CHAPTER 21 Summarizing and Graphing Survival Data 309

Columns B, C, and D

Column B includes the number of participants known to be alive at the start of

each year after surgery. This is equal to the number of participants alive at the

start of the preceding year minus the number who died (Column C) or were

censored (Column D) during the preceding year. Here’s the formula, written in

terms of the column letters: B for any year = B – C – D from the preceding year.

Here’s how this process plays out in Figure 21-3:»

» ^{Out of the ten participants alive at the start, one died and one was last seen}

alive during the first year. This means eight participants (10 – 1 – 1) are

known to still be alive at the start of the second year. The missing partici-

pant is #5, who was LFU during the first year. They are censored and not

counted in any subsequent years.»

» ^{Zero participants died or were last seen alive during the second year. So, the}

same eight participants are still known to be alive at the start of the third year.»

» ^{Calculations continue the same way for the remaining years.}

Column E

Column E shows the number of participants at risk for dying during each year. You

may guess that this is the number of participants alive at the start of the interval,

but there’s one minor correction. If any were censored during that year, then

they weren’t technically able to be observed for the entire year. Though they may

die that year, if they are censored before then, the study will miss it. What if you

don’t know exactly when during that year they became censored? If you don’t

have the exact date, you can consider them being observed for half the time

period (in this case, 0.5 years). So the number at risk can be estimated as the

number alive at the start of the year, minus one-half of the number who became

censored during that year, as indicated by the formula for Column E: E = B – D/2.

(Note: To simplify the example, we are using years, but you could use months

instead if you have exact censoring and death dates in your data to improve the

accuracy of your analysis.)

Here’s how this formula works in Figure 21-3:»

» ^{Ten participants were alive at the start of Year 1, and one participant was}

censored during Year 1. To correct for censoring, divide 1 by 2, which is

0.5. Next, subtract 0.5 from 10 to get 9.5. After correcting for censoring, only

9.5 participants are at risk of dying during Year 1.