Once upon a time, I heard that at age 100 you have a steady chance of about 10% per year of dying. That data was only up to 110, though, after which there may be other degeneration that can increase the death rate. I don’t have a reference, but there should be more up-to-date information anyway.
There’s a massive amount of supposition in that article, which is surprising for something written by a Russian blogger.
Some recent research indicates that after turning 105, your chance of dying each year doesn’t increase. From then on, your chance of living one more year is 50%. Up to that point, your chance of dying in the next year is a little more each year. Your chance of dying in the next year is more when you’re 100 than when you’re 90, which is more than when you’re 80, which is more than when you’re 70, which is more than when you’re 60, etc.:
If you count the oldest females and group them by year you get:
114: 56 (undercounted, since the list only includes the 100 oldest.)
115: 24
116: 10
117: 7
118: 0
119: 1
120: 0
121: 0
122: 1
What model do you think rules out the outliers while allows for almost equal numbers of 116 and 117 year olds?
What if we group by quarter year instead:
114.25: 22
114.50: 24
114.75: 11
115.00: 8
115.25: 7
115.50: 7
115.75: 2
116.00: 4
116.25: 3
116.50: 0
116.75: 3
117.00: 2
117.25: 1
117.50: 3
117.75: 0
118.00: 0
118.25: 0
118.50: 0
and so on.
What model do you think we should fit to this?
Fact is we’re dealing with hundreds of millions of people generally dying much earlier than their hundred-and-tens. These are all outliers, and even if you remove the two oldest the data is still far from smooth.
I’m not a statistician either, but I would expect a couple of extremes in any model that accurately reflects the bulk of the 100 oldest people list.
But in fairness, I think he concedes that he is guessing and surmising on those points where he is guessing and surmising.
The biggest points are the nose, ear, and jawline. They don’t match Jeanne, but are dead on for Yvonne.
I’m a little unclear on this.
If she is a fraud, when exactly did she take over her mother’s life? What age was she and what year?
Was it just something that started as a tax dodge and she never expected to live long enough for it to become a thing, and now she’s trapped in the lie? How old is she really, if she’s a fraud?
There’s a journal war going on over the possible existence of a “mortality plateau”. If you live to 105 plus the mortality rate doesn’t keep going up. Here’s an anti article to counter the WP one. (It says stats are being thrown off by a few age inflations.)
But I wonder: It might sort of be like measuring the decay of a radioactive sample with two isotopes. You start off with the faster decaying isotope breaking down quickly and after most of it is gone you are left with the slower decaying isotope contributing most of the radiation. So the resulting curve has a steep drop and then a much slower drop.
With people you have a few “slow decay” folks. Once most of the “fast decay” folks are gone the curve reflects their death rate.
The official version is that Jeanne b. 1875, had a daughter Yvonne b. 1898 (therefore if it was really Yvonne who became famous, she was “only” 99 instead of 122). In 1934, Yvonne died at age 36 while Jeanne was age 59.
This research alleges that it was actually Jeanne who died and Yvonne assumed her mother’s identity for tax purposes because the law at the time would have required a hefty inheritance tax to transfer her properties (and the family had first hand experience of this when a different family member died in 1931). They were on shaky financial grounds anyways as the family went bankrupt in 1937.
There has been no formal counterargument by the Calment supporters, but from the snips and blurbs, the argument seems to be: How could a 36 year old pass for a 59 year old in a relatively tight knit community? Wouldn’t the neighbors and all associates immediately figure it out?
The rejoinder to that is that: 1) the family owned several properties throughout the country and became rather reclusive, and 2) several close friends and associates knew exactly what had happened and as it was in the middle of the Great Depression, they were all on board with the Calment’s keeping what was theirs and screwing the government.
The “daughter” died in 1934. If it was the mother instead, that’s when it started. If it was the daughter she was 99 when she died.
The poor family who bought her apartment using a life estate would have legal grounds to sue but I doubt there’s any money to be reclaimed.
That’s another minus against the new research. In 1965, this guy bought a remainder interest in her property at an arms length transaction when she was supposedly 90 years old. If this story is true, then she was only 67. Could any 67 year old really pass for 90? Or was this transaction done through agents and nobody ever laid eyes on “Jeanne”?
