Actuarial or Kaplan-Meier Analysis
Actuarial Analysis
Actuarial analysis uses life tables to determine the probability of an individual to survive a specific time interval. The table is arranged like the one below.
| i | ni | di | wi |
| 1 | n1 | d1 | w1 |
| 2 | n2 | ||
| … |
where i is the number of time intervals since the group entered the study, n is the number of individuals alive in the group at the beginning of the interval, di is the number of individuals that died during the interval, and wi is the number of individuals that were withdrawn alive from the study during the interval. Using these numbers, the probability of survival through the current interval for an individual in a given group can be calculated by
This probability is dependent upon the individual’s having survived all previous time intervals. In other words, it is a conditional probability where pi is the probability of survival given survival of previous intervals. By multiplying the conditional probability by the probability of surviving each previous interval, the cumulative probability of surviving a specific interval and all previous ones can be calculated by
The standard error of Si is
Kaplan-Meier Product Limit Method
This is a similar method that may be more appropriate for small sample sizes. The main difference is that time intervals are defined by the time at which one or more individuals dies. Therefore, the probability of surviving the current interval is
Cumulative probability of survival is
and standard error is
