New Research Claims Jeanne Calment, thought to be worlds longest living human at 122, a fraud.

Miscellaneous and Personal Stuff I Must Share
41

Some more statistical observations, looking at longevity data from the worlds oldest (dead) people.

I went and grabbed the list of verified oldest people from wikipedia and threw out all the ones who are still alive, leaving 92 humans who died after age 114 years, 93 days.

When you look at the data by ‘number of days lived since 114+93’ (I would have made it a round 114, if I’d had the data…) it’s messy. Even 92 data points is a moderately small set. You can call Calment an inexplicably far outlier, but you could also point to the area at around +250 days as being inexplicably low. Is there some weird factor suppressing deaths at age 114 and 10 months? It doesn’t seem likely. It’s just a random variation.

Next, working on the model that after age X you have a constant whatever-percent chance of dying in each time period, I did three models to figure out what the mosty likely per-day chance of survival was under three conditions: using all the data, removing just Jeanne, removing Jeanne and Sarah Knauss. The result was.

All data: 99.802% per day
Exclude Jeanne: 99.756% per day
Exclude Jeanne and Sarah: 99.756% per day

IOW if you make it to 114+93, on any given day your chance of making it to the next day is very close to 99.8%. Assuming Jeanne is an invalid data points makes a noticeable difference to the calculated value, but assuming Sarah is invalid makes nearly none. At this point, I’d say that the statistical argument for being suspicious of Sarah Knauss’ age at death is basically DOA, but Jeanne needs a little more investigating.

I did a plot of the number of people who have ever lived to an age of “n days after 114+93”, plus the predicted values of how many people should have been alive, given the chances of death calculated above. The red line is using a chance-of-death-per-day of 99.802%, the blue line is using 99.756%. The blue line certainly fits the data somewhat better. However, as you can see, BOTH lines fit the “Jeanne” data point reasonably well - given that we start with 92 people at age 114+93, both models predict that we’re left with about half a person at day 2991 (Jeanne’s death day). So this is consistent with Jeanne just being a not-unreasonable outlier

Furthermore, if we assume someone has already lived as long as Sarah Knauss, I calculate the chance of living another 1160 days (the difference between Sarah and Jeanne’s age at death) to be .99756**1160 = 0.059 (5.9%). That’s really not a particularly low chance, given that we measure thousands of different statistics about the world all the time. It certainly isn’t statistically suspicious enough to base a conspiracy theory off.

42

As far as the photo evidence goes … the article spends a lot of space on proving that bow-tie-hat-girl is Yvonne, not Jeanne. Yeah, okay, it’s Yvonne, mislabelled as Jeanne (sometimes).

But I don’t actually think hat-girl looks that much like the photos of old Jeanne. Yvonne has a snub nose - Jeanne has a pointy nose in her old photos, and old Jeanne also has a pointy nose. Her jaw’s fuller, but that happens to everyone as they get older.

43

Looking at all the threads posted here - thanks to the people who provided them, there is much that is fishy about Jeanne Calment’s claim. Some of the claims are based on census data, which is notoriously unreliable. While there is proof of the both of both Jeanne and her daughter Yvonne, the evidence for the death of Yvonne at age 36 is very sketchy indeed. The photo evidence indicates that the older “Jeanne” is most likely Yvonne, and the fact the “Jeanne” was unusually fit for a centenarian is another issue.

Statistically, both Knauss and Calment are anomalies, outliers. If the oldest verified person is 117, why is there nobody who reached 118? 120? 121? There is always a cluster at the ends, when the record is broken it is only by a few weeks or days each time.

It looks as if the French government knows that calment’s claim is false but the whole thing has become a matter of national pride, and everything else flies out of the window.

44

Brayne Ded writes:

> . . . There is always a cluster at the ends . . .

