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Cited by 299Insurance, Mortality, Demography, Risk ManagementGenetics, Aging, and Longevity in Model OrganismsAging and Gerontology Research

The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index; 4 of the 21 sources its claims cite were checked for support.

The plateau of human mortality: Demography of longevity pioneers

Open access
Barbi, Elisabetta, Lagona, Francesco, Marsili, Marco, Vaupel, James W., Wachter, Kenneth W.·2018·Science
DOI 10.1126/science.aat3119PMC PMC6457902
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Abstract

Mortality rates level off at extreme age: The demography of human longevity is a contentious topic. On the basis of high-quality data from Italians aged 105 and older, Barbi et al. show that mortality is constant at extreme ages but at levels that decline somewhat across cohorts. Human death rates increase exponentially up to about age 80, then decelerate, and plateau after age 105. Science , this issue p. 1459

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

Using validated ISTAT data on all Italian inhabitants aged 105+ from 2009–2015, the authors find essentially level mortality hazards beyond age 105. The results provide strong evidence for an extreme-age mortality plateau in humans.

Key findings

  • Across 3,836 carefully documented cases (463 males) in 15 birth cohorts (1896–1910), hazard curves are essentially constant beyond age 105.
  • The Gompertz slope estimate is \(b = 0.013\) (SE 0.017), not statistically significant; a likelihood ratio test fails to reject the constant-hazard null at a level of 0.44, in contrast to a slope as large as 0.103 at ages 65–80.
  • For the baseline 1904 cohort, the estimated plateau is \(a = 0.645\), corresponding to an annual probability of dying of 0.475 and an expectation of further life of 1.55 years.
  • The cohort effect is \(\beta_1 = -0.020\) (SE 0.008), statistically significant; the male effect \(\beta_2 = 0.033\) is plausible but not statistically significant.

Methods

  • Data: ISTAT-collected and validated individual survival trajectories of all Italian inhabitants aged 105 and over from 1 January 2009 to 31 December 2015; 3,836 cases, 463 males, 15 birth cohorts (1896–1910), with 2,883 observed deaths and 953 right-censored individuals.
  • Validation: municipality contacts, death certificates, survival certificates, and birth certificates for supercentenarians; age misreporting is believed minimal and the data are free of age ascertainment bias.
  • Analysis: maximum likelihood for truncated and censored survival data under a hazard model \(a\exp(bx)\exp(\beta_1 C + \beta_2 M)\), where \(C\) is cohort birth year minus 1904 and \(M\) indicates male; the null model constrains \(b = 0\), with likelihood ratio tests and cumulative-hazard checks.

Limitations

  • Stated: with 90% of person-years at risk before age 108, the ISTAT data cannot rule out alternatives such as a plateau followed later by decline, though supercentenarian estimates argue against such alternatives.
  • Stated: the 463 male survivors beyond 105 are too few for the gender effect to reach statistical significance.
  • Evident from the text: the analysis is based on a single nation, Italy, so generalization to other populations is not directly tested.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1126/science.aat3119

Cites

25 of 25 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

4 of 21 cited sources checked · 2 supported · 0 flagged · accuracy not yet measured

  • Interpretationcitation

    These well-estimated hazard curves share the qualitative pattern observed at extreme ages in widely differing species.

    “Thus these well-estimated hazard curves share the qualitative pattern observed at extreme ages in widely differing species (8, 18)”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [8] Vaupel JW, Carey JR, Christensen K, Johnson TE, Yashin AI, Holm NV, Iachine IA, Kannisto V, Khazaeli AA, Liedo P, Longo VD, Zeng Y, Manton KG, Curtsinger JW, Biodemographic Trajectories of longevity. Science 280, 855– 860 (1998). 9599158 source
    • cites [18] Vaupel JW, Biodemography of human aging. Nature 464, 536– 542 (2010). 20336136 PMC4010874 source

      In “Delay not deceleration,” the paper reports a constant annual probability of death at validated human ages 110–114. Its discussion of other species describes varied age-related mortality patterns, and its References list a study of slowing mortality in medflies; it does not establish that well-estimated hazard curves share the same extreme-age pattern across widely differing species. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
  • Premisecitation

    The fixed-frailty proportional hazard model of Vaupel, Stallard, and Manton implies approach to plateaus.

