Josh GoldsteinA first #demography post: Just read an interesting article called "The (Im)precision of Life Expectancy Numbers" by James Hanley in AJPH. In it, he gives a "rough empirical rule of thumb" that SE(e0) is about 150/sqrt(PYL) and about 15/sqrt(number of deaths). Here's a naive way to explain those numbers. 1/n
For a cohort, the SE of life expectancy would be something like SD(individual age at death)/sqrt(N). The standard deviation of age at death is about 15-17, so that gives us one of the rules of thumb formulas. 2/n
Hanley's rule of thumb turn out to be a bit on the high side of the more exact calculations. I wonder why the above cohort approach would tend to be bigger than a more exact period approach? Any ideas? 3/n
The 150/sqrt(PYL) formula can be obtained from the 15/sqrt(D) formula by assuming that life expectancy is on the order of 100 years, which would make PYL ~ 100*D. n/n
Eddie Hunsinger@josh_goldstein
I am still struggling through it but it’s interesting: https://ajph.aphapublications.org/doi/10.2105/AJPH.2022.306805#
It is too bad I think that it doesn’t include Lo et al (2016). I like rules of thumb like these because they can be readily useful when we understand them. I’ve used info from state and county empirical pop forecast errors by Rayer and Smith a number of times, for instance. On cohort vs period the only difference in interpretation that comes to my mind is time.
I am still struggling through it but it’s interesting: https://ajph.aphapublications.org/doi/10.2105/AJPH.2022.306805#
It is too bad I think that it doesn’t include Lo et al (2016). I like rules of thumb like these because they can be readily useful when we understand them. I’ve used info from state and county empirical pop forecast errors by Rayer and Smith a number of times, for instance. On cohort vs period the only difference in interpretation that comes to my mind is time.
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. (Am J Public Health. 2022;112(8):1151–1160. https://doi.org/10.2105/AJPH.2022.306805)
@josh_goldstein
I think it’s esp important that the definition of any reported uncertainty is as clear as possible
I think it’s esp important that the definition of any reported uncertainty is as clear as possible