Jeanne Calment on her 121st birthday in 1996
Jeanne Louise Calment (1875-1997)
is widely considered the oldest person in history – at least, the
oldest verified by Guinness’ World Records’ stringent standards. (There
appear to be
others who are/were older, but there usually isn’t enough documentation to absolutely prove it.) She lived for an impressive
122 years, 164 days.
However, a theory has been making the rounds in the media recently –
and gaining in popularity – is that the French supercentanarian was a
fraud, that she was really Calment’s daughter Yvonne (1898-1934). The
theory goes that Yvonne didn’t die in 1934, but her mother did instead,
and that she took her identity, dying at the age of 99. This theory is
nothing new, but has been largely dismissed until recently. Her age is
one of the most well-documented in history. The new proponent – Nikolay
Zak – has presented an interesting case; but gets some of his facts
wrong. The following paper by the original researchers who verified
Calment’s age – Jean-Marie Robine, DED, Michel Allard, MD,
François R. Herrmann, MD, MPH, and Bernard Jeune, MD – presents the case that Calment was almost certainly authentic, the only
officially documented person to reach – or overtake – 120 years.
Abstract
Background
The 122 years and 164 days age claim of Jeanne Calment, the world
oldest person who died in 1997, is the most thoroughly validated age
claim. Recently the claim that families Calment and Billot organized a
conspiracy concerning tax fraud based on identity fraud between mother
and daughter gained international media attention.
Methods
Here, we reference the original components of the validation as well
as additional documentation to address various claims of the conspiracy
theory and provide evidence for why these claims are based on inaccurate
facts or unrelated to the death of Yvonne Billot-Calment, the daughter
of Jeanne Calment, in 1934.
Results
Also, countering the contention that the occurrence of a 122 year old
person is statistically impossible, mathematical models are presented
which also supports the hypothesis that though extremely rare, as would
be expected for the oldest person ever, Jeanne Calment’s age claim is
plausible.
Conclusions
In total, the quality of the investigation supporting the claim of
conspiracy as well as the mathematical analysis aiming to back it do not
reach the level expected for a scientific publication.
Since she died at the age of 122 in 1997, Jeanne Calment (JC) has
been recognized as the record-holder for longevity of the human species.
Though a few researchers have been skeptical based on statistical
arguments, most researchers in the field have been convinced by the
thorough documentation and validation carried out and published by
French researchers, Michel Allard (MA) and Jean-Marie Robine (JMR) with
the help of her Doctor Victor Lèbre (1–6). She was at that time and still is among the best documented supercentenarians, that is, people over 110 years old (5,7–9).
However, in December 2018, JC’s record of longevity was contested by
the gerontologist Valery Novoselov in an interview published on a
website (10) and by the laboratory technician Nikolay Zak in a manuscript posted on ResearchGate.net (11).
Based upon inaccurate or unrelated facts, they propose a conspiracy
theory, claiming that JC died in 1934 and that her daughter, Yvonne
Billot (YB), committed an identity fraud in order to avoid paying
inheritance taxes. Novoselov and Zak accused the Calment and Billot
families having conspired to commit this identity fraud. Eventually, Zak
revised his preprint and it was accepted for publication by Aubrey De
Grey, for the journal Rejuvenation Research (12).
Most of age claims 115 years and older are false, either
intentionally or unintentionally, and thus, it is particularly important
to compile multiple forms of proof that agree with one another in order
to sufficiently substantiate such claims (13–16).
This is even more so the case when a claim would establish a new record
for the world’s ever-oldest person. JMR and MA therefore compiled and
described multiple pieces of intraconsistent evidence supporting the age
of death of JC at 122 years (1,2,4).
In the process of validating the claim, particularly one as rare as
the oldest person ever, one must carefully rule out all the possible
causes of a false positive. It is particularly helpful, as was the case
with JC, for the claimant to be alive at the time of the validation and
to be able to ask them questions to both rule in a true positive and
rule out a false positive. During the 3 years, from 1993 to 1995, JMR
and MA regularly visited and interviewed JC and despite few small
inconsistencies not once did these conversations produce a suspicion of
fraud and especially not a possibility of an identity switch between
mother and daughter.
The hypothesis of an identity switch between mother and daughter is
not new. It was already considered in 1995 when the epidemiologist
Bernard Jeune (BJ) and demographers Väinö Kannisto (VK) and James W.
Vaupel (JWV) went to visit JC the day after her 120 years anniversary
and went through all the 30 documents that the French researchers had
found in the archives of Arles. In their book about her (1), MA and JMR had included a photo of JC and her daughter Yvonne with the following caption in French “Quelle est l’une, quelle est l’autre?”, meaning “Who is who?”
