## Did she really live 122 years?

Even more famous than “the Japanese dude who won the hot dog eating contest” is “the French lady who lived to be 122 years old.”

But did she really?

Paul Campos points us to this post, where he writes:

Here’s a statistical series, laying out various points along the 100 longest known durations of a particular event, of which there are billions of known examples. The series begins with the 100th longest known case:

100th: 114 years 93 days

90th: 114 years 125 days

80th: 114 years 182 days

70th: 114 years 208 days

60th: 114 years 246 days

50th: 114 years 290 days

40th: 115 years 19 days

30th: 115 years 158 days

20th: 115 years 319 days

10th: 116 years 347 days

9th: 117 years 27 days

8th: 117 years 81 days

7th: 117 years 137 days

6th: 117 years 181 days

5th: 117 years 230 days

4th: 117 years 248 days

3rd: 117 years 260 days

Based on this series, what would you expect the second-longest and the longest known durations of the event to be?

These are the maximum verified — or as we’ll see “verified” — life spans achieved by human beings, at least since it began to be possible to measure this with some loosely acceptable level of scientific accuracy . . .

Given the mortality rates observed between ages 114 and 117 in the series above, it would be somewhat surprising if anybody had actually reached the age of 118. Thus it’s very surprising to learn that #2 on the list, an American woman named Sarah Knauss, lived to be 119 years and 97 days. That seems like an extreme statistical outlier, and it makes me wonder if Knauss’s age at death was recorded correctly (I know nothing about how her age was verified).

But the facts regarding the #1 person on the list — a French woman named Jeanne Calment who was definitely born in February of 1875, and was determined to have died in August of 1997 by what was supposedly all sorts of unimpeachable documentary evidence, after reaching the astounding age of 122 years, 164 days — are more than surprising. . . .

A Russian mathematician named Nikolay Zak has just looked into the matter, and concluded that, despite the purportedly overwhelming evidence that made it certain beyond a reasonable doubt that Calment reached such a remarkable age, it’s actually quite likely, per his argument, that Jeanne Calment died in the 1930s, and the woman who for more than 20 years researchers all around the world considered to be the oldest person whose age had been “conclusively” documented was actually her daughter, Yvonne. . . .

I followed the link and read Zak’s article, and . . . I have no idea.

The big picture is that, after age 110, the probability of dying is about 50% per year. For reasons we’ve discussed earlier, I don’t think we should take this constant hazard rate too seriously. But if we go with that, and we start with 100 people reaching a recorded age of 114, we’d expect about 50 to reach 115, 25 to reach 116, 12 to reach 117, 6 to reach 118, 3 to reach 119, etc. . . . so 122 is not at all out of the question. So I don’t really buy Campos’s statistical argument, which all seems to turn on there being a lot of people who reached 117 but not 118, which in turn is just a series of random chances that can just happen.

Although I have nothing to add to the specific question of Jeanne or Yvonne Calment, I do have some general thoughts on this story:

– It’s stunning to me how these paradigm shifts come up, where something that everybody believes is true, is questioned. I’ve been vaguely following discussions about the maximum human lifespan (as in the link just above), and the example of Calment comes up all the time, and I’d never heard anyone suggest her story might be fake. According to Zak, there had been some questioning, but it it didn’t go far enough for me to have heard about it.

Every once in awhile we hear about these exciting re-thinkings of the world. Sometimes it seems that turn out to be right (for example, that story about the asteroid collision that indirectly killed the dinosaurs. Or, since we’re on the topic, the story that modern birds are dinosaurs’ descendants). Other times these new ideas seem to have been dead ends (for example, claim that certain discrepancies in sex ratios could be explained by hepatitis). As Joseph Delaney discusses in the context of the latter example, sometimes an explanation can be too convincing, in some way. The challenge is to value paradigm-busting ideas without falling in love with them.

– The Calment example is a great illustration of Bayesian inference. Bayesian reasoning should lead us to be skeptical of Calment’s claimed age. Indeed, as Zak notes, Bayesian reasoning should lead us to be skeptical of any claim on the tail of any distribution. Those 116-year-olds and 117-year-olds on Campos’s list above: we should be skeptical of each of them too. It’s just simple probabilistic reasoning: there’s some baseline probability that anyone’s claimed age will be fake, and if the distribution of fake ages has wider tails than the distribution of real ages, then an extreme claimed age is some evidence of an error. The flip side is that there must be some extreme ages out there that we haven’t heard about.

