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Algorithms for Conditional Survival


Conditional survival intervals are sets of the regular intervals. Each interval range has a beginning interval (a) and an ending interval (x). The 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

\({\Large CP_{a - x} = P_a \cdot P_{a+1} \cdots P_x}\)


Relative Survival

\( {\Large CP^\ast_{a - x} = \frac{1}{L_a}\sum_{i=1}^{L_a}\left(\widetilde{P}_a \cdot \widetilde{P}_{a +1} \cdots \widetilde{P}_x\right)i}\)

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

\( {\Large CR_{a - x} = \frac{CP_{a - x}}{CP^\ast_{a - x}}}\)

\(\Large SCR_{a - x} = CR_{a - x} \sqrt{\sum_{j=a}^{x}\frac{D_j}{L^\ast_j\left(L^\ast_j - D_j \right)}}\)