The purpose of the photo was to show just how young JC appeared for her
age and thus how slowly she was aging. However, in 1995 when BJ, VK,
and JWV were working in the archives of Arles, they focused on any
possible confusion of birth records among family members particularly
between siblings, but also JC and YB. They found a fraud improbable
given the position and the life circumstances of the Calment family in
this relatively small city of Arles where many people knew JC and her
daughter. BJ, VK, and JWV were more looking for an identity switch with a
younger sister than one between mother and daughter.
In this current paper, we are more specifically focused on the switch
hypothesis between daughter and mother raised by Zak and Novoselov.
After a summary of the steps taken to validate JC’s age in the 1990s, we
specifically address Zak’s contention with new facts of the case.
Finally, we discuss why his belief that her claim is mathematically too
improbable is incorrect.
Summary of the Validation of JC’s Age
Several publications provide the details of the validation of JC’s
age at death of 122 years. Much of these validation efforts occurred
while JC was alive, once she surpassed the age of 117 years. The first
step to validate her age claim was to look up her birth record. Since
the 16th century and the French Revolution and in the case of Catholics,
there are usually two birth registrations, one civil and one religious.
In the case of JC, we located both the civil birth record and the
baptism record and they exactly corresponded with one another. At that
time, the civil vital events were noted in sequential individually bound
books, with a new book created for each year. We located her civil
birth record in the 1875 book on the correct page of the book
corresponding to her birthdate.
Familial Reconstitution Method
Familial reconstitution is a critical part of the validation process,
in which one determines that all the relative’s ages make reproductive
sense (13–16). For
example, a case would not be valid if a mother appeared to have a child
before the age of 10 or if one sibling was 60 years older than another.
In the case of JC’s pedigree, all of the ages make sense. Beginning with
her birth documents and the information she provided, we constructed a
family pedigree that included JC’s parents, siblings, and descendants.
All of the birthdates made sense. Her parents married at the age of 23
years. They had four children born in 1862, 1863, 1865, and 1875. The
two oldest siblings, Antoine and Marie died in infancy. Her brother,
François was born 10 years before her (1,2,4–6).
Regarding the family pedigree, Zak argues that a case such as JC
should demonstrate familial evidence of exceptional longevity. Indeed,
about 50% of current centenarians have a history of an ancestor living
into their nineties or older, but the other half do not, and in the case
of supercentenarians (those ages 110+ years), the frequency appears to
be even less (Thomas Perls, personal communication). Many potential
centenarians died as infants when infant mortality was so high. Also,
many adults who had a familial predisposition for longevity did not
achieve such ages because of what today would be a readily reversible
cause of death (eg, infection, trauma). Still, in the case of JC, JMR
and MA have disclosed an exceptional concentration of long-living
ancestors. Indeed, JC had a Total Immediate Ancestral Longevity (TIAL)
of 477 compared with 289 for the sum of the ages at death of the six
immediate controls of the reference family (6).
Multiple Documents from Throughout the Person’s Life That Are Consistent in Their Documentation of the Claimant’s Age
One of the most important tenets of age validation is that the
claimant should have been known within the local community well before
the age of 100 years, thus not appearing suddenly at a claimed
extraordinary age. Thus, JMR and MA searched for proofs of the existence
of JC well before she surpassed the age of 100 years. The general
census of the French population, administered by each municipality,
offered such proofs. From 1801 to 1946, the census was conducted every 5
years except for 1916 and 1941 because of the wars. Since 1946, the
census was carried out irregularly in 1954, 1962, 1968, 1975, 1982, and
1990.
The details of the comprehensive multiple forms of written proof of
JC’s ages throughout her life, including the above, are noted in
reference (4). In the discussion of that article, the gathered evidence was summarized as:
…seven direct civil status documents (i) bear witness to
the identity of Jeanne Louise Calment from her birth date to her death.
(ii) They are complemented by numerous indirect civil status documents
which confirm the sequence of the information (iii) by 14 direct
documents from censuses that confirm the age or the birth date of Jeanne
Calment [1876, 1881, 1886, 1901, 1906, 1911, 1921, 1926, 1936, 1946,
1954, 1962, 1968, 1975], (iv) and by direct or indirect parish
documents, (v) by notarial documents (marriage contracts, sale of a
house), (vi) by a medical doctorate dissertation, (vii) and by newspaper
articles.
Links to copies of these censuses are provided in the Supplementary Material (SOM, A1).
