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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
  • Fig. 1 Yearly hazards on a logarithmic scale for the cohort of Italian women born in 1904.

    Confidence intervals were derived from Human Mortality Database (HMD) data for ages up to 105 and from ISTAT data beyond age 105. (A) Closeup with 95% confidence intervals based solely on single-cohort data. (B) Broad view with estimated plateau beyond age 105 (black dashed line) and 95% confidence bands (orange) predicted from the model parameters based on the full ISTAT database, along with a straight-line prediction (black) from fitting a Gompertz model to ages 65 to 80.

  • Fig. 2 Cumulative hazard beyond age 105 for the cohort of Italian women born in 1904, as determined by the Nelson-Aalen estimator.

    Straight lines represent cumulative hazards of the estimated plateau predicted from ISTAT data, under a constant hazard (light blue) and a Gompertz hazard model (darker blue). The shaded area indicates the 95% confidence bands of the Nelson-Aalen estimate.

  • Table 1 Distribution of the observed cases.

    Age at entry into study is given in computed years.

    CohortAge at entry into studyMales FemalesNo. reaching
    105
    CensoredObserved deathsCensoredObserved deaths
    189611200 04≥4
    189711100 01≥1
    189811000 05≥5
    189910900 112≥13
    190010800 023≥23
    190110707 046≥53
    1902106017 2134≥153
    1903105023 2195≥220
    1904105035 5302342
    1905105240 10331383
    1906105248 19348417
    19071051155 40354460
    19081051957 106345527
    19091052833 219296576
    19101056422 423150659
    Total 126337 8272546≥3836
  • Table 2 Parameter estimates for preferred model.

    Difference in log-likelihoods: 0.292. AIC, Akaike information criterion; a, baseline hazard; b, Gompertz slope; β1, cohort effect; β2, gender effect.

    ParameterEstimate (SE)Log-likelihoodAIC
    Constant hazard model
    a0.645 (0.016)−4250.6628507.325
    β1−0.020 (0.008)
    β20.033 (0.058)
    Gompertz hazard model
    a0.629 (0.026)−4250.3708508.740
    b0.013 (0.017)
    β1−0.016 (0.009)
    β20.034 (0.058)

Supplementary Materials

  • The plateau of human mortality: Demography of longevity pioneers

    Elisabetta Barbi, Francesco Lagona, Marco Marsili, James W. Vaupel, Kenneth W. Wachter

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods 
    • Fig. S1
    • Tables S1 to S3
    • References 

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