    “The fixed-frailty proportional hazard model of Vaupel, Stallard, and Manton (19) (with precursor 20) implies approach to plateaus (5, 8, 18)”
    Quote in the paperSubstantial claim1 of 4 sources checked
    • cites [19] Vaupel JW, Manton KG, Stallard E, The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439– 454 (1979). 510638 source
    • cites [5] Thatcher AR, Kannisto V, Vaupel JW, The force of mortality at ages 80 to 120. (Odense University Press, 1998).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [8] Vaupel JW, Carey JR, Christensen K, Johnson TE, Yashin AI, Holm NV, Iachine IA, Kannisto V, Khazaeli AA, Liedo P, Longo VD, Zeng Y, Manton KG, Curtsinger JW, Biodemographic Trajectories of longevity. Science 280, 855– 860 (1998). 9599158 source
    • cites [18] Vaupel JW, Biodemography of human aging. Nature 464, 536– 542 (2010). 20336136 PMC4010874 source

      The References section lists Vaupel, Manton, and Stallard’s work on individual frailty and separately lists work on mortality-rate deceleration, but does not say that a fixed-frailty proportional-hazard model implies an approach to plateaus. Searches for plateaus, proportional hazards, frailty, and mortality deceleration found no passage in our copy establishing that implication. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
  • Findingown data

    The study estimates hazard rates from data on all Italian inhabitants aged over 105 between 2009 and 2015 (born 1896-1910), comprising 3836 carefully documented cases.

    “Here we estimate hazard rates from data on all Italian inhabitants aged over 105 between 2009 and 2015 (born 1896–1910), 3836 carefully documented cases.”
    Quote in the paperSubstantial claim
  • Findingown data

    Hazard curves are level, essentially constant beyond age 105.

    “We find level hazard curves, essentially constant beyond age 105.”
    • Also stated in: § Abstract · plain
      “Here we report a curve of death rates by age for recent cohorts of Italians, a curve essentially level over 105.”
    • Also stated in: § Abstract · hedged
      “Our best-estimated trajectory for the 1904 cohort from our modeling is the flat curve, the plateau, shown in Fig. 1b.”
    Quote in the paperSubstantial claim
  • Findingown data

    Increases in samples from row to row in Table 1 bear testimony to improvements in survival from cohort to cohort at ages before 105.

    “Increases in samples from row to row bear testimony to improvements in survival from cohort to cohort at ages before 105”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. 8
  • It may state two separate claims as one. 15

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Elegant Gamma-Gompertz distributions for deaths arise naturally in the framework.

    “and elegant Gamma-Gompertz distributions for deaths arise naturally in the framework (21–24).”
    Quote in the paperNot a substantial claim1 of 4 sources checked
    • cites [21] Finkelstein MS, Esaulova V, Asymptotic behavior of a general class of mixture failure rates. Adv. Appl. Prob. 38, 244– 262 (2006). source
    • cites [22] Steinsaltz DR, Wachter KW, Understanding mortality rate deceleration and heterogeneity. Math. Pop. Studies 13, 19– 37 (2006). source
    • cites [23] Missov TI, Finkelstein MS, Admissible mixing distributions for a general class of mixture survival models with known asymptotics. Theor. Pop. Bio. 80, 64– 70 (2011). 21600234 source
    • cites [24] Missov TI, Vaupel JW, Mortality implications of mortality plateaus. SIAM Review 57, 61– 70 (2015). source

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Interpretationcitation

    Evolutionary theories of senescence including the mutation accumulation theory and age-dependent effects of genetic load offer promising ingredients toward a joint explanation of both the phases of exponential increase and extreme age plateaus.

    “Evolutionary theories of senescence including the mutation accumulation theory and age-dependent effects of genetic load (25) also offer promising ingredients toward a joint explanation of both the phases of exponential increase and extreme age plateaus.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [25] Wachter KW, Steinsaltz DR, Evans SH, Evolutionary Shaping of Demographic Schedules PNAS 111(s3), 10846– 10853 (2014). 25024186 PMC4113925 source

  • It may state two separate claims as one.

    Findingown data

    Under the alternative hypothesis, the Gompertz slope parameter estimate b = 0.013 with standard error 0.017 is not statistically significant at the 5% level and is practically indistinguishable from zero.

    “Under the alternative hypothesis, the Gompertz slope parameter estimate b = 0.013 with standard error 0.017, is not statistically significant at the 5% level and is practically indistinguishable from zero.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Death rates which increase exponentially up to about age 80 do decelerate thereafter and reach or closely approach a plateau after age 105.

    “In this setting with clean data from a single nation and straightforward estimation, death rates which increase exponentially up to about age 80 do, as we report here, decelerate thereafter and reach or closely approach a plateau after age 105.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Findingown data

    Death during the follow-up was observed in 2883 cases and 953 individuals are right-censored, i.e., still alive at the end of the study.

