Human mortality at extreme age

Abstract

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.

A Proposal for Finite But Unbounded Human Lifetimes

“…From being non-significantly different to 0, the authors concluded that κ should be taken as exactly zero, indicating an exponential distribution for the data, and argue from this for an unlimited human lifespan. Later ( 14 ) and ( 15 ) updated ( 13 ) with more data and analyses but ultimately still concluded in favour of an exponential model for lifetimes and an unlimited human lifespan.…”

“…However, these analyses obtaining non-significant positive (and in some cases non-significant negative) κ values are in fact consistent with those in ( 5 ) and ( 6 ), where the estimated κ are strongly positive. Only limited data from extreme ages is used in ( 13 ), ( 14 ) and ( 15 ), whereas in ( 5 ) and ( 6 ) more extensive data sets spanning ages from 65 on was used, thus obtaining greater statistical power in a demographically-informed model.…”

Why Gilgamesh failed: the mechanistic basis of the limits to human lifespan

“…1). A few studies 12,13 have estimated the shape parameter of the GEV function to be zero, while several others have come up with estimates that are negative [14][15][16][17] . In the latter case, the finding may be due to survival dropping so low as to be indistinguishable from zero.…”

Improved inference on risk measures for univariate extremes

“…Old age in Italy. The existence or not of a finite upper limit for human lifetimes has recently sparked interest in the extreme value community (Belzile et al (2021) and ( 2022); Hanayama and Sibuya (2016); Rootzén and Zholud (2017); Einmahl, Einmahl and de Haan (2019)). The Italian centenarian data set, kindly provided by Holger Rootzén, contains the birth dates and ages of 3836 individuals from a study of semisupercentenarians conducted by the Istituto Nazionale di Statistica (Istat); see Barbi et al (2018).…”