DEMOGRAPHIC METHODSAbridged Life Table for the United States, 1996Exact Age x nDxnPxnqx (^) xndxnLx Tx ex
(in 1,000s)
0 28,487 3,769 .00732 100,000 732 99,370 7,611,825 76.1
1 5,948 16,516 .00151 99,268 150 396,721 7,512,455 75.7
5 3,780 19,441 .00097 99,118 96 495,329 7,115,734 71.8
10 4,550 18,981 .00118 99,022 117 494,883 6,620,405 66.9
15 14,663 18,662 .00390 98,905 386 493,650 6,125,522 61.9
20 17,780 17,560 .00506 98,519 499 491,372 5,631,872 57.2
25 20,730 19,007 .00544 98,020 533 488,766 5,140,500 52.4
30 30,417 21,361 .00710 97,487 692 485,746 4,651,734 47.7
35 42,499 22,577 .00944 96,795 914 481,820 4,165,988 43.0
40 53,534 20,816 .01283 95,881 1,230 476,549 3,684,168 38.4
45 67,032 18,436 .01801 94,651 1,705 469,305 3,207,619 33.9
50 77,297 13,934 .02733 92,946 2,540 458,779 2,738,314 29.5
55 96,726 11,362 .04177 90,406 3,776 443,132 2,279,535 25.2
60 136,999 9,999 .06649 86,630 5,760 419,530 1,836,403 21.2
65 200,045 9,892 .09663 80,870 7,814 385,659 1,416,873 17.5
70 273,849 8,778 .14556 73,056 10,634 339,620 1,031,214 14.1
75 321,223 6,873 .21060 62,422 13,146 280,047 691,594 11.1
80 342,067 4,557 .31754 49,276 15,647 207,474 411,547 8.4
85 576,541 3,762 1.00000 33,629 33,629 204,073 204,073 6.1
Table 3
SOURCE: nDx and nPx values are obtained from Peters, Kochanek, and Murphy 1998, and from the web site, http://www.cdc.gov/
nchswww/datawh/statab/unpubd/mortabs/pop6096.htm, respectively.
nMx =
nDx
nPx
( 3 )
For each death rate, we compute the correspond-
ing probability of dying within that age interval,
given that one has survived to the beginning of the
interval. This value, denoted by nqx, is computed
using the following equation:
nqx =
n^.^ nMx
1 + (n–nax). nMx
( 4 )
where nax is the average number of years lived by
those who die within the age interval x to x+n.
(Except for the first year of life, it is typically
assumed that deaths are uniformly distributed
within an age interval, implying that nax=n/2.)
Given the values of q and a, we are able to generate
the entire life table.
The life table may be thought of as a tracking
device, by which a cohort of individuals is followed
from the moment of their birth until the last
surviving individual dies. Under this interpreta-
tion, the various remaining columns are defined in
the following manner: lx equals the number of
individuals in the life table surviving to exact age x.
We arbitrarily set the number ‘‘born into’’ the life
table, lo, which is otherwise known as the radix, to
some value—most often, 100,000. We generate all
subsequent lx values by the following equation:
x+n = x. [1– nqx^ ] (^5 )
ndx equals the number of deaths experienced
by the life table cohort within the age interval x to
x+n. It is the product of the number of individuals
alive at exact age x and the conditional probability
of dying within the age interval:
ndx = x.^ nqx^ (^6 )
The concept of ‘‘person-years’’ is critical to
understanding life table construction. Each indi-
vidual who survives from one birthday to the next
contributes one additional person-year to those
tallied by the cohort to which that person belongs.
In the year in which the individual dies, the dece-
dent contributes some fraction of a person-year to
the overall number for that cohort.
nLx equals the total number of person-years
experienced by a cohort in the age interval, x to
x+n. It is the sum of person-years contributed by
those who have survived to the end of the interval