Well, no, there isn’t. It isn’t necessarily true that there will either be a few people a little beyond the end or that there won’t be a few beyond the end. It’s estimated that there are now about 20,000 people of age 105 or greater in the world. If it’s really true that at 105 you’re about 50% likely to die in each following year, then the chances that you will live to 117 is 2*(-12), which is 1/4096. So about 5 of those 20,000 will live to 117, 2 or 3 will live to 118, and 1 will live to 119. Again, assuming that at 119, you have a 50% chance of living to 120, a 25% chance of living to 121, and a 12 1/2% chance of living to 122. If Calment had claimed to live to be 145, that would be very good evidence that she was lying. We would only expect 2*(-26) people who live to 119 to live to 145. That means we think that the chance that a person now alive will live to 145 is less than 0.0000015%. That’s a small enough probability that we would be justified in saying that it’s too improbable. A chance of 12 1/2% is not small enough to say that that purely based on statistics that it’s too unlikely. Note that this says nothing about any other evidence on whether Calment was lying.

45

Is she that woman who claimed she only had one wrinkle- and that was what she sat on?

46

It appears so:

47

Sorry, but I still think that you are playing with statistics. The problem for me - and others - is that the only fully verified age is 117, given that Sarah Knauss’s claim to be 119 has been queried, on what grounds I cannot say, as I have not found a detailed discussion of the validity of her age. In short, when there are a number of verified claimants for 116, and a very few for 117, then the jump to 119 and 122 respectively is improbable. Why only those two people? In Calment’s case the family background shows no indications that the family as a whole is long-lived, merely slightly better than average. And the average is a key fact; in my own family there have been a lot of eighty-plus and a number of ninety-plus, but no centenarians to date.

And then there is the question as to how reliable the documentary evidence is, if it is still available. And let us not forget the medical evidence; an examination of Calment’s teeth would soon settle the issue. Also, an examination of Yvonne’s grave, if it is indeed hers. Note that the burials of both Yvonne and Jeanne were done hastily, with few witnesses and no post mortem. It seems that there has been a cover up and the French government refuses to allow the case to examined.

48

dropzone’s Law: As an online discussion of statistics grows longer, the probability that the discussion involves baseball approaches 1.

49

Do you have any background in statistics, Brayne Ded? No, well, I have a master’s degree in mathematics. Unless you tell me that you have a Ph.D. in statistics, I don’t consider you more qualified than me to talk about this. There is nothing terribly surprising about a jump to 119 and 122 after several people at 117. Seven people made it to 117. On average a person who’s 117 (or any age over 105) has a 50% chance of living one more year. Actually, there are slightly less people living to 118 or 119 or 120 on the list linked to below than one would expect at random, but, again, it’s within a reasonable probability.

If you don’t believe this, go to your nearest university and talk to someone in the mathematics department who specializes in probability. The university might have a separate department for statistics, so go there if there is one. Show them the table linked to below and ask them if it’s that all-fired surprising that there’s one person living to 119 and one living to 122. See what they say.

Again, I will not address any other part of the evidence about whether Jeanne Calment was lying. I am not an expert on that sort of evaluation of evidence, and I suspect that neither are you. I am a mathematician, and I have some qualifications to discuss the statistical evidence:

50

Well proof from authority counts for something. But I’d put it in a different fashion.

If Brayne Ded has taken any college level course in probability, he would quickly encounter a number of counter-intuitive results. This is one of them: while averages tend to be reasonable well behaved, outliers are typically not, since outliers are by definition small in number.

A good way to get a sense of some of these apparent abnormalities is to play around with the random number generator in Excel. Use this function to obtain a random variable with a normal distribution (mean 0, standard deviation 1):

 =NORMINV(RAND(),0,1)

I took a sample of 1000 observations. Here are my results:
mean 0.046554367
st dev 0.960326581

The mean isn’t exactly zero and the standard deviation isn’t exactly 1, but they are close.