The apartment thing is fascinating. I think I remember way back when of the story of the annuity holder dying before ever receiving the apartment, but never associated it with Calmet. Funny how they all fit together.
What did Yvonne (purportedly) die of? I’ll admit that it seems surprising that the world’s oldest person would have had a daughter who died at 36, if it was natural causes.
Exactly.
naita has already explained the basic problem with your reasoning here, so I’ll just chip in again to point out that “all the coin flipping in the world” is not a helpful measure of sample size. Sure, if you flip a coin an infinite number of times, you would expect to see 30-heads runs (and 31-heads, 32-heads, 33-heads, and 34-heads runs) occurring more frequently than 35-heads runs, in accordance with their theoretical probability.
But even “all the coin flipping in the world” is nowhere near an infinite number of flips. You would have to have at least many, many billions of flips to be reasonably confident that the Law of Large Numbers would put the relative frequencies of the different lengths of heads-runs close to their expected values. And there’s no guarantee that “all the coin flipping in the world” amounts to many, many billions.
So it would not surprise me in the least, statistically speaking, if somebody flipping a coin mere millions of times (which, by the way, would still require solid consecutive months of constant coin-flipping) happened to come up with 4 runs of 30 heads, 1 run of 31, 1 run of 35, and no runs of 32, 33, or 34.
As I tell my calculus students, “The basic problem with mathematical intuition is that there are too many numbers, and most of them are too big.” It takes a lot of conscious scrutiny and checking to bring “what you would expect to see” in line with what we can mathematically demonstrate to be true.
This objection is even more stringent when we’re talking about the infinitesimally tiny sample size of known supercentenarians. We simply cannot extrapolate from theoretical expected values to any remotely reliable conclusions about a mere few dozen people. Another thing I tell my students is that besides the Law of Large Numbers there’s also “the Lawlessness of Small Numbers”: namely, small sample sizes cannot be trusted to agree with theoretically predicted results, because the noise of statistical fluctuations will drown out the signal of probabilistic outcomes.
This fundamental mathematical fact about insufficient data doesn’t change simply because insufficient data is all that’s available. Statistics doesn’t care that you really want to draw some mathematical inferences and have no way of getting enough additional data to make your inferences mathematically reliable. Too bad, pal: if your statistical reasoning about how this tiny set of outliers “ought” to behave is unreliable because the sample size is inadequate, then your attempted conclusions are invalid, and that’s that.
The same issue comes up a lot in other areas with a lot of empirical complications and limitations, such as studies trying to compare genetic vs. environmental influences on behavior, for example. When it’s difficult or impossible to collect all the data you need for a scientifically reliable analysis, a lot of people try to argue that their analysis of the insufficient data should be considered reliable anyway, because it’s the best we can do. Nope. Statistics doesn’t work that way.
A 1995 article says
So it sounds as though M. Raffray, the guy who bought her apartment “en viager”, knew Jeanne Calment personally. In fact, it appears that Calment lived in Arles all her life as a member of a well-known upper-class family, so it’s not as though she was a hermit squirreled away in some village somewhere where her identity could be kept very obscure.
Also, the daughter, Yvonne Calment Billiot, bore a son in 1926 who was raised by his grandmother Jeanne after Yvonne’s death from pneumonia in 1934. It would be rather peculiar for the 36-year-old mother of a seven-year-old son to successfully pass off her 59-year-old mother’s death as her own and assume the older woman’s identity for the next 63 years, in a city where both women were well known. I’m not saying it couldn’t happen, but I’d definitely want more concrete evidence in order to believe it.
Great posts, Kimstu.
To give a demonstration of the problems with trying to extrapolate from very small sample sizes, there’s always Joe DiMaggio in baseball. He is best known for his 56-game hitting streak–that is, he got at least one base hit in 56 consecutive games.
The second-longest hitting streak in well over 100 years of baseball belongs to Wee Wille Keeler of the old Baltimore Orioles, who hit safely in…45 straight games. Almost two weeks short of DiMaggio.
There are about three dozen hitters with 30-33-game streaks, another dozen or so in the 34-39 range, a half dozen in the 40-45 range…and then DiMaggio, with a streak eleven games longer than anyone else, ever.