    “Death during the follow-up was observed in 2883 cases and, as a result, 953 individuals are right-censored, i.e., still alive at the end of the study.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    This near-negligible slope stands in striking contrast to the slope as large as 0.103 at younger ages (65-80) in Fig. 1b, which is paired with a log hazard at 65 of log(0.015).

    “This near- negligible slope stands in striking contrast to the slope as large as 0.103 at younger ages (65–80) in Fig. 1b, which is paired with a log hazard at 65 of log(0.015).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data

    Less than 4% of these individuals were born abroad.

    “Less than 4% of these individuals were born abroad.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    The present study based on ISTAT data includes 3836 cases, 463 of whom are males, across 15 birth cohorts (1896-1910).

    “The present study based on ISTAT data includes 3836 cases, 463 of whom are males, across 15 birth cohorts (1896 – 1910).”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    A straight-line fit based on ages 65 to 80, where the Gompertz model does appear to hold, fails at later ages and far overshoots the estimated plateau beyond age 105.

    “A straight-line fit based on ages 65 to 80, where the Gompertz model does appear to hold, fails at later ages and far overshoots our estimated plateau beyond age 105.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Fig. 2 shows absence of curvature for Italian women born in 1904, as do plots for other cohorts not included.

    “Fig. 2 shows heartening absence of curvature for Italian women born in 1904, as do plots for other cohorts not included here.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingcitation

    The estimated cohort effect β1 = −0.020 with standard error 0.008, though small, is in line with expectations, statistically significant, and important.

    “The estimated cohort effect β1 = −0.020 with standard error 0.008, though small, is in line with expectations, statistically significant, and important (13).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [13] Materials and methods are available as supplementary materials.

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Findingown data

    Some 472 individuals born before 31 December 1903 (birth cohorts 1896-1903) enter the study at ages greater than exactly 105 and provide left-truncated survival trajectories.

    “Some 472 individuals born before 31 December 1903 (birth cohorts 1896 – 1903) enter the study at ages greater than exactly 105 and, as such, provide left-truncated survival trajectories.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    The hazard function appeared constant at least up to age 114, after which data become too sparse for reliable statements.

    “The hazard function, the usual continuous-age version of mortality rates as a function of age, turned out to appear constant at least up to age 114, after which data become too sparse for reliable statements.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [12] Gampe J, Human mortality beyond age 110 in Supercentenarians, Meier H, Gampe J, Jeune B, Robine JM, Vaupel JW, Eds. (Springer, 2010), pp. 219– 230.

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Premisecitation

    The International Database on Longevity (IDL) at the Max Planck Institute for Demographic Research is the result of a decade-long effort collecting, analysing, and meticulously checking data on people who reach ages of 110 years or more, supercentenarians, in fifteen countries including Italy, updated through 2010.

    “The International Database on Longevity (IDL) at the Max Planck Institute for Demographic Research is the result of this decade-long effort (www.supercentenarians.org), updated through 2010.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites www.supercentenarians.org

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim.

    Premisenone given

    Hazards that are constant imply cumulative hazards that are linearly increasing.

    “Hazards that are constant imply cumulative hazards that are linearly increasing.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Study design and conductreasoning

    The project includes all those 105 and older in the period 1 January 2009 to 31 December 2015, so that the data are free of age ascertainment bias.

    “The project includes all those 105 and older in the period 1 January 2009 to 31 December 2015, so that the data are also free of age ascertainment bias.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationown data

    The increasing number of exceptionally long-lived people in Table 1 and the fact that their mortality beyond 105 is declining across cohorts, lowering the mortality plateau or postponing the age when it appears, strongly suggest that longevity is continuing to increase over time.

    “The increasing number of exceptionally long-lived people in Table 1 and the fact that their mortality beyond 105 is seen to be declining across cohorts lowering the mortality plateau or postponing the age when it appears strongly suggest that longevity is continuing to increase over time”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim.

    Study design and conductnone given

    In these data, age misreporting is believed to be minimal.

    “In these data, age misreporting is believed to be minimal.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Study design and conductnone given

    The validation procedure has been developed specifically for this population segment and meets the highest validation criteria provided by the IDL protocol.

    “Second, the validation procedure has been developed specifically for this population segment and meets the highest validation criteria provided by the IDL protocol.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationown data

    The results contribute to a recently rekindled debate about the existence of a fixed maximum lifespan for humans, underwriting doubt that any limit is as yet in view.