– The above discussion also leads to a sort of moral hazard of Bayesian inference: If we question the extreme reported ages without correspondingly researching other ages, we’ll be shrinking our distribution. As Phil and I discuss in our paper, All maps of parameters are misleading, there’s no easy solution to this problem, but we at least should recognize it.

I hadn’t considered that the clustering at 117 is probably just random, but of course that makes sense. Calment does seem like a massive outlier, and as you say from a Bayesian perspective the fact that she’s such an outlier makes the potential holes in the validation of her age more probable than otherwise. What I don’t understand about the inheritance fraud theory is that Jeanne’s husband lived until 1942, eight years after Jeanne’s hypothesized death. It would be unusual, I think, for French inheritance law not to give a complete exemption to a surviving spouse for any inheritance tax liability (that’s the case in the legal systems I know something about), but I don’t know anything about French inheritance law.

1. Terry says:

I find it helpful to flip the question. Out of about 10 billion observed lifespans what are the odds that there was a major screwup in one that went undetected and caused a substantial overestimate? Pretty hard to eliminate that possibility with any certainty.

• Andrew says:

Terry:

It is said that my Grandma Ida lied about her age all her adult life, for several decades claiming she was younger, then in her later years switching it around and claiming she was older than she really was. I thought about that a few years ago when reading this article by Michael Kinsley on aging as a competitive sport.

2. Luis says:

May be you are dealing with some fundamental data issue. Oldest people has no good data records…
Besides, it would be interesting to run a computer simulation to see how data behaves on the tail: I think its probably not as intuitive as it looks with Bayesian inference.

• Andrew says:

Luis:

A simulation is Bayesian predictive inference! The issue here is not so much the statistical model as the data quality, I think.

• luis g de la fuente says:

Talking about running some Python with eg 1000 different independent simulations of the tail (universes) and see what % of them match this ‘outliers’ pattern you describe. I don´t believe Bayesian inference is going to help with almost no data :-)

• Keith O’Rourke says:

> help with almost no data :-)
With almost no data you can investigate the properties that result from Bayesian inferences (given assumed prior and data generating model and a set fake universe) with such little data. This will make precise how much help it would or would not be (in different universes).

• Keith O’Rourke says:

> not so much the statistical model as the data quality
But those are not separate here – you need to at least have some model for recorded ages not being real ages and here there is likely little sense of what that model should be along with choices being very influential.

3. Arno says:

Huh. Zak proofs appear flimsy to stay polite -Facebook survey, really?-,
are full of surprising elements for a french person -“in French, the names Jeanne and Jean have the same pronunciation”, huh, no, lol, not really
and imply an identity switch for tax evasion by a “notable” in a sizable french town.
Sounds a lot like nonsense to me.
Looking forward for a probability analysis of 9/11 events not happening, will be similarly useful imho.

4. Nikolay says:

Hi, I suggest you read the first chapter of my paper and look at the figure with simulations, it is quite easy and straightforward, no rocket science. And yes, the data for other SC is not reliable, but it was a good lack that she has got this red flag and now we should question everybody else.

5. Justin says:

Ahh, this is the same Paul Campos who has made a cottage industry of arguing that obesity carries no health risks by cherry-picking studies that don’t address known sources of confounding.

• Paul F Campos says:

I don’t make the ridiculous argument you attribute to me, but nice strawmanning.

• Kyle C says:

Prof Campos — I’ve followed your work with interest. In a 2008 interview with the Atlantic, you said the statement that “high weight has no relevance to health” was “about 97% true.” Were you misunderstood?

• Paul F Campos says:

That was an off the cuff use of hyperbole in an informal context. I lay out my argument in the book THE OBESITY MYTH. Short version:

The health risks associated with high weight tend to be overstated.

The extent to which those associations have been shown to be causal also tends to be overstated.

The health benefits associated with higher weight tend to be understated or ignored.

Trying to make people thinner as a matter of public health policy is a terrible harm reduction strategy, that is useless at best and actively harmful in many instances.

The “obesity crisis” is a classic moral panic, analogous to things like reefer madness. (Pointing out that trying to stamp out marijuana use is a terrible public health policy doesn’t mean claiming there are no adverse health effects to using cannabis).

