# 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 Public Health.

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 DSHS 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 - ndx-1

5) Number dying (ndx): number of persons dying during the age interval.

ndx = lx * nqx

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) Lx

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 lx

The value e0, the life expectancy at birth, is the first value in the ex column and is the most frequently cited life table statistic.

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 communication.

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.

Last updated December 31, 2010