    “Our results contribute to a recently rekindled debate (15–17) about the existence of a fixed maximum lifespan for humans, underwriting doubt that any limit is as yet in view.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [15] Dong X, Milholland B, Vijg J, Evidence for a limit to human lifespan. Nature 538, 257– 259 (2016). 27706136 PMC11673931 source
    • cites [16] Lenart A, Vaupel JW, Questionable evidence for a limit to human lifespan. Nature 546, E13– E14 (2017). 28658239 source
    • cites [17] Rootzn H, Zholud D, Human life is unlimited but short. Extremes 20, 713– 728 (2017).

  • Probably not a substantial claim. It may be too vague to check against evidence.

    Interpretationreasoning

    These regularities call for common structural and evolutionary explanations.

    “regularities calling for common structural and evolutionary explanations.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    The estimate β2 = 0.033 is plausible.

    “though the estimate β2 = 0.033 is plausible.”
    Quote in the paperNot a substantial claim
22 of 22

  • The paper relies on this without support.

    Accurate mortality data at advanced ages are difficult to obtain.

    “Accurate mortality data at advanced ages are difficult to obtain.”

  • The paper relies on this without support.

    In vital statistics, the very old are often aggregated in one age-group.

    “In vital statistics, the very old are often aggregated in one age-group.”

  • The paper relies on this without support.

    Even in countries with reliable vital registration, age exaggeration is common among the oldest-old.

    “Even in countries with reliable vital registration, age exaggeration is common among the oldest-old.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Death rates at ages more than 105 years now are at 50 per cent or higher.

    “As a frame of reference, death rates at ages more than 105 years now are at 50 per cent or higher (17,18).”

    From Inconvenient Truths About Human Longevity (2019) · cites this paper as [17]

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. V. Kannisto Development of Oldest-Old Mortality 1950-1990: Evidence from 28 Developed Countries (Odense Univ. Press 1994).
  2. A. R. Thatcher V. Kannisto J. W. Vaupel The Force of Mortality at Ages 80 to 120 (Odense Univ. Press 1998).
  3. L. A. Gavrilov N. S. Gavrilova V. N. Krutko >“Mortality of supercentenarians: Does it grow with age?”in 2017 Living to 100 Monograph T. F. Harris Ed. (Society of Actuaries 2017) pp. 1–24.
  4. R. E. Beard >“Notes on some mathematical mortality models” in The Lifespan of Animals G. E. W. Wolstenholme M. O’Connor Eds. (Little Brown 1959) pp. 802–811.

Cited by

Sorted by citations

Related

Metadata

Authors
Barbi, E., Lagona, F., Marsili, M., Vaupel, J. W., & Wachter, K. W.
Affiliations
  • Sapienza University of Rome (IT)
  • Roma Tre University (IT)
  • Istituto Nazionale di Statistica (IT)
  • Duke University (US)
  • University of California, Berkeley (US)
Corresponding author
Barbi, Elisabetta
ORCID
Venue
Science
Publisher
American Association for the Advancement of Science (AAAS)
Published
2018-06-29
Volume
360
Issue
6396
Pages
1459-1461
ISSN
  • 0036-8075 (ISSN-L)
  • 1095-9203
DOI
10.1126/science.aat3119
PMC
PMC6457902
OpenAlex
W2811063823
Cited by
299
References
23
Citations by year
2026: 28 · 2025: 15 · 2024: 21 · 2023: 22 · 2022: 32 · 2021: 81 · 2020: 43 · 2019: 39 · 2018: 18
FWCI
70.98
Type
journal article
Language
en
Open access
Licence
cc-by-nc
Locations
  • Science (publishedVersion)
  • PubMed (publishedVersion)
  • University of Southern Denmark Research Portal (University of Southern Denmark) (publishedVersion, cc-by-nc)
  • Europe PMC (PubMed Central) (acceptedVersion)
  • PubMed Central (acceptedVersion)
  • Iris (Roma Tre University) (submittedVersion)
  • eScholarship (California Digital Library) (submittedVersion)
  • IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
Funders
U.S. National Institute on Aging (5P30AG012839)
Topics
  • Social Sciences › Demography › Insurance, Mortality, Demography, Risk Management
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Aging › Genetics, Aging, and Longevity in Model Organisms
  • Social Sciences › Psychology › Developmental and Educational Psychology › Aging and Gerontology Research
Keywords
mortality plateau, hazard function, longevity, centenarians, oldest old
MeSH terms
Aged, 80 and over, Demography, Female, Humans, Italy, Longevity, Male, Mortality, Proportional Hazards Models

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