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

$C{P}_{a-x}=P_a\cdot P_{a+1}\cdots P_x$

Relative Survival

$C{P}_{a-x}^{\ast }=\frac{1}{L_a}\sum _{i=1}^{L_a}({\tilde{P}}_a\cdot {\tilde{P}}_{a+1}\cdots {\tilde{P}}_x)i$

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

$C{R}_{a-x}=\frac{C{P}_{a-x}}{C{P}_{a-x}^{\ast }}$

$SC{R}_{a-x}=C{R}_{a-x}\sqrt{\sum _{j=a}^x\frac{D_j}{L_j^{\ast }(L_j^{\ast }-D_j)}}$