The Life Table The life table has been a key tool of actuaries for some 200 years and is the basis
for calculating Consider a large group, or "cohort", of U.S. males, for example, who were born on the same day. If we could follow the cohort from birth until all members died, we could record the number of individuals alive at each birthday -- age x, say -- and the number dying during the following year. The ratio of these is the probability of dying at age x, usually denoted by q(x). It turns out that once the q(x)'s are all known the life table is completely determined. In practice such "cohort life tables" are rarely used, in part because individuals would have to be followed for up to 100 years, and the resulting life table would reflect historical conditions that may no longer apply. Instead, one generally works with a period, or current, life table. This summarizes the mortality experience of persons of all ages in a short period, typically one year or three years. More precisely, the death probabilities q(x) for every age x are computed for that short period, often using census information gathered at regular intervals (every ten years in the U.S.). These q(x)'s are then applied to a hypothetical cohort of 100,000 people over their life span to produce a life table. An example from the National Center for Health Statistics (1997) is given below.
The columns of the table, from left to right, are:
In the above life table, mortality rates for U.S. males at each age were determined from census data for a short period (3 years). The rates applied to the hypothetical cohort of 100,000 U.S. males in the table throughout the lifetime of the cohort. All the other columns of the life table are derived from m(x) as indicated above. See Schoen (1988), Anderson (2002), or National Center for Health Statistics (1997) for details. Notes Life expectancy is not the same as **median survival time**,The calculation of life expectancy for a person should not be confused with predicting their survival time. While newborn U.S. males have a life expectancy of 71.8 years, any given U.S. male may die tomorrow or live to age 100. One need not predict actual survival times in order to compute life expectancy (the average survival time).
Anderson RN (1999). United States life tables, 1997. National vital statistics reports; vol 47 no 28. Hyattsville, Maryland: National Center for Health Statistics. Anderson TW (2002). Life expectancy in court: A textbook for doctors and lawyers. Vancouver BC: Teviot Press. National Center For Health Statistics (1997). U.S. decennial life tables for 1989-1991, volume 1, number 1. Hyattsville, Maryland: Author. Schoen R (1988). Modeling multigroup populations, chapter 1. New York: Plenum Press. |