# Can somebody please explain where these numbers in survival analysis Life Tables come from?

Specifically, the Cumulative Proportion Surviving at the Time. I've tried reading elsewhere but can't seem to wrap my head around it.

The trick with this type of data format is to consider the number of cases still at risk just before each event time. Just before time = 2 there were 78 at risk, of whom 2 had events at time = 2. A fraction of 0.02564 (2/78) of those at risk had the event then. No one had the event previously, so a fraction of (1-0.02564) = 0.97436 survived past time = 2.
Just before time = 3 there were 72 still at risk. Of those, 1 had the event at time = 3, or a fraction 0.01389 of those still at risk then. A fraction (1-0.01389) = 0.98611 of those at risk just before time = 3 survived past that time. As a fraction 0.97436 of the original group was estimated to have survived past time = 2 up to just before time = 3, 0.97436 * 0.98611 = 0.96083 is the estimated fraction of the original group surviving past time = 3.