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Contributions
J.d.B. developed the model and calculated the population projections, A.B. estimated the time series model and projected the parameters, J.d.B. and A.B. drafted the Supplementary Information, F.J. aided in interpreting the results, J.d.B. and F.J. wrote the manuscript.
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Extended data figures and tables
Extended Data Figure 1 Death probabilities of Japanese women.
a, The solid black line shows the average observed death probabilities for the years 2012–2014 for ages 70–109. The dashed blue line shows the fit of the Gompertz model for ages 70–100. Using the estimated parameters of the Gompertz model, the death probabilities are projected for ages 101–109. The dashed red line shows the fit and projection of the logistic-type function used in the CoDe 2.0 model. b, The solid black line shows the changes in the average observed values of the death probabilities between successive ages. The dashed blue line shows that the Gompertz model projects an acceleration of the increase in the death probabilities. The dashed red line shows that the logistic-type model used in the CoDe 2.0 model describes the levelling off of the increase in the death probabilities at ages 90 and over. c, The solid line shows the logarithm of the observed death probabilities in 2014. The dashed line shows the fit of the CoDe 2.0 model if the slope parameter of the logistic model b would not change with age. d, The blue line shows the probability that at least one woman aged 115 will reach age 116, and the red line shows the probability that at least one woman will reach age 120. These probabilities depend on both the size of the population at risk and the level of death probabilities.
Extended Data Figure 2 Death probabilities and age-at-death distribution of Japanese women.
The red lines show the values for 1960, the blue lines those for 2014, and the green lines the projection for 2070. The dashed lines show the observed values, the solid lines show the fit of the CoDe 2.0 model. The grey area represents the ages for which we extrapolate our estimations. The projections for 2070 are calculated using the CoDe 2.0 model in which the parameter values are assumed to equal the median values of the projections of the parameters for 2070. a, The increase in the death probabilities q levels off at older ages. b, The decrease in the logarithm of the death probabilities between 1960 and 2014 is smaller at older ages than at young and adult ages. c, The age-at-death distribution in 2014 is more compressed around the modal at death than in 1960. d, The slope parameter b of the logistic term increases more strongly at older ages in 2014 than in 1960. This results in compression of mortality in old age. This development is projected to continue up to 2070.
Extended Data Figure 3 Estimates and projections of the parameter values of the CoDe 2.0 model.
The solid lines show the estimates for the period 1960–2014 and the median values of the projections for the period 2015–2070. The dashed lines show the 95% projections intervals. The increase in the modal age at death, Mt, indicates that the CoDe 2.0 model projects a continuation of the delay of mortality. Note that the projection interval is relatively narrow. Thus, based on the observed increase in the modal age at death in the 1960–2014 period, our time-series model projects that it is highly likely that the delay of mortality to older ages will continue. The projected decrease in the values of A representing infant mortality and a representing the increase in mortality in adolescence indicate further reduction in mortality in young age contributing to compression of mortality. The increase in the value of β3, representing the increase in the slope of the logistic term with age, indicates that a continuation of the compression of mortality at older ages is projected. The projected constant level of the asymptotic value g indicates that the death probabilities in very old age will be constant.
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Supplementary Information
This file contains Supplementary Methods, Acknowledgements and Supplementary References. (PDF 297 kb)
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de Beer, J., Bardoutsos, A. & Janssen, F. Maximum human lifespan may increase to 125 years. Nature 546, E16–E17 (2017). https://doi.org/10.1038/nature22792
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DOI: https://doi.org/10.1038/nature22792
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