Life expectancy, life disparity

This is a serious post about life expectancy and inequality. But first a short rant.

Quick: Life expectancy in the U.S. is 78.7 Your parents are 85. How much longer are they expected to live? If you were worried about how much time you had left to spend with them, and you asked the helpful site seeyourfolks.com, you would get this:

This app, and the Slate piece about it, managed to combined two of my pet peeves: the understandable difficulty with understanding life expectancy, and the inexcusable use of second-person reporting on social science findings, which does more to discredit than to disseminate important research.

The error here (apart from “you”) is the common notion that “life expectancy” is the average age at which people of any current age can expect to die. If we were more rigorous about using the phrase “life expectancy at birth” it would be easier to grasp.

In 2008 the life expectancy at birth in the U.S. was 78.1. That means that if a group children born in 2008 lived every year of their lives exposed to the risks of death observed in 2008, their average lifespan would be 78.1 years. But those who made it to age 60 would live an average of 22.7 more years, for a total of 82.7. And those who live to age 99 would live an average of 2.4 more years, for an average of 101.4.

So “life expectancy” as commonly used is not a prediction of how long today’s babies will live — since we hope the future is better than living 2008 over and over — and it’s not a prediction of how long your elderly loved ones will live.

Life disparity

Life expectancy — for any age — is a measure of central tendency: the average number of years of life remaining. And so there is a dispersion around that mean. That dispersion is inequality. A very nice article in the open-access journal BMJ Open, by James Vaupel, Zhen Zhang and Alyson A van Raalte, describes the measure of life disparity. It’s complicated, but a neat tool.

Life disparity is the average number of years people are expected to live when they die. For example, in the U.S. in 2008 an infant who died on the first day of life died 78.1 years early. And a 78-year-old who died, counterintuitively, died 10 years early (since the life expectancy at 78 is 10). To understand what this measure means, consider that if everyone died at exactly 78.1 years of age, life expectancy would be unchanged but life disparity would be 0. On the other hand, the greatest life disparity would occur if all early occurred at age 0.

Life disparity and life expectancy usually go together. That’s because reducing early deaths has the biggest effect on both measures. Here is the cool figure from that paper:

The association between life disparity in a specific year and life expectancy in that year for males in 40 countries and regions, 1840–2009. The black triangle represents the USA in 2007; the USA had a male life expectancy 3.78 years lower than the international record in 2007 and a life disparity 2.8 years greater. The brown points denote years after 1950, the orange points 1900–1949 and the yellow points 1840–1900. The light blue triangles represent countries with the lowest life disparity but with a life expectancy below the international record in the specific year; the dark blue triangles indicate the life expectancy leaders in a given year, with life disparities greater than the most egalitarian country in that year. The black point at (0,0) marks countries with the lowest life disparity and the highest life expectancy. During the 170 years from 1840 to 2009, 89 holders of record life expectancy also enjoyed the lowest life disparity.

Countries at the bottom left (0,0) have both the world’s highest life expectancy and the lowest life disparity in the world for that year, which occurred 89 times over 170 years. Countries below the diagonal have relatively low life disparity given their life expectancy; those above the diagonal (like the U.S.) have higher-than-expected life disparity for their level of life expectancy. In our case that reflects the fact that we do a pretty good job keeping old people alive, but let too many young people die.

U.S. improvement

The good news is that life expectancy is increasing in the U.S. (and most other places), and that the inequality between Blacks and Whites is getting smaller, as reported by the National Center for Health Statistics. That is, the Black-White inequality in average expectation of life at birth has shrunk.

The mixed news is that life disparity is much higher for Blacks than Whites — but that gap is falling as well. Here are those numbers for 1998 and 2008 (I did the life disparity calculations from this and this, and will happily share the spreadsheet). Click to enlarge:

So Black deaths are more dispersed than White deaths: 14 and 13 for males and females, compared with 12 and 11. For comparison, the Swedish female life disparity is 9. What does a higher disparity mean? Generally, a larger share of early deaths. That’s why the race gap in life expectancy at birth is greater than the race gap in life expectancy at older ages — average 65-year-old Whites and Blacks have more similar life expectancies than do infants.

Why is life disparity more interesting than life expectancy alone, and how does this help explain Black-White inequality in the U.S.? For one thing, high life disparity indicates either relatively unhealthy or dangerous living conditions at younger ages. So it’s partly a measure of the quality of life. Vaupel et al. add:

Reducing early-life disparities helps people plan their less-uncertain lifetimes. A higher likelihood of surviving to old age makes savings more worthwhile, raises the value of individual and public investments in education and training, and increases the prevalence of long-term relationships. Hence, healthy longevity is a prime driver of a country’s wealth and well-being. While some degree of income inequality might create incentives to work harder, premature deaths bring little benefit and impose major costs. Moreover, equity in the capability to maintain good health is central to any larger concept of societal justice.

I think what they say about differences between countries would apply to differences between groups within a society as well.