Lowest 4 numbers: 2 clusters with 1 hop.
-2.732902933
-2.705766188
-2.580533898
-2.500981489

Largest 4 numbers: 4 hops.
3.308270247
3.132253566
2.838211351
2.628009157

Now don’t get me wrong: the above isn’t the proper statistical model by any means for longevity. It’s simply designed to show that gaps between extreme values are by no means unusual. I could do a similar exercise with, say, 5 million observations in Stata and I would expect analogous results. But lots of people have Excel on their computer; for those who don’t Libre-Office has a free spreadsheet program called Calc, which would also work. Or try locating any dataset with a sample above, say, 500.

This is a pretty good thread actually. Ultravires made an entirely reasonable statistical observation: that’s it was poorly ground is surprising, but not at all his fault. This isn’t a statistical gimmick at work: it’s a widely observed yet still surprising result.

ETA: Rounding to some extent can also create these effects. Here are the 1st differences of above outliers: they aren’t exactly evenly spaced, though they are a little better than the first eyeball of the data:

Lowest numbers, 1st diffs:
-0.03
-0.13
-0.08

Highest numbers, 1st diffs:
0.18
0.29
0.21

Note that this is a symmetric distribution, so in the perfect case the absolute value of those 1st differences would all be equal. They aren’t close.

51

In response to that, the linked articles talk about how a French insurance company in 1997 was bitching about having to continue to pay when it “knew” it was really Yvonne and not Jeanne. It doesn’t explain how it “knew” that or give any supporting documentation, but I suppose it is possible that M. Raffray took out an insurance policy against his annuity agreement.

I’m obviously just guessing as there is no evidence of that, and I’ve never heard of such a policy in the United States, but I’m sure such an insurance product could exist. And if he did so, perhaps he was helping “Jeanne” cash in further on her fraud by giving her an annuity based upon a 90 year old when she was only 67.

As far as passing for her mother, I know that a similar scheme would not be possible in the United States. For example, when my father passed away in 2008, there would be no chance that I could pull off such a ruse. In Arles, France in 1934? I’m not sure, especially if the government was lax and many of her friends and associates went along with it.

Also, keep in mind that “going along with it” would only mean not challenging official government paperwork. It doesn’t mean that they couldn’t play cards or drink wine or eat cheese or do whatever French people did in 1934 and still not call her Yvonne or Mom or whatever. Even as her claims came to light in the 1990s, there would have been very few adults still alive that remembered the ole switcheroo and most if not all of them would have not wanted to upset the apple cart. Today, I would gather that none are still alive.

I think that there is enough here, given the interest in human longevity, for the French government to consent to these exhumations for DNA purposes.

52

And there was a World War and an occupation in between the purpoyted fraud and Mrs/Miss Calament becomiung famous, nearly 40 years infact. Plenty of time for most people to die.

Admittedly, I find the claim to be untenable, since investigators of extreme ages do infact check for exactly this fraud. And while I don’t doubt it would have been possible to withstand the scrutiny of the bureacracy, of investigators, not so much.

53

I seem to remember something about a similar set of frauds in the Caucasus mountains in the days of the Soviet empire. Before the internet I am afraid. But apparently villagers in the Caucasus mountains were none too fond of the Soviets or the years of military conscription they imposed.

So when an old man died, his son would take over his identity, his son again would take his, etc. This led to many young men dodging military service, and many middle aged men getting a pension a generation early. And of course, a very high average lifespan, curiously with the males living far longer than the females. The fraud was heavily aided by everyone being in on it and perceiving themselves as an outgroup to the Muscovites, as well as the harsh sunlight in the Mediterranean-latitude mountains leading to the basically light-skinned population wrinkling up very early in life.

Of course statisticians noticed and it resulted in a fad about the yogurts from the region being very healthy.

But I would not be surprised if Russians believe there must be similar frauds in the west.

54

Useful article on longevity myths and misconceptions.

