The plateau of human mortality: Demography of longevity pioneers

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Science  29 Jun 2018:
Vol. 360, Issue 6396, pp. 1459-1461
DOI: 10.1126/science.aat3119

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  • RE: Unsupported model choices generate a plateau

    Barbi et al. (1) use the poor fit of the model shown in their Figure 1b to justify a separate late-life mortality model, one that supports the existence of a late-life plateau. As they put it, a Gompertz model fit to ages 65-80 “fails at older ages and far overshoots our estimated plateau” (1).

    However, the poor fit of this model and its apparent failure at older ages are a result of biased model choices, not nonlinear trends.

    Barbi et al. fit their model to an age range of 65-80 years. Substituting any different age range into an otherwise identical model reveals this as a highly inappropriate model choice (2). Out of 861 alternative age ranges, the age range used by Barbi et al. generates the single largest late-life mortality plateau, and the single worst fit of mid-life (50 years) and late-life (> 90 years) mortality data.

    Of more than 150 models with an equivalent 15-year age range, the model chosen by Barbi et al. had the single worst mean squared error, the highest Aikake’s information criteria and the highest Bayesian information criteria (2).

    In short, Barbi et al. have used a model with the worst fit of mid-life and late-life data, and with the largest empirical bias towards a late-life plateau. They have then justified their own hypothesis and models through the poor fit of this regression, which is a result of their unsupported choices, and not nonlinear data trends.

    Despite repeat requests for clarity, the rationale behi...

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    Competing Interests: None declared.
  • Evidence for limited lifespan in semisupercentenarians
    • Brandon Milholland, Researcher, Albert Einstein College of Medicine
    • Other Contributors:
      • Xiao Dong, Research Fellow, Albert Einstein College of Medicine
      • Jan Vijg, Professor, Albert Einstein College of Medicine

    In their paper (1) Barbi et al. analyzed data from 3,638 Italian semisupercentenarians and concluded that not only does mortality plateau after age 105, but later cohorts plateaued at lower levels. They take their finding that “mortality beyond 105 is seen to be declining across cohorts” as evidence that “longevity is continuing to increase over time and that a limit, if any, has not been reached.” The report of no limit is in contrast with previous reports, including: a study of 46,666 Belgians aged over 95, which found that mortality did not plateau with age and was not changing with cohort (2); a study of 285,000 Dutch individuals aged 92 an up, which found a finite limit to life span, with no trend over time (3); and a study of 13,969 Swedish and Danish centenarians which found no improvement in later cohorts (4). Nonetheless, the work presented by Barbi et al., with its stringently verified data and emphasis on very elderly ages, could provide insight into patterns of late-life mortality, if the findings are robust. However, they are not.

    The data presented by Barbi et al. do strongly suggest that mortality in the population studied plateaus—or at least falls below the expected exponential increase—after age 105, but, their finding of a cohort effect is not robust and is unlikely to hold for very elderly individuals. To assess the strength of the cohort effect, we used the data from Barbi et al.’s paper and re-analyzed it with a gradually increasing minimum ag...

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    Competing Interests: None declared.
  • RE: Premature claim of a plateau of human mortality: the role of sample size
    • Carlo Giovanni Camarda, Researcher, French Institute for Demographic Studies
    • Other Contributors:
      • Linh Hoang Khanh Dang, PhD student, French Institute for Demographic Studies
      • France Meslé, Researcher, French Institute for Demographic Studies
      • Jean-Marie Robine, Researcher, French National Institute of Health and Medical Research
      • Jacques Vallin, Researcher, French Institute for Demographic Studies

    The paper published by Barbi et al. (1) makes a stimulating contribution to the debate about the shape of the mortality curve at old ages. Modeling newly available Italian data on survivors and death, the authors show that the hypothesis of constant hazards beyond age 105 cannot be rejected. While interesting, it seems that the results are not strong enough to infer “the existence of extreme age mortality plateaus in humans” (p. 1459).
    Leaving aside the quality of data and the plausibility of their conclusion within horizon, we have concerns about the role of sample size itself to draw reliable statistical findings. The authors model their individual data using a parametric proportional hazard model where the baseline hazard is described by a Gompertz model with a starting level of mortality (a) and rate-of-aging (b). Two covariates act linearly on the log-hazard: year of birth (cohort) and gender. Based on the likelihood ratio test, the authors conclude that the parameter b is not significantly different from zero, and claim to “show a clean case where the plateau is real” (p. 1459).
    By means of an extensive simulation study, we showed the influence of the dataset size on the significance of the parameters: multiplying the number of observations by six is enough to gauge a 0.013 b significant (Table 2, p. 1461). From our simulations, we also found that a model with a constant hazard can be simply selected due to the combination of a relatively small sample siz...

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    Competing Interests: None declared.
  • RE: Strong evidence for a plateau: But where is it?

    The article presents a rigorous and cogent analysis of centenarian mortality for cohorts of Italians born between 1896 and 1910 and argues that “we have shown that death rates...reach or closely approach a plateau after age 105” (1, p. 1461). Very high quality data sources with minimum statistical biases are used so the results ought to be fairly representative of the Italian context. However, the results may not extend to other populations and could prove difficult to generalize.
    Due to the inherent data scarcity, studies of mortality trajectories beyond age 100 are rare. Since the phenomena of a roughly constant hazard rate of 0.7 (annual probability of death of 0.5 ) beginning at age 110 years was first reported by (2), substantiation of both the level of the plateau and the age at which the plateau occurs is in fact still open to debate.

