Human mortality at extreme age




Figure 3.
Figure 3. Power functions based on the IDL (excluding French records), France 2019 and ISTAT databases and combined dataset, with rugs showing the lifetimes above 115. (a) Power for testing the null hypothesis of infinite endpoint against the alternative of a finite endpoint ι, based on the likelihood ratio statistic. The endpoint cannot be below the largest lifetime in each database. (b) Power of the Wald statistic for testing the null hypothesis γ = 0 against the one-sided alternative γ < 0, as a function of γ; the dashed line represents the power obtained by rejecting exponentiality when any of the three one-sided tests rejects. The curves are obtained by conditioning on the birthdates and left-truncated values in the databases, then simulating generalized Pareto data whose parameters are the partial maximum likelihood estimates (σˆγ,γ). The simulated records are censored if they fall outside the sampling frame for the ISTAT data and are simulated from a left- and right-truncated generalized Pareto distribution for IDL and France 2019. See appendix A.6 for more details.


We use a combination of extreme value statistics, survival analysis and computer-intensive methods to analyse the mortality of Italian and French semi-supercentenarians. After accounting for the effects of the sampling frame, extreme-value modelling leads to the conclusion that constant force of mortality beyond 108 years describes the data well and there is no evidence of differences between countries and cohorts. These findings are consistent with use of a Gompertz model and with previous analysis of the International Database on Longevity and suggest that any physical upper bound for the human lifespan is so large that it is unlikely to be approached. Power calculations make it implausible that there is an upper bound below 130 years. There is no evidence of differences in survival between women and men after age 108 in the Italian data and the International Database on Longevity, but survival is lower for men in the French data.

Author(s): Léo R. Belzile, Anthony C. Davison, Holger Rootzén and Dmitrii Zholud

Publication Date: 29 Sept 2021

Publication Site: Royal Society Open Science