• gregor says:

“Trying to make people thinner as a matter of public health policy is a terrible harm reduction strategy”

In my opinion, it is a valid public health concern. But people often talk as though it’s just a matter of “eating right” and “exercise,” implying the problem is simply one of individual self-control. I find it hard to believe though that past generations were so much slimmer because they had superior self control than we do! It’s because of systemic factors. And I think it makes sense to look at those systemic factors and see what went wrong. Individual effort can overcome systemic headwinds, but I think it is unrealistic to expect this of the population at large. That’s almost as dumb as Gerald Ford’s Whip Inflation initiative.

Industrial food is predominately made from refined grains, sugars, and vegetables oils (all taxpayer subsidized). This food is engineered to be palatable. It is high in calories and nutritionally deficient. And it is ubiquitous and requires little prep time. I believe the problem lies with the food, but no one wants to go there because money (public choice problem). Lifestyle and culture factors like lack of cooking in the home are another key factor I think. That is probably at heart an economic phenomenon (stagnant male wages).

• Kyle C says:

I don’t think Campos would disagree, but I think he reads the evidence to suggest that fatness is only a marker of certain health problems and not a cause of them.

6. Jonathan (another one) says:

So where does this leave Methuselah? His documentation is quite widespread, and he’s not that far out in his family tree, relatively, because the spreads are much wider. (See what I did there?)

7. The big picture is that, after age 110, the probability of dying is about 50% per year. For reasons we’ve discussed earlier, I don’t think we should take this constant hazard rate too seriously

In fact, we shouldn’t take that constant rate seriously *at all*. The mechanisms of biological failure in old age are that multiple systems are failing simultaneously: immune, digestive, neural, circulatory… etc and that failure in one will lead to increased failure rates in another. If constant failure rate is the zeroth order model then the first order model would be that failure rate increases to some power law with time, r = C*t^k for k > 0.

This produces the following differential equation for the percentage of people living to our initial time (say t=70 yrs or something) who die by time t, D(t), (in Maxima notation):

clear(all);
reset();

assume(k >= 0);

deq:'diff(D,t) = c*t^k*(1-D);

sol:ode2(deq,D,t);

spsol:ic1(sol,D=0,t=0);

ourHaz:1-rhs(ratexpand(spsol));

draw2d(color=green,explicit(subst([c=.5,k=0],ourHaz),t,0,10),
color=orange,explicit(subst([c=.5,k=1],ourHaz),t,0,10),
color=red,explicit(subst([c=.5,k=2],ourHaz),t,0,10));

if you copy and paste this code into maxima you can plot the hazard curve for the three values k = 0, k = 1, k = 2 and compare them to the shape of the hazard curve published in the CDC life tables (for example figure 3 here)

https://www.cdc.gov/nchs/data/nvsr/nvsr67/nvsr67_07-508.pdf

Just by eye, I’d say k = 1 was a reasonable starting place for say “Non-Hispanic white female” curve. We could do some inference using Stan and the data series you provide to find a posterior distribution for k if someone is inclined.

8. zbicyclist says:

The statistical arguments of this type are never conclusive — e.g. you might get 100 heads in a row out ofa fair coin, or might get certain unusual voting patterns by chance (e.g. North Carolina absentee ballots).

All the stat argument can do is to point you to things that are likely fraudulent, for some value of likely, and deserve further investigation.

I found this interesting:

“In addition to many biographies that do not question Jeanne’s identity, I managed to find a rare book
on insurance published in 2007 [10], where there is a short paragraph in the chapter on insurance fraud
devoted to Madame Calment. The author describes the rumor that a certain insurance company has found
out that instead of Jeanne Calment, it was her daughter who received the rent, but by agreement with the
authorities, it kept the secret given how much the character of the “doyenne of the French” had become
legendary. The details of the story are not clear. An officially sanctioned visit to Arles and Marseille and an investigation into various archives could clear some of the remaining questions”

My career goes back to the early days of supermarket scanning data, when quality control was not good. I recall more than one management project urging us to find “really successful promotions”, so they could be repeated. But basically looking for extreme positive outliers was useful primarily for finding highly questionable data points. You didn’t want to call these to the client’s attention, but censor them before the client saw them. I suspect the same thing is true with those who live an exceptionally long time.

• zbicyclist says:

And remember those old Dannon yogurt commercials, based on the longevity of Georgians?

And the stories from Japan, such as this one about someone dead 30 years but still collecting a pension:

My point is that we’re likely to be pushing a lot of noise here. Beyond saying 122 is highly questionable, it’s not worth trying to make a sophisticated statistical argument.

