**Algorithms for Special Intervals/Conditional Survival**

Special intervals and conditional survival intervals are sets of the regular intervals. Each special interval range has a beginning interval (a) and an ending interval (x). We use the term "special interval" when the range begins at interval 1, and "conditional survival interval" otherwise. The special interval/conditional survival interval information, which is displayed at the bottom of each output survival table and can be included in Summary tables, can be divided into an Observed Survival and Relative Survival.

**Observed Survival**

**Relative Survival**

where the sum is over all persons entering interval "a" alive.