Last Revised: January 30, 2007
probabilities of death (qx) directly from the data and perform no smoothing at older ages.12 From these qx values, a complete cohort life table is calculated using the same formulas used for period tables.
The above description assumes that all members of a cohort have died before we compute the life table. Yet, it is often desirable to compute life tables for cohorts that are almost extinct (see definition of almost extinct below). In such cases, we must make some assumption about future mortality for cohort members who are still alive at the moment of observation. We assume that their future probabilities of dying are identical to those of a five-year cohort of comparable age observed just before the end of observation. For example, if our observation period ends on December 31, 2000, then the 1900 birth cohort has complete mortality data only up to exact age 99. So, we assume that mortality from exact age 99 to exact age 100 for the 1900 cohort will be the same as mortality rates at the same age among the 1895-1899 birth cohort. We consider a cohort “almost extinct” if the total person-years remaining to be lived (based on our estimate) for that cohort is no more than one percent of the total lifetime person-years lived for that cohort (assuming the life table begins at age 0).13 In practical terms, this typically means that we treat cohorts that have reached age 90 or older by the end of observation as almost extinct (and therefore estimate their future mortality in order to complete the life table).
Multi-year life tables
Period life tables for multi-year time intervals (e.g., 10-year periods) are based on death rates calculated by pooling deaths and exposures across the time interval before dividing the former by the latter. Similarly, life tables for multi-year cohorts (e.g., 10-year birth cohorts) are derived by pooling data across cohorts before calculating probabilities of death.14 In both cases, multi-year life tables are then computed as described above. Thus, death rates and life table quantities from multi-year life tables are not simply the average of the respective values across periods or cohorts.
Abridged life tables
For both periods and cohorts, “abridged” life tables (e.g., by five-year age groups) are extracted directly from “complete” life tables (i.e., by single year of age).15 Deriving abridged tables from complete ones (rather than computing them directly from data in five-year age intervals) ensures that both sets of tables contain identical values of life expectancy and other quantities.
Changes in population coverage
Some countries and areas have experienced changes in their territorial boundaries over the period covered by the HMD. In other cases, there have been changes in the coverage of demographic data (e.g., vital statistics change from covering the de facto population to covering the de jure population). These changes must be taken into account when computing death rates and life tables. In general, death counts must always refer to the same territory as the exposure-
12 13 14 15
See pp. 40 for the formulas used to derive cohort qx values. For more details regarding almost extinct cohorts, see pp. 42-44 of the Methods Protocol. For more details on computing multi-cohort life tables, see pp. 41-42 of the Methods Protocol. For details regarding abridged life tables, see p. 44 of the Methods Protocol.