Though we discuss Zak’s arguments below regarding what he views as
inconsistencies in the JC age claim, we point out here one issue that he
asserts, which is the lack of mention of JC’s 100th birthday in the
local newspaper. However, this is clearly countered by the 1975 census
indicating her date of birth and the fact that many centenarians do not
have their birthdays celebrated in the news for a range of reasons.
Furthermore, Zak’s coinvestigator, Novoselov, in a published interview,
indicated that JC was visited by the Mayor of Arles on the occasion of
her 100th birthday (10).
Zak also believed that JC’s apparent absence from the 1931 census was
supportive of his accusation of identity fraud. 1931 was a difficult
year for the census since hand-written entries were replaced with
typewritten entries and that year’s entries are well known for many
mistakes; so much so that census officials returned to hand-written
entries in 1936 and did not begin to use typed entries until 1962. Some
of the many incorrect entries in the 1931 census are shown in the SOM
(see SOM, A2)
Claimant Interviews
From their 1993 and 1994 interviews with JC (ages 117 and 118 years),
JMR and MA listed the following facts stated by JC who provided these
details from memory (Table 1) (4):
Table 1.
Facts Provided by Jeanne Calment to Jean Marie Robine and Michel Allard During Their 1993 and 1994 Interviews with Her
| (i) |
She was born on February 21st, 1875 in Arles; |
| (ii) |
Her father, Nicolas Calment, was a shipbuilder; |
| (iii) |
Her mother, Marguerite Gilles, was from a family of millers; |
| (iv) |
Her godfather was named Louis Pages [or Paget]; |
| (v) |
Her godmother was Jeanne Gilles, her maternal aunt; |
| (vi) |
She had a brother, François Calment, who was ten years older than her and who died at 97 years of age; |
| (vii) |
She married her cousin, Fernand Calment; |
| (viii) |
They lived for some time with Mrs. Maria Calment, [maiden name Felix], her mother-in-law; |
| (ix) |
Ever since, she lived in the same house in Gambetta Street [at the
corner of St-Estève Street, next to Rue de la République], in an
apartment located above their department store named “Grand Magasin
Calment”; |
| (x) |
She left this house when she was 110 years old to live in a nursing home, “La Maison du Lac” where we met her; |
| (xi) |
She gave birth to one child, a daughter, Yvonne, [Calment], born in Arles; |
| (xii) |
Her daughter married [Captain] Joseph Billot; |
| (xiii) |
They had one son, Frédéric [born Billot]; |
| (xiv) |
Her daughter Yvonne died when she was 36 years old; |
| (xv) |
Her grandson, Frédéric Billot, also died at 36 years old; |
| (xvi) |
She mentioned Marthe Fousson, one of the first servants she had in
her service, when she was newly married [Marthe was noted in the 1906
and 1911 censuses as living with the family]. |
Again, regarding Zak’s hypotheses, he posited that JC’s daughter,
Yvonne, could have provided facts to JMR and MA by perhaps access to a
diary or other set of records previously in the possession of her
mother. In considering this hypothesis, note that had she not died in
1934, at the age of 36, in 1993 YB would have been 95 years old. It is
not reasonable to claim that she could provide, for example, the names
of JC’s godparents based upon her recollection of what she might have
read many years previously in an attempt to maintain a fraud.
Additionally, Zak indicated that there was a family move in 1888,
when JC was 13, that was not mentioned by JC in the interviews of her by
JMR and MA and thus this oversight is an important inconsistency that
supports an assertion of a conspiracy to commit fraud. Indeed, we did
not learn about this move during our interviews with JC, but we have
since determined that the move was only 150 m away in the same
neighborhood in 1884 or 1885 when JC was 9 or 10 (not 13) years old (see SOM B). We do not feel it is remarkable that a minor move such as this at the age of ten would not be mentioned.
The Conspiracy Theory of an Identity Switch
According to a published interview, Novoselov asserted that JC did not look frail enough to be a supercentenarian (10).
He referred to the surprise of the Mayor, who made it a habit to visit
centenarians on their birthdays, that at age 100 years, JC appeared so
spry. Actually, such spryness is exactly what one would expect from a
100-year-old destined to live another 22 years, to the age of 122 years.
In their study of people living to supercentenarians, New England
Centenarian Study (NECS) investigators noted that the morbidity and
disability profiles of these individuals support James Fries compression
of morbidity hypothesis (17,18).
That is at the limit of human life span, aging-related diseases and
syndromes that increase mortality risk must be delayed towards the time
of death. The NECS found that supercentenarians generally require
minimal or no assistance with their activities of daily living or
clinically manifest any of the major aging-related diseases (heart
disease, stroke, diabetes, hypertension, cancer, or chronic obstructive
pulmonary disease) at the mean age of 106 years (17).
