The use of the Gompertz function to relate changes in life expectancy to the standardized mortality ratio

Abstract

BACKGROUND: Change in life expectancy may be more readily appreciated by a lay person as a measure of risk than the standardized mortality ratio (SMR). METHODS: The linear increase in the logarithm of the age-specific mortality rates with age (the Gompertz function) is used to deduce formulae connecting SMR with change in life expectancy. Their validity is checked by a comparison between the 1992 and 1952 mortality data for England and Wales, and between smokers and non-smokers in the American Cancer Society's second Cancer Prevention Study. RESULTS: It is shown that the Gompertz function is a good fit to mortality data for England and Wales from age 30 years upwards. Changes in life expectancy at ages 15, 25, 45 and 65 are presented for values of SMR from 0.5 to 3. A very simple formula connecting the two is valid at ages 15 and 25, and provides a reasonable approximation at age 45. CONCLUSIONS: The Gompertz relationship can be used to calculate the change in life expectancy corresponding to a particular SMR over a greater range than have previous methods, and, although subject to some uncertainties, can provide a quick method of judging the change in life expectancy that is associated with a given SMR value.