The (Im)precision of Life Expectancy Numbers

Life expectancy figures for countries and population segments are increasingly being reported to more decimal places and used as indicators of the strengths or failings of countries' health and social systems. Reports seldom quantify their intrinsic statistical imprecision or the age-specific numbers of deaths that determine them. The SE formulas available to compute imprecision are all model based. This note adds a more intuitive data-based SE method and extends the jackknife to the analysis of event rates more generally. It also describes the relationships between the magnitude of the SE and the numbers of person-years and deaths on which it is based. These relationships can help quantify the statistical noise present in published year-to-year differences in life expectancies, as well as in same-year differences between or within countries. Agencies and investigators are encouraged to use one of these SEs to report the imprecision of life expectancy numbers and to tailor the number of decimal places accordingly.

Automated summary

Life expectancy is an important indicator for assessing the strengths and weaknesses of a country's health and social systems. This article presents a new intuitive method for calculating the standard error based on actual data, and extends the use of the jackknife method for analyzing event rates. The article also examines the relationship between the magnitude of the standard error and the number of person-years and deaths, and recommends using these standard errors to report the uncertainty of life expectancy numbers.