Photos of both JC and Sarah Knauss, who died at the age of 119 years
in 1999, are examples of how supercentenarians have a history of aging
so remarkably slowly. Supercentenarians are typically characterized as
having delayed or escaped major diseases and compressed the time they
experience severe decline towards the end of their extremely long lives,
and it is not until the relatively short time at the end of their lives
that they demonstrate frailty (Figure 1).
Figure 1.
Photos of Sarah Knaus, ages 99 years and 119 years (the latter by
Theo Westenberger) and Jeanne Calment at 116 years and 122 years.
Nonetheless, Novoselov approached Zak to analyze available mortality
data to determine whether mathematically, JC was an impossible outlier (10).
From his preprint uploaded on Researchgate.net, it appears that Zak
concludes that it was mathematically impossible for a person to reach
the age of 122 years. He then researched what had been written about JC
and subsequently constructed a story that he believes supports a case of
fraud (11,12).
In the preprint, Zak devotes just a few paragraphs to his
mathematical refute of JC’s age claim. He bases his conclusion on two
assumptions in both the preprint and later in his article, that “the
force of mortality is almost constant after 105 years” thus half of
supercentenarians die “during any year of follow up,” and that it “does
not vary much with sex, country and year of birth” (11,12).
Initial studies argued for an exponential increase in the mortality
rate at older age but then a deceleration at extreme ages. In fact, it
is difficult to assess if mortality rates keep increasing with age or
tend towards some mortality plateau. Data quality issues combine with
small numbers to render these issues to be quite complex and thus
approaching the problem with one possible model is incorrect. Zak
declined to investigate multiple possible models of mortality. Also,
given that generally 85% of centenarians and 90% of supercentenarians
are female, considering that there are no differences in sex is grossly
incorrect. We formally address the statistical plausibility of a person
living to age 122 years later in this paper.
To support the hypothesis of an identity switch one must have a
motive justifying such a fraud, and then show that such a substitution
was practically possible. As for a motive for why the Calment and Billot
families would conspire to commit fraud, Zak wrote,
“Perhaps the Calment family suffered from taxation
after the death of Maria Felix (widow of the founder of the store,
Jacques Calment) and especially after the death of Jeannes father
Nicolas Calment, the owner of land and real estate in the surrounding
villages in 1931. The inheritance tax for the farm in Saint Martin de
Crau could amount to hundreds of thousands of dollars in modern money.
It is not hard to imagine that the family had neither desire nor ability
to pay the tax, especially twice in a row (here, one should recall that
Jeanne hated socialists).” (12)
This motive is not only speculation, it has no basis. In actuality,
French real estate transactions have resulted in notarial deeds for
centuries. These documents are publicly available after 70 years and in
the case of JC a dozen transactions established before 1949 are
available (see SOM B). Zak is negligent in not noting
that Nicolas Calment (NC) had given all his property to his children on
March 15, 1926 in exchange for an annual life annuity of 5,000 francs
that his children had to pay him until his death. The only financial
consequence upon the death of NC in 1931 is the extinction of the life
annuity.
According to Zak, another motive could be an annuity contract
presumably signed before 1934 and still in operation at the time of her
death in 1997 (12).
This second motive seems also to have no basis as it is not reported in
the declaration of assets that JC made in 1946 on the occasion of the
national solidarity tax in application of the Ordinance of August 15,
1945 (see SOM B).
An important argument against Zak’s conspiracy theory is the fact
that the Calment family was a well-known family in Arles. Her
father-in-law had established the local and prominent department store,
Grand Magasin Calment, and her father was a city councilman. Yvonne’s
husband was a member of the French Legion of Honor. Novoselov, in his
interview (10) stated
that the community would not have noticed a switch because Arles is
actually based in a large county and that JC and her daughter spent some
of their time in a homestead 16 km away from Arles. Zak himself negates
this notion in his preprint stating that “Jeanne Louise Calment had
been alive for 12 years and 164 days after her 110th anniversary and was
under close (and with growing age) scrutiny from the general public and
scientific community” (12).
Since Zak’s accusations of fraud and conspiracy, at least four
relatives have released photos showing that Yvonne was, before her
marriage in 1926, active and well- integrated within her social group of
young women (See SOM C). Of course, this social circle
of friends would have been deceived into believing that it was JC who
lived beyond 1934, rather than her daughter, YB. According to the local
press, at the funeral of YB in 1934, “A huge crowd drove last Saturday to her last home, Mrs. Billot Calment died at the age of 36 years.” (see SOM C).