    An important study by (3) combined data from the countries in the International Database of Longevity (IDL) and also found a plateau of 0.7 beginning at age 110. In a recent reanalysis using updated IDL data, a plateau of 0.7 at age 110 was again found (4). However attempts to find a plateau for separate regions (United States, Europe, Japan) produced mixed findings. While results were confirmed for the USA and Europe, the plateau for Japan was estimated to be at a lower level, at about 0.6 (annual probability of death of 45%).

    On the contrary, another recent study estimated the plateau to be at a higher level. Usin...

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    Competing Interests: None declared.
  • RE: World’s oldest person

    Jeanne Calment is said to have been the oldest person who ever lived (1), a claim repeated 15 times in the Science archive, and by Olshansky & Carnes (see previous eLetter here, July 17). However, her neighbour Marie-Anne Durand has a far stronger case.
    Marie died on Nov 10 1885 at Auberives-en-Royans (2), the widow of Pierre Girard, her place of birth unknown. Significantly, the space in the parish register for her age, 125 years, was left blank and completed later by a different hand. Evidently, someone had had to check this out! The Journal de Tournon (3) on Nov 15 confirmed her death, noting she had been born in 1760, so it had been reasonable, but wrong, to assume she was over 124. She had retained all her faculties until the very end. She had seen the deaths of all her family. For more than 20 years she had been recognised locally as a centenarian; all the octogenarians confirmed that as children they had known her as having grandchildren. (Making plausible assumptions, we can estimate her age as 85 – 10 + 50 = 125y).
    Marie-Anne was born and baptized (4) on Nov 30 1760 in St Just-de-Claix on the river Isere, a tributary of the Rhone, where lies the port of Arles, Jeanne Calment’s birthplace. Is there something in the water? Or were they related?
    Of the three persons with a 118th birthday (1), Knauss lived for over a year, Calment for over four years, Durand for nearly seven, consistent with (or healthier than?) Barbi et al’...

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    Competing Interests: None declared.
  • RE: Mortality Plateaus and Unlimited Lifespan: Let’s Get Real
    • S. Jay Olshansky, Professor, School of Public Health, University of Illinois at Chicago and Lapetus Solutions
    • Other Contributors:
      • Bruce A. Carnes, Professor, University of Oklahoma and Lapetus Solutions

    Barbi et al. (29 June) add to the debate about upper limits to human longevity by observing a plateau in death rates at age 105, and small improvements in old age mortality in a small group of Italians born more than a century ago. Previously, researchers estimated that maximum lifespan for humans is about 115 (with occasional outliers) (1), and maximum life expectancy for males and females combined in a national population is about 85 (88 for women and 82 for men) (2). The life expectancy limit for humans identified in 1990 has never been exceeded in any national population, and no one has even come close to reaching the documented maximum lifespan for humans of 122 since Jeanne Calment set the record in 1997.
    Let’s assume the data in this latest study are reliable; death rates do in fact level off at ~0.5 for all humans at ages 105+ based on a small sample of Italians born in the late 19th and early 20th centuries; and small improvements in mortality at extreme old age have been observed in this population in recent years. Does this really mean, as the authors claim, that there is no discernible limit to the lifespan of humans? (3; p.1461).
    A plateau in mortality at ages 105+ means that in order for just one person to live to the world record of 122 years, 131,100 people would have to be alive at age 105. In order to break the longevity record by just one year (e.g., survival to age 123), 262,200 people would have to be alive at age 105. One person surviving...

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    Competing Interests: None declared.
  • RE: Evolution of late life
    • Laurence D. Mueller, Professor, Department of Ecology & Evolutionary Biology, University of California, Irvine
    • Other Contributors:
      • Michael R. Rose, Professor, Department of Ecology & Evolutionary Biology, University of California, Irvine

    In their report (29 June, p. 1459) Barbi et al. provide impressive evidence that human populations show mortality rates that level off at advanced ages, in this case around 105 years of age. In laboratory organisms amenable to large-scale, carefully controlled, demographic experiments, mortality plateaus have been observed in fruit flies (1), medflies (2), Mexican fruit flies (3), parasitoid wasps (3), nematodes (4), yeast (3), and beetles (5). Whatever doubts some may raise about particular studies of human data, the existence of late-life mortality plateaus is a general phenomenon among animal species that calls for scientific explanation.

    Barbi et al. conclude their work by suggesting that “Evolutionary theories … offer promising ingredients toward a joint explanation of both the phases of exponential increase and extreme-age plateaus.” We note that evolutionary explanations for mortality plateaus were first proposed over 20 years ago (6). Indeed, the existence of mortality plateaus is an unanticipated, but nonetheless natural, corollary of Hamilton’s forces of natural selection acting on age-specific fitness components. Experimental evolution of model organisms shows that the onset of mortality plateaus can be moved to earlier or later ages as Hamilton’s forces are experimentally shifted from earlier to later ages, and vice versa (7). Hamiltonian analysis also predicts that other fitness components can show a leveling at advanced ages. Such post-aging patterns...

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    Competing Interests: None declared.

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