9. gregor says:

-Records before the late 19th century are not very reliable.
-Records in many parts of the world are not very reliable even today.
-Asking old people their age is not very reliable. For example, according the 2000 US Census, there were nearly 1,400 people who were 110 or older. But this is implausibly high compared to the number of people over 100 in the 1990 census.

10. gregor says:

“But if we go with that, and we start with 100 people reaching a recorded age of 114, we’d expect about 50 to reach 115, 25 to reach 116, 12 to reach 117, 6 to reach 118, 3 to reach 119, etc. . . . so 122 is not at all out of the question. So I don’t really buy Campos’s statistical argument, which all seems to turn on there being a lot of people who reached 117 but not 118, which in turn is just a series of random chances that can just happen.”

Starting with X people at 117, the probability of attaining 122 (taking your model as a given) would be 1/2^5 or about 3%. This is of course possible. But I think Campos might have a legitimate point that the counts here don’t look quite right. i.e., there are a lot of missing deaths at 118, 119, etc. There should be 16 times as many people dying at 118 as 122, 8 times as many at 119, etc. Only two deaths over five years (7 exposures) implies an annual mortality rate of only about 2/7 after age 117.

11. Carlos Ungil says:

> It would be unusual, I think, for French inheritance law not to give a complete exemption to a surviving spouse for any inheritance tax liability (that’s the case in the legal systems I know something about), but I don’t know anything about French inheritance law.

The surviving spouse is completely exempt from paying inheritance tax in France only since 2007. But it should be noted that, even today, in the presence of children (or their descendants) they do necessarily get most of the estate (1/2 if there is one child, 2/3 if there are two, 3/4 if there are three or more). I don’t what the rule was in the 1930’s but it was surely even less flexible and inheritance tax rates were quite high. (Maybe not as high as today, though: France has one of the largest estate taxes in the OCDE – 45% for descendants/parents/siblings, 55% for family members up to 4th degree and 60% otherwise – and one of the lowest exemptions – EUR 100k in the best case. Inheriting 5mn means paying between 2mn and 3mn in taxes.)

• none says:

One of the claims in the paper was that the French government in the mid 1930s knew that war was coming, so it was trying to collect as much tax as it could for the buildup. Therefore inheritance taxes were unusually high.

12. David says:

It seems to me that a statistical argument for disputing Jeanne Calment’s claimed age is not valid. There is a good reason for her to be a statistical outlier. Calment was, simply by virtue of having (or claiming to have) the age record, was something of a celebrity for a number of years before her death. She was the subject of a significant number of interviews and this gave her a reason for living–a focus to her life–that most people of a similar age living in nursing homes wouldn’t have. Being the world’s oldest person (or claimed oldest person) became something of a job or a second career for Calment. I would posit that the attention she got and the focus that it gave her life was a strong reason for her to live significantly longer than her supercentenarian contemporaries.

I also read at one point it was decided that Calment would no longer give any more interviews. With this focus to her life now removed, she finally died shortly thereafter.

Note that I think it is perfectly plausible that she wasn’t actually Jeanne Calment but was Jeanne Calment’s daughter having assumed her identity. Other supercentenarians have been claimed by Guinness in the past to be incontrovertibly authenticated, only to later be discovered to have been bogus claims. But I think we must look for direct evidence that the daughter assumed the mother’s identity. Statistical evidence is unsatisfactory because, if she really was 122 years old, there is a perfectly good reason for her to have been a statistical outlier.

13. Joshua Pritikin says:

The topic reminds me of this fascinating study, “Do centenarians die healthy?” https://www.ncbi.nlm.nih.gov/pubmed/16079208

14. Ethan Steinberg says:

“Supercentenarians and the oldest-old are concentrated into regions with no birth certificates and short lifespans”

The degree to which the number of supercentenarians declines after stricter record keeping is just striking: https://www.biorxiv.org/content/biorxiv/early/2019/07/16/704080/F1.large.jpg?width=800&height=600&carousel=1

• Robert Young says:

That’s NOT a study, it’s a self-published, rejected by peer review pre-print full of errors.

15. Carlos Ungil says:

A recent piece on the subject: “WAS JEANNE CALMENT THE OLDEST PERSON WHO EVER LIVED—OR A FRAUD?”

https://www.newyorker.com/magazine/2020/02/17/was-jeanne-calment-the-oldest-person-who-ever-lived-or-a-fraud