55

Here’s another way to think about the statistical qualities of the list of the verified oldest people according to Wikipedia:

There are 26 people who were 115 when they died (24 women and 2 men), 11 people who were 116 when they died (10 women and 1 man), 7 people who were 117 when they died (all women), 1 woman who was 119 when she died, and 1 woman who was 122 when she died. (The list in Wikipedia doesn’t include everyone who live to be 114 at death, so we can’t go further using it.) So there are 46 people who lived to be 115. Let’s now make two assumptions. Let’s first suppose that this list is at least pretty close to being accurate about the ages being verified and not filled with false ages. Second, let’s suppose that it’s true, as proposed in the articles I linked to, that the mortality rate plateaus at age 105. At that point, if you live to age X (X equal to or greater than 105), you have exactly a 50% chance of living to age X + 1. We would then expect the following on average if that were true:

23 people of the 46 would die at 115 (and 26 did, in fact).
11.5 people of the 46 would die at 116 (and 11 did, in fact).
5.75 people of the 46 would die at 117 (and 7 did, in fact).
2.875 people of the 46 would die at 118 (and 0 did, in fact).
1.4375 people of the 46 would die at 119 (and 1 did, in fact).
0.78575 people of the 46 would die at 120 (and 0 did, in fact).
0.359375 people of the 46 would die at 121 (and 0 did, in fact).
0.1796875 people of the 46 would die at 122 (and 1 did, in fact).

This strikes me as pretty close, but that’s just my guess based on a quick look. Someone might want to run a chi-squared test on it or do some Monte Carlo testing (or something equivalent) to tell me how close. And, of course, all this requires the two assumptions I made.

56

I really do wonder why some people live so much longer than others who share their ancestry and living conditions.

My maternal grandmother was just short of 108 years old when she died, and nobody else in the family has even come close to that. My mom has one cousin who is in his early 90’s, but given his health will no live much longer. For anyone else on my mother or father’s side the upper 80’s has been the oldest. My mom will turn 87 in May, but she broke her hip recently and may, or may not, have to go into assisted care.

My grandmother was born earlier than any of the rest of us of course, when times were more difficult and more children were lost. Of her five other siblings only she and her next oldest brother lived to see grandchildren.

57

If these claims are true that Jeanne Calment was a fraud, that means no one has lived past 120. I wonder how long it will be before someone is verified to have lived over 120. It seems like 120 may be the upper barrier to human life expectancy.

58

There is no reason to think that there is an upper limit to human life expectancy. At any particular age, there is a particular probability that you will live another year. It doesn’t matter if the probability that a 120-year-old has a 50% chance or a 25% chance or a 10% chance or a 5% chance or a 1% chance or a 0.1% chance that they will live another year. If enough people live to be 120, the chances are good that one of them will live to 121.

59

Seems like living to 120 is just a matter of replacing enough body parts. We’ll get there eventually.

60

It’s also a matter of there being enough people over history to live to any given age. There have been a total of 105 billion people who have ever lived since 50,000 B.C. Currently, the odds that you will live to 100 vary between 1.5 per 10,000 to 3.5 per 10,000 in some typical first-world countries. If the probability that you will live one more year stays at 50% after 100, that means the probability that you will live to 120 is somewhere between 1.5 * ((-2)**20) and 3.5 * ((-2)**20). If all 105 billion people who had ever lived so far had lived in the equivalent of current first-world conditions, we would then expect that somewhere between 15 and 35 of them would have lived to 120.

But that’s still low compared to what would happen if mankind continues to exist for another billion years and spreads out over the entire Milky Way galaxy. Suppose over the entire past and future history of the human race there will be 105 quadrillion people. Suppose it is impossible to make the average lifespan greater than is possible in the most long-lived countries of today. Then we can expect there will be 35,000,000 people who will ever live to be 120 over the history of the human race in the past and the future. If it continues to be true that at 120 you have a 50% chance of dying every year, it will then be true that we can expect someone to live to 145. To have more people living past 120, you can either (1) make great medical improvements or (2) have enough people who ever live or (3) both.