Recently there were a couple of notable deaths, with different reactions.
Bill Paxton died at age 61, and many said “how young”.
Similarly, Judge Wapner died recently, at age 97. Most people I know remarked “I didn’t realize he was so old” or “I didn’t realize he was still alive!”
But maybe 150+ years from now people will be exclaiming “How young!” when some notable celebrity dies at age 97.
So…. how can we figure out how young is too young?
TIME TO DIE
I think we have a natural “feel” for the shape of mortality, but the issue is that there are a couple slices going on at the same time. There’s the cohort slice — following everybody born in a specific year; there’s a calendar slice — following everybody who died in a specific year (and all the people who survived that year). These aren’t the same distributions, for some obvious reasons, especially if mortality rates are changing for various conditions.
That said, I’m going to use cohort mortality tables, because those are easier to think about. To make the numbers easier to see/understand, they’re scaled up to 100,000 people in total.
Let’s look at a cohort that is pretty much all dead currently: those born in 1900.
Here’s their “death curve”:
Yeesh, infant mortality was awful. Note the odd blip at around age 18: that was the Spanish flu pandemic.
Still, looking at the whole distribution isn’t all that helpful – not that way. We can’t eyeball to figure out what the median age at death was, for example. But we’ll get there in a bit.
Let’s look at the 1970 cohort, which is my closest group. Obviously, these people are at most 47 years old, so most of this mortality curve is projected:
(check out that heightened mortality for males from about age 15 to 25. The fatal stupidity period.)
Finally, let us look at a completely projected cohort: 2100.
A few things to note on all three graphs:
- Males die younger than do females — though with later cohorts, we see the male & female distributions getting closer.
- Part of this difference may be due to differential smoking rates… but that’s not the only thing explaining the gender gap in life expectancy
- Check how much infant mortality has gone down!
- The peaks are moving rightward, and seem to be getting “bunched up” — that is, people in general are living later, but have less variability in their age at death.
But it’s really difficult to look at these curves and pick points on them to say whether someone died really young or really old.
WAYS TO COMPARE: CUMULATIVE DISTRIBUTIONS
So there’s a better way to look at these graphs: cumulative death age distributions, which one can use to read off percentiles. So let’s look at the three cohorts, for males, and mark off a few points.
And here is the same for females:
Ah, now we can eyeball different percentiles (this is assuming at 100k people in each group to begin with.)
- First off, I can’t mark off the 10th percentiles for the 1900 cohort, because more than 10% of babies died before they were 1 year old. Yeeeesh.
- 10th percentiles for both males & females of the 1970 cohort has not even been experienced yet! Basically, anybody born in 1970 who has already died have definitely died way too young.
- Notice that the 90th percentiles aren’t too different between the 1900, 1970, and 2100 cohorts. To be sure, there’s a shift, but nothing like the shift at lower percentiles.
- Also notice I’m having trouble marking off the higher percentiles for the later cohorts — because the curves are so steep. This is called squaring of the mortality curve — this is reflecting how “bunched up” projected death ages are.
We’ll see if these projections are anywhere close to ultimate reality. And by “we”, I mean the 2200 cohort.
Here’s a table of selected percentiles (these are approximate, fwiw. I didn’t feel like interpolating.)
|Percentile||1900 Cohort, Male||1970 Cohort, Male||2100 Cohort, Male||sss||1900 Cohort, Female||1970 Cohort, Female||2100 Cohort, Female|
Yes, one really should be planning for living to be old. Buy annuities!
WAS BILL PAXTON SO YOUNG?
Oh, all right.
He was born in the year 1955, halfway between the 1950 and 1960 cohorts. So let’s look at the tables and see where he falls percentile-wise:
For the 1950 cohort, age 61 is approximately the 20th percentile for males.
For the 1960 cohort, age 61 is approximately the 18th percentile for males.
So yes, it’s young, but not 10th percentile young.
WAS JUDGE WAPNER SO OLD?
Okay, fine. Wapner was born in 1919, so I’ll use the 1920 cohort table.
97 is at about the 99th percentile for males. That’s damn old.
I do compose Mortality Monday & Friday Trumpery posts well in advance. Stuff has been happening to me lately, so other regularly planned features are delayed.
In the meantime, check out the 12th Actuarial Speculative Fiction Contest!. Thanks to Nate Worrell for giving me the following cover art:
Read my story, The Nested Horror, in which an unnamable horror is stalking the financial reporting actuaries at quarter end. Will they escape?
Mortality Monday (with a little Trumpery): Supreme Court Probabilities Take 2
Mortality Monday: Suspicious Russian Deaths
Mortality Monday: Supreme Court Probabilities