## 23 July 2007

### life expectancies

The Numbers Behind Life Expectancy, from Carl Bialik's "The Numbers Guy" column at the Wall Street Journal.

Michael Moore said in Sicko that life expectancy is higher in Cuba than in the U.S.; CNN says it's the other way around; it turns out that so much computation goes into these calculations that there's probably a substantial amount of error. You might naively think that if life expectancy is, say, 77 years, that means that the average person born 77 years ago (in 1930) is just now getting around to dying. But the problem is that medical care isn't static, so this doesn't tell us how long people being born now should expect to live. So what's actually done is that one looks at how many people of age N in, say, 2005 survive to age N+1 (in 2006), and then these are chained together to tell us how many people would live to, say, age 80 if medical care remained as it is today and so the mortality rates remained constant. Basically, life expectancy is a moving target, because medical care changes substantially during a single person's life.

However, although the number "77" might not be that meaningful, I would guess that differences between those numbers for different populations which had been computed in the same way are valid to look at. A society where this number is 80 is probably healthier than one where it's 70.

But as many people point out, the Cuban statistics might not reflect what's actually going on in that country. It's difficult to know for sure.

Also, this means that the low life expectancies for countries in sub-Saharan Africa which have been affected by the AIDS epidemic are probably lower than one would naively expect; one hopes that the AIDS epidemic won't keep killing people at the same rates that it is now.

Anonymous said...

I can't help but wonder what Little's Law can tell us:
http://en.wikipedia.org/wiki/Little's_law

Paraphrasing...
The average number of things in a system, N, is equal to their average arrival rate, R, multiplied by their average time in the system, T, or:
N = R * T
or
T = N / R

It seems not ridiculous to let...

N : population
R : births/year
T : average life expectancy

N = current world population = 6,600,000,000 people

R = per www.who.int/whr/2005/media_centre/facts_en.pdfR = 133,000,000 new people / year

6600/133 = 49.6 years

I'm not sure how to account for the fact that the system is growing rather than stable.

The Probabilist said...

anonymous,

I'm not sure how to take into account that the system is growing. But I think what your computation might tell us is that if life expectancy were 49.6 years, then population would be stable.

Even that seems a bit strange, though; just because the life expectancy is shorter, that doesn't mean the population should stop growing. If we adopted a policy of killing everyone at 50, population would go down but then it would grow again.

John Armstrong said...

If we adopted a policy of killing everyone at 50, population would go down but then it would grow again.

It would grow again because the number of births per year is also increasing. You don't just have to account for the fact that the system is growing, you have to account for the fact that it's accelerating.

Mary Pat said...

Of course, you could ask the actuary what this stuff is supposed to mean. I've actually looked at historical mortality tables and life expectancy (mainly from the U.S. Social Security office) as part of my job.

When various groups give life expectancy, they're generally not assuming mortality stays constant (say probability of 65-yr-old surviving to 66) -- many times they use a projected mortality table (and yes, there are assumptions in there). When I looked at historical mortality, I had cohort mortality tables, meaning the mortality experienced by the people born in 1920, plus some projections for those who've made it to age 80 and beyond (the tables were from 2000). You need to be careful with regards to infant mortality, too. Sometimes, to not deal with the separate issue of infant and young child mortality, they start the mortality table at age 5 in calculating life expectancy. And, with regards to infant mortality, you've got to be careful, too. Some countries require the baby to have survived birth for a few days for it to be included in stats. The standard in the U.S. is that if the baby is born alive, and it dies minutes later, it counts for infant mortality. Which is why it can be a good idea to compare life expectancy of those who have reached some non-zero age.

I have no particular reason to trust the Cuban stats. They're the same people who claim that nigh unto 99% of the Cuban population is literate, which is not credible considering mental retardation, learning disabilities, and the like. Chances are, the stats are faked. Who's going to gainsay them? It's not like there are independent life insurance companies operating in Cuba.

Mary Pat said...

Reading the column carefully, I see they're talking CDC-ish numbers, as opposed to Social Security (which do have different methodologies).

Smoking is indeed a huge factor impacting mortality. It was the life insurance companies who learned very early on the great impact smoking has on life expectancy (I don't have a table with me now, but I believe the hit regular smoking puts on adult life expectancy is about 7 years.)

Also, which I don't see particularly noted, there are noticeable differences in life expectancy in the U.S. between blacks and non-latino whites. Again, measured in years (and no, not just due to not having reliable birth certificates). I don't know what the numbers are for other races/ethnicities.

The violent death aspect is interesting, because that impacts men mostly, and men of a certain age (you can see it in the mortality tables - greatly heightened male mortality from age 15 - 25 or so, then the mortality rate drops, until about age 35 where it starts climbing again... the age 35+ is the death by heart trouble/cancer incidence increasing.) I call it the "stupid period", and it's a pretty common pattern throughout the 20th century in the U.S., even if you remove deaths from war.