Example

In Table 2, we quantify the potential gains in life expectancy that would arise from deleting external injuries as a cause of death. As explained above, we do this by assuming that the cause-specific force of mortality in the age interval is constant. This assumption is almost certainly violated, but its effect on the estimated gains in life expectancy will be small, and would have been negligible if we did these calculations for a complete life table. The construction of a cause-deleted life table is fairly straightforward once the (cause-deleted) conditional probabilities of dying have been computed.

interaction We have highlighted some of the cells. You can hover over these cells to reveal their computation.

Table 2: all cause and cause-deleted (external injuries) for Japanese male (1960-65)

age   m l e m-e *q-e *l-e *L-e *T-e *e-e
0 0.026648 100000 66.89 0.025793 0.025463 100000 97745 6886181 68.86
1 0.001881 97396 67.67 0.001113 0.004442 97454 388796 6788437 69.66
5 0.000811 96667 64.17 0.000423 0.002113 97021 484578 6399640 65.96
10 0.000528 96276 59.42 0.000332 0.001659 96816 483669 5915062 61.1
15 0.001069 96022 54.57 0.000459 0.002292 96655 482724 5431393 56.19
20 0.001719 95510 49.85 0.000617 0.003080 96434 481425 4948669 51.32
25 0.001885 94693 45.26 0.000854 0.004261 96137 479655 4467245 46.47
30 0.002138 93804 40.66 0.001253 0.006245 95727 477142 3987590 41.66
35 0.002762 92807 36.08 0.001901 0.009460 95129 473394 3510448 36.9
40 0.003875 91534 31.54 0.002968 0.014730 94229 467668 3037054 32.23
45 0.005927 89778 27.11 0.004924 0.024319 92841 458539 2569385 27.68
50 0.009402 87156 22.85 0.008306 0.040679 90583 443641 2110847 23.3
55 0.015612 83154 18.83 0.014357 0.069269 86898 419264 1667206 19.19
60 0.025263 76910 15.16 0.023811 0.112241 80879 381250 1247942 15.43
65 0.040917 67783 11.87 0.039235 0.178132 71801 325986 866692 12.07
70 0.067231 55242 9.02 0.065213 0.278242 59011 251780 540706 9.16
75 0.108987 39471 6.68 0.10634 0.412395 42592 165174 288926 6.78
80 0.171976 22889 4.87 0.168451 0.569262 25027 84576 123752 4.94
85 0.253875 9687 3.58 0.249526 0.712815 10780 30795 39175 3.63
90 0.357028 2722 2.67 0.351113 0.827190 3096 7294 8380 2.71
95 0.484303 457 2.03 0.476771 0.907806 535 1019 1086 2.03
100 0.612209 41 1.62 0.599333 1.000000 49 68 68 1.37

There is one statistic that interests us most from this exercise, namely the number of life-years gained from deleting external injuries. This can be computed as the difference between the all-cause life expectancy (e0) at birth and the cause-deleted life expectancy (*e0-e): 68.86 - 66.89=1.97 years. In other words, Japanese men would have live about 2 years longer if fatal external injuries could be avoided.

1 - exp ( - 5 * 0.000423 )
= ( 96655 - 96434) / 0.000459