But we’re not going to conclude that the streak didn’t happen, because of course it did. Was it unlikely? Sure. Was it very unlikely? That, too. Impossible? Nah. The “lawlessness of Small Numbers” [great phrase btw–may I steal it?] allows DiMaggio’s streak to be real, and would also allow for a woman reaching 122 when no one else ever reached 120.
[This is not to disagree with the idea that Calment was actually two people–I don’t have an informed opinion one way or the other, though I kinda like the idea–just to give an example of how outliers can happen in extremely extreme situations.]
Of course, thanks! Coincidentally, I believe that term is already used to some extent by baseball-stats aficionados, e.g., here.
I had not seen that phrase used in baseball contexts–or did not remember if I had seen it. I’ll attribute it to you anyway 
Another fun example: stolen base records, lifetime:
500s: 21 players
600s: 8
700s: 5
800s: 2
900s: 2
1000s: 0
1100s: 0
1200s: 0
1300s: 0
1400s: 1
Good ol’ Rickey henderson!
I agree, and also thank you Kimstu.
But is a baseball hitting streak a good comparison? That involves factors like skill, the strength of the hitter behind you (so you are not walked), running speed to beat infield ground balls, the quality of opposing pitching including the fact that DiMaggio would typically see the same pitcher for 3 to 5 at-bats per game, but today’s hitters see relievers, etc.
But anyways, the idea of a mortality plateau is interesting. I guess the idea is that these people have a genetic immunity to things like heart disease, cancer, or diabetes: things which will likely get us in our 70s-90s. But once it is shown that they are not susceptible to these things, they will not get them even at extreme ages.
I wonder if anyone who has survived cancer or a heart attack, for examples, have ever lived to be even 100, let alone 110.
I don’t imagine there’s any really great comparison to mortality, but that’s not really my point; I’m just giving an example of the “lawlessness of small numbers,” as kimstu so aptly put it :). That is, there have been however millions of 46-game “sets” for hitters in major league history, and only once has a hitter gotten a hit in every one of them…and that wasn’t 47 or even 48 games, but 56.
But to address the similarities or differences, of course some hitters are more likely to get a 56-game streak going. Yes, speed helps. yes, playing for an offensive powerhouse helps, because you get more plate appearances that way; yes, opposing pitching matters (DiMaggio didn’t have to face the Yankee staff if nothing else); yes, not drawing many walks helps. Etc. Joey Gallo is never going to have a 20-game hitting streak, let alone a 56-game one.
But the same can be said for long-lived persons, as you actually note. It helps to live in a developed country, it helps to be born with good genes. It helps to eat well, I’m sure. It helps to not come down with cancer. Lots of factors which will make it extremely unlikely that some people will make it to 75, let alone 100, let alone 120, but which through luck (or “skill,” if you want to consider “deciding not to jump out of airplanes” a skill) will make it possible for others to make it that far. Baseball isn;t a level playing field, but then again neither is mortality.
I grabbed another statistic because it was there, from the realm of finance. I took IBM’s daily percentage changes in their adjusted closing price. I also looked at daily percentage changes in the volume of traded IBM shares. UltraVires might reasonably question whether this is a good comparison. No: it’s a terrible comparison, except for making my narrow point that outliers can be weird. Tack it on to the baseball example.
Sample size: 14,343
IBM closing prices daily percentage changes:
median: 0
mean: .0003024
std dev: .015773
Largest 4 percentage changes:
.1172
.1202
.129
.1316
That looks ok. But consider the smallest percentage changes:
-.2352 (10/19/1987)
-.1554 (10/18/2000)
-.1495 (10/21/1999)
-.1074 (12/15/1992)
Those are all over the map. So outliers can be well behaved and they can be weird. (Though tacking on dates gives a hint of what the underlying process might be.)
Let’s look at percentage change in daily volume, something that most of us will have little intuition for, except that it will have high variance.
median: -.0132
mean: .0846
std dev: .5877
Largest percentage changes:
26
22.83
15
14.50
So we have a cluster, followed by 2 hops.
Smallest percentage changes:
-.9630 (4/9/1962)
-.9363 (2/8/1962)
-.9309 (6/17/1991)
-.9248 (9/21/1983)
We have one hop at the tail, which is actually more dramatic than it looks. It’s a 27x drop vs a 16x drop. The dates mean little to me.