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.

Eight participants were alive at the start of Year 2, and zero were censored during Year 2. So all

eight participants continued to be at risk during Year 2.

Calculations continue in the same way for the remaining years.

Column F

Column F shows the Probability of Dying during each interval, assuming the participant has survived

up to the start of that interval. To calculate this, divide the Died column by the At Risk column. This

represents the fraction of those who were at risk of dying at the beginning of the interval who actually

died during the interval. Formula for Column F: F = C/E.

Here’s how this formula works in Figure 22-3:

For Year 1, the probability of dying is calculated by dividing the one death by the 9.5 participants

at risk: 1/9.5, or 0.105 (10.5 percent).

Zero participants died in Year 2. So, for participants surviving Year 1 and alive at the beginning of

Year 2, the probability of dying during Year 2 is 0. Woo-hoo!

Calculations continue in the same way for the remaining years.

Column G

Column G shows the Probability of Surviving during each interval for participants who have survived

up to the start of that interval. Since surviving means not dying, the equation for this column is 1 –

Probability of Dying, as indicated by the formula for Column G: G = 1 – F.

Here’s how this formula works out in Figure 22-3:

The probability of dying in Year 1 is 0.105, so the probability of surviving in Year 1 is 1 – 0.105,

or 0.895.

The probability of dying in Year 2 is 0.000, so the probability of surviving in Year 2 is 1 – 0.000,

or 1.000.

Calculations continue in the same way for the remaining years.

Column H