The death notice of YB has been sent on behalf of 34 people and their
children, the staff of the House Calment and 13 different families (see SOM C
for the notice). People were invited to gather at the family house and
we can guess that many of them attended the funeral wake. In these
circumstances, unless we accept the idea of the complicity of dozens of
people, a substitution between the bodies of JC and YB was virtually
impossible.
Also, such a substitution would have led to an incestuous family
configuration. Frédéric Billot, the son of YB, was 7 years old when his
mother died in 1934 and Fernand Calment, the husband of JC was still
alive for several years beyond Yvonne’s death. Therefore, according to
Zak, YB took the place of her mother and therefore Fernand and Yvonne
would have had to act as if they were married. Frédéric, at the age of
seven would have had to act as if his mother had died and pretend that
Yvonne was really his grandmother, rather than mother. His own father,
Captain Joseph Billot, the husband of Yvonne, would have had to be
complicit with the ruse. A conspiracy to commit identity fraud would
have required the participation of many people.
Zak also asserted that Yvonne’s absence from the 1931 census was
evidence of fraudulent behavior. In fact, the reason she is not listed
is because at the time, she was staying in Leysin, Switzerland, being
possibly treated for tuberculosis (Figure 2).
Leysin was home to a number of sanatoriums for the treatment of
tuberculosis, and a famous one in particular, the Sanatorium
Universitaire (19).
Figure 2.
Photo of Yvonne in 1931, staying in Leysin, likely at one of its numerous sanatoriums for treatment of tuberculosis.
Yvonne’s stay in Leysin, 3 years before her death underlies that she
was an ill woman at the time and speaks to the authenticity of her death
at the age of 36 in 1934. JC had told MA and JMR that her daughter’s
illness had started after the birth of Frédéric. At the end of this
conversation, JC turned to Victor Lèbre, her doctor, saying, “When
they put me in the coffin, put the photo of my grandson at my right, and
the one of my daughter at my left, and they will be buried with me. Oh,
that will only be an imaginary burial, they are both in the ground
already, but that way, they will be beside me.” (1,2)
A military file of Joseph Billot, YB’s husband, indicates a granted
leave on personal grounds for 5 years from June 10, 1928 and then
renewed for another 5 years on June 10, 1933 (See SOM C).
A 1928 letter written by Joseph Billot’s superior, indicates the
reasons for the requested leave; namely the poor health of his wife. He
wrote “Captain Billot made an application on March 30, 1928, to be
admitted for a granted leave. It is with regret that he leaves the army,
but his interests and the health of his wife oblige him to go to live
in the South, near Arles.” (see SOM C). The new
documents consulted since Zak’s story are consistent with the fact that
Yvonne was sick, presumably suffering from tuberculosis, a major cause
of death at the time (20).
The paragraph of Zak on a possible fibroma is another weakness “In
one of the few photographs of the young Yvonne that exist, one can see a
small fibroma on the nose (it could be a scan defect, but it is also
visible on different scans). A similar fibroma can be seen in one of the
photos of the old Calment. Interestingly, it is absent from later
photos, indicating that it was removed. If Yvonne removed it more than
once, that could explain its slightly different locations inFigure 3A and Band also the fact that the fibroma appears smaller in the older woman, even though fibromas grow over time.” None of the photos of the young YB (see SOM D) and the many photos of JC taken after 1936 (see SOM D) shows a fibroma. In Figure 3B,
of the Zak paper, JC is 114 years old. Zak suggests that the fibroma
has been removed when JC was a resident of the nursing home Maison du
Lac. Of course, there is no mention of such intervention in the
dissertation of Catherine Levraud (21)
where she summarizes, with great detail, the medical history of JC
after her arrival in the nursing home, between the ages of 111 and 118.
Other weaknesses of his arguments, for instance about JC’s size and JC’s
eye color have already been pointed out by the publication by Le Bourg (22).
Figure 3.
Number of deaths at aged 100 years and older, France 1818–2016, according to the Human Mortality Database. Source:
https://www.mortality.org.
The Statistical Plausibility of a Human Surviving to Age 122 Years
Zak’s interest in the sociodemographic aspects of the JC age claim
began with his contention that JC’s ability to survive to age 122+ years
is mathematically impossible. Thus, here we also refute his
mathematical argument.
In the broadest sense, the statistical universe of JC is composed of
all the lifetimes of human beings throughout the world. Of course, the
ages of survival for the vast majority of these lives are unknown.
