Life Table Construction
Life tables were prepared using the computer program Survival 5.0, written by
David P. Smith, University of Texas Houston Health Science Center, School of
Life tables are statistical tools which are typically used to portray the
expectation of life (ex) at various ages. Life expectancy at birth
(e0) is the most frequently cited life table statistic. However, life
tables also provide information on the numbers of individuals who survive to
various ages, median age at death, age-specific death rates, and the probability
of dying at certain ages.
Two approaches to life table construction can be taken: the generational
(cohort) life table and the current (period) life table.1 The
generational life table allows the researcher to follow a group of individuals
who were born during the same time period from birth through death in order to
profile their mortality experience. Changing environmental or technological
phenomena may influence mortality patterns through time; thus, a generational
life table approach will be sensitive to those changes.
Conversely, a current life table provides a cross-sectional 'snapshot' of a
population at a specific point of time. Individuals included in the current life
table may have been born as much as 100 years apart and experienced a wide
variety of life conditions. However, using this kind of life table we can
estimate the mortality experience of generations who are not yet dead. For
example, when we say that an infant born this year can expect to live 76 years,
we are estimating the infant's life span according to the mortality experience
of the current population. Infants born this year may actually live much longer
if future public health or medical advances reduce death rates. Life expectancy
at birth simply constitutes our best estimate of how long that infant might live
according to information we have at this moment. For purposes of this report,
the current life table is used.
There are several columns which make up both kinds of life tables. These are:
1) Age interval (x to x+n): the period of life between two exact ages.
2) For the estimated population value N0, the value is calculated
using live births, N(0), as N0 = N(0) - (infant deaths*0.85).
3) Proportion dying (nqx): the proportion of persons
alive at the beginning of each age interval who die before reaching the end of
the age interval. For infants, 1q1 is calculated as
D1 (infant deaths) / N(0) (unweighted live births).
The TDH life tables use the actual number of births in calculation
1q0, and weight cohort life tables values (specifically
Lx) to adjust for differences in the numbers of individuals dying at
any given time within a particular age cohort. Estimates of q0 were
found from annual births and deaths, to be consistent with the infant mortality
rates in other tables. At all other ages the estimated population was used to
find q0.2 For all other age cohorts the calculation is
nqx = (2n)(nmx) / 2 +
(n)(nmx) where n = the number of years within an age
interval and nmx = the age-specific death rate.
4) Number surviving (lx): number of persons living at the
beginning of each age interval.
l0 = 100,000; lx = lx-1 -
5) Number dying (ndx): number of persons dying during
the age interval.
ndx = lx *
6) The number of person-years lived in each age interval:
nLx = nxlx+1 + (dx*
ax) where nx is the number of years in interval x and
ax is the average amount of time lived in interval x to x+1 by those
dying in the interval.
7) The number of person-years lived in each age interval and all subsequent
age intervals: nTx.
nTx = (w-1Sum of X)
8) Average remaining life time (ex): the expectation
of life at any given age (the average years remaining to be lived by those
surviving to that age).3
ex = nTx divided by
The value e0, the life expectancy at birth, is the
first value in the ex column and is the most frequently cited life
1.Shryock, HS and Siegel, JS. The Methods and Materials of Demography (Condensed
Edition). Academic Press, NY. 1976.
2. David P. Smith, University of Texas School of Public Health, Personal
3. Life expectancy at age 75 is extrapolated from 1985 and 1990 U.S. life
tables by sex and ethnicity. Hispanic life expectancy is assumed to equal white
life expectancy at that age.
Return to the 2003 Annual Report
Center for Health Statistics