you

need only one column indicating whether or not the participant in that row died (Column C). If they

died during the observation period, use code 1, and if not and they were censored, use code 0.

These changes mean that Column D labeled Alive at Start now decreases by 1 for each subsequent

row.

The At Risk column in Figure 21-4 isn’t needed, because it can be calculated from the Alive at

Start column. That’s because if the participant is censored, the probability of dying is calculated as

0, regardless of the value of the denominator.

To calculate Column E, the Probability of Dying, divide the Died indicator by the number of

participants alive for that time period in Column D, Alive at Start. Formula: E = C/D.

The probability of surviving (Column F) and the cumulative survival (Column G) are calculated

the same way as in the life-table method.