Therefore, we consider a subset within a defined period of time where we
have some degree of confidence in its completeness and a substantial
similarity in terms of sociodemographic and culture to JC. Thus, we
chose France where JC was born and where she lived, and for which we
have continuous information on the ages at death since 1816. These data,
assembled by the General Statistics of France, and then by the National
Institute of Statistics and Economic Studies are available at the Human
Mortality Database (HMD, https://www.mortality.org).
In this database, approximately 142 million deaths were recorded in
France between 1816 and 2016 and are segregated by sex, by single age
from age 0 to an open-ended age group “110+,” by year of birth from 1706
to 2016 and by year of death. Figure 3 displays the changes over time in the number of deaths recorded at aged 100 years and older for both males and females.
Overall, the number of deaths of centenarians did not increase in
France until the post WW II period for women and the 1990s for men. The
zoomed in view on the right panel shows that the number of centenarians
decreased during the initial period, from 1816 to 1880, probably due to
the improvement in the quality of the statistics and then remains stable
during a second period, from 1880 to the end of the WWII. In 1975, when
JC turned 100 years old, 684 deaths of centenarian women were
registered, and in 1997, the year of her death, there were 2,727 deaths
recorded. As the HMD data are censored beyond the age of 109, we have
supplemented them with data from the International Database on Longevity
– IDL (https://www.supercentenarians.org),
compiling lifetimes greater than 105 years. These data relate to 9,466
individual records of people who died between 1982 and 2017 in France.
Although virtually no one died at age 105 or older in the 1980s, there
are several 100 deaths recorded above this age in the most recent years.
They are mostly women.
The Exceptional Case of JC
Figure 4 depicts
the age at death of JC (1997, age 122 years) in the context of the above
described data. Over the long term, changes in the Maximum Reported Age
at Death (MRAD) demonstrated large fluctuations and much smoother
changes were observed with the measure Highest Age Providing at Least 30
deaths (HAPaL_30). Thus, we chose HAPaL_30 to assess the limits of
longevity without its extreme fluctuations. The 122-year lifetime of JC
is not only quite far from the value of HAPaL_30 which reached 106 years
in 1997 when JC died but also from the values of the MRAD in the
neighboring years, that is, 112 years. Obviously, 122 years appears as
an outlier, even among the extreme values measured by the MRAD.
Cohort Reconstruction and Modeling
Using the death data described above, organized by single age,
period, and cohort of birth (Lexis triangles), we reconstructed the
cohorts born in 1875 as in the case of JC and in 1903, the most recent
extinct cohort, and computed the probability (qx) that someone aged A[x] will die before reaching age A[x+1]. Then, we plotted the mortality risk expressed as the line plots of qx over age and modelized it using three usual functions: three-parameter exponential (b0 + b1*b2age), four-parameter Gompertz function = b0 + b1*exp(-exp(-b2*(age – b3))), and four-parameter logistic function = b0 + b1/(1 + exp(-b2*(age – b3))) (equations 1–3).
- Equation 1: Exponentialqx=b0+b1bAge2
- Equation 2: Logisticqx=b0+b11+e−b2(Age−b3)
- Equation 3: Gompertzqx=b0+b1e−e−b2(Age−b3)
Modeling of the mortality risk of the 1875 and 1903 birth cohorts
using exponential (short dash line), Gompertz (plain line), and logistic
(long dash line) functions are shown in Figure 5.
The open dots correspond to the one used to compute the models. The
plain dots correspond to ages above (HAPaL_30), those with less than 30
deaths occurrence and excluded from the models. The parameters of the
models are given in Table 2 along with their coefficient of determination, which exceeds 99%.
Table 2.
Parameters of the Mortality Models with Their Coefficient of Determination
| (R2) Model |
b0 |
b1 |
b2 |
b3 |
R2 |
| Logistic 1875 |
0.0071 |
0.6819 |
0.1078 |
97.8033 |
0.9921 |
| Logistic 1903 |
0.0062 |
0.6403 |
0.1241 |
99.7883 |
0.9986 |
| Gompertz 1875 |
0.0160 |
1.4365 |
0.0379 |
108.0642 |
0.9917 |
| Gompertz 1903 |
0.0138 |
1.1814 |
0.0463 |
106.1697 |
0.9979 |
Figure 5.
Modeling of the mortality risk of the 1875 and 1903 birth cohorts.
For determining the probability of reaching JC’s age, we used the
fitted parameters to generate three sets of simulations. The exponential
function diverging too quickly was not used here.
- Simulations set 1: starting with a sample of 10 centenarians, we
applied at each age the mortality risk of the logistic and Gompertz
functions with a pseudo-random number generator determining the death or
living status of each virtual centenarian until the extinction of the
whole sample. The simulations were run 500,000 times to determine the
maximum age that could be reached and the probability of reaching it
with its binomial exact 95% confidence interval.
- Simulations set 2: same as above but starting with 500 centenarians and 100,000 runs.
- Simulations set 3: same as above but starting with 100,000
centenarians and 500 runs. All computations were performed with the
Stata software release 15.1. Results of the 12 sets of simulations (3
samples size × 2 models × 2 cohorts) are given in Table 3.
Table 3.
Maximum Age Reached According to 12 Simulations Sets with Varying Sample Size and Resampling
| Model |
Simulations Set 1 |
Simulations Set 2 |
Simulations Set 3 |
| Sample size (number of centenarian) |
10 |
500 |
100,000 |
| Number of resampling |
500,000 |
100,000 |
500 |
| Logistic 1875 |
|
|
|
| Maximum age |
119 |
121 |
121 |
| Probability of maximum age or 122+ |
3/50,000,000 |
4/50,000,000 |
3/50,000,000 |
| Lower bound 95% CI |
0.0000000124 |
0.0000000218 |
0.0000000124 |
| Upper bound 95% CI |
0.0000001750 |
0.0000002050 |
0.0000001750 |
| Logistic 1903 |
|
|
|
| Maximum age |
121 |
123 |
123 |
| Probability of maximum age or 122+ |
2/50,000,000 |
2/50,000,000 |
5/50,000,000 |
| Lower bound 95% CI |
0.0000000005 |
0.0000000005 |
0.0000000325 |
| Upper bound 95% CI |
0.0000001110 |
0.0000001110 |
0.0000002330 |
| Gompertz 1875 |
|
|
|
| Maximum age |
120 |
122 |
120 |
| Probability of maximum age or 122+ |
1/50,000,000 |
1/50,000,000 |
1/50,000,000 |
| Lower bound 95% CI |
0.0000000005 |
0.0000000005 |
0.0000000005 |
| Upper bound 95% CI |
0.0000001110 |
0.0000001110 |
0.0000001110 |
| Gompertz 1903 |
|
|
|
| Maximum age [year] |
119 |
122 |
121 |
| Probability of maximum age or 122+ |
1/50,000,000 |
1/50,000,000 |
2/50,000,000 |
| Lower bound 95% CI |
0.0000000005 |
0.0000000005 |
0.0000000005 |
| Upper bound 95% CI |
0.0000001110 |
0.0000001110 |
0.0000001110 |
With samples of 500 and 100,000 centenarians, the maximum age ranged
from 120 to 123. The Logistic and Gompertz models yield similar results,
with the Logistic 1903 outperforming the others by a small margin. It
must be underlined that these maximum ages were observed even when
extrapolation of the functions leads to qx exceeding 0.6 that
is a probability of dying above 60%. Thus, in silico, JC’s age can be
reached and even exceeded, even though the probability remains very low.
In the best simulation set (set 3 and Logistic 1903), this event
occurs on average once every 10 million centenarians. Such a result is
compatible with previous estimations (23,24) including a first estimation proposed by Väinö Kannisto and Roger Thatcher (unpublished in 1993, available on request).
Based on these data, the survival of JC to 122 years is possible.
Considering that the world has experienced somewhere between 8 and 10
million centenarians since at least the 1700s, then a person age 122
years by around the late 1900s is reasonable. According to the
Population Division of the United Nations, by 2100, the global number of
centenarians within a single year could be as high as 25 millions (25) and so the observance of yet another person age 122 or perhaps even a little older is also reasonable.
Conclusion
Jeanne Calment claim as the record-holder for longevity for the human
species, at the 122 years and 165 days, remains valid. The material
gathered in favor of its accuracy far outweigh Zak’s hypothesis of
identity fraud. Our mathematical models show that a person achieving the
age of 122 years by the late 1990’s would be possible. Empirically
though, the only way to assess that it is an accurate observation is to
examine the evidence supporting and challenging the age claim.
Zak never mentioned the existence of well-validated extreme cases of
longevity. Sarah Knauss, who passed away at age 119 in 1999, and
Marie-Louise Meilleur, who died at age 117 years in 1998, make JC
appears less exceptional than if, for example, the next oldest person
was 115 years old. Since 2015, five other women have reached the age of
117 years: three of them in 2017 (the Japanese woman Misao Okawa (26), the Italian woman Emma Morano (27) and Violet Brown from Jamaica) and two of them in 2018 (the Japanese women Nabi Tajima and Chiyo Miyako (26)). The cases of Violet Brown and Nabi Tajima have not yet been thoroughly validated.
Should Zak and his colleagues wish to contest Sarah Knauss’ age, they
should keep in mind that not only was her age also well validated with
multiple documents throughout her life, the age of her daughter Kitty,
who lived to 101 years, was also validated (correspondence with the New
England Centenarian Study).
We have identified three main limitations of this study. First, time
and space limitations to answer in this journal to the dozens of
arguments challenging the reported age of JC gathered by Zak and
Novoselov. Therefore, we only focused on the main arguments concerning
the motive and the practicability of the identity fraud. However, we
examined many other arguments and we discovered some errors which at
least show great negligence in their work. Second, legal limitations as
the most recent financial transactions concerning JC will not be
publicly available before 2067, 70 years after her death. Third, ethical
limitations as the most recent transactions involved people who are
still alive. For instance, some allied families close to the
Calment/Billot family informed us about the most recent financial
transactions but asking us not to circulate this information. In other
words, there is still many material to confirm the biography of JC.
As expected for the age of the oldest person in the world, the
probability of her occurrence is extremely small. In his published
interview in leafscience.com, Novoselov requests a revalidation of the
case of Jeanne Calment. In a way, it is what we have provided with this
paper showing that JC remains the oldest human whose age is
well-documented.
In conclusion and coming back to the paper published by Zak, we would
like to stress the unacceptability of publishing an article with such
unfounded accusations claiming that members of the Calment and Billot
families collectively committed fraud. How was it possible that a paper
so full of unsubstantiated assertions could survive a responsible peer
review and subsequently be published in Rejuvenation Research? Based on the evidence that we bring in this paper, we call for a retraction of Zak’s article.
Acknowledgments
We thank the members of the families allied with the family
Calment/Billot, especially the family Billot/Guillet with Robert Billot
and Frédérique Skyronka, the family Billot/Taques with Claudie et
Christian Taque, the family Fassin with Claude Chaix, and the family
Mery with Gilberte Mery and her grand-son, who provided photographs and
new documents concerning JC, YB, and Captain Joseph Billot. We thank
national, regional, and municipal institutions which opened their
archives providing marriage contracts and other private financial
transactions, personal military files as well as personal tax files,
especially Les Archives départementales des Bouches-du-Rhône. We thank
Rémi Venture, director of the Arles library (Médiathèque) and Aurélie
Samson, acting director of the Arlaten museum for their help and advice,
as well as Les Amis du Vieil Arles (AVA) and Bernadette
Murphy. We thank our more regular collaborators, Caroline Bisson
genealogist in Marseille, Laurent Toussaint, a passionate researcher on
the supercentenarians and centenarians of ancient times, and Cyril
Depoudent, French correspondent of the Gerontological Research Group
(GRG), who helped us to collect and read these new documents. We thank
François Robin-Champigneul who read our initial manuscript and spotted a
few errors. We would like to thank the journalists who discovered and
circulated new documents such as Prescillia Michel and Olivier Sibille,
journalist at France 2, and Camille Le Pomellec, who conducted an
investigation into the JC case for Paris-Match, as well as all the
members of the Facebook group “Contre-enquête sur l’enquête Jeanne Calment”
who searched and provided some of the new documents. Finally, we would
like to thank Dr. George Garoyan and Dr. Catherine Levraud for the time
spent remembering JC’s health status in the 1990s.
Author Contributions
All authors, J.M.R., M.A., F.R.H., and B.J., equally contributed to
the design of the study and the writing of the paper. J.M.R. and B.J.
drafted the first version of the paper. F.R.H. and J.M.R. coordinated
the mathematical part.
Funding
This paper was published as part of a supplement sponsored and funded
by AARP. The statements and opinions expressed herein by the authors
are for information, debate, and discussion, and do not necessarily
represent official policies of AARP.
Conflict of Interest
None reported.
Read the original paper here (I left out their list of references):
Photos of Sarah Knaus, ages 99 years and 119 years (the latter by Theo Westenberger) and Jeanne Calment at 116 years and 122 years.
Photo of Yvonne in 1931, staying in Leysin, likely at one of its numerous sanatoriums for treatment of tuberculosis.
Number of deaths at aged 100 years and older, France 1818–2016, according to the Human Mortality Database. Source: https://www.mortality.org.
Individual observations and statistical indicator of Maximum Life Span (MLS): Maximum Reported Age at Death (MRAD) and Highest Age Providing at Least 30 deaths (HAPaL_30), females, France, 1818–2016. Source: https://www.mortality.org and https://www.supercentenarians.org.
Modeling of the mortality risk of the 1875 and 1903 birth cohorts.
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