Human life is unlimited but short Holger Rootzn

Human life is unlimited – but short Holger Rootzén Dmitrii Zholud Chalmers university of Technology and Gothenburg University Paper at https: //arxiv. org/abs/1708. 02184

Jeanne Calment Died August 4, 1997 Age 122 years, 164 days 1 glass of port, 2 cigarettes, and 150 gr chocolate per day, tennis, gymnastics, piano, don’t worry! Jiroemon Kimura Died June 12, 2013 Age 116 years, 54 days Exercise, eat small portions, read news, live without attachment, laugh often, break life up into small parts.

Nabi Tajima World’s oldest living validated person 117 years, 82 days ramen noodles and beef stew, hashed beef and rice mackerel sushi

• Is human life unlimited? • Are there difference in survival at extreme age between: women and men; persons with different lifestyles; persons with different genetic backgrounds; persons who lived earlier or later; or between different ages, say between 110 year-olds and 115 -year-olds? • What will the record life-length be during the next 25 years? These results, and the analysis methods we have developed, can help testing biological theories of ageing, and aid confirmation of success of efforts to find a cure for ageing.

We use the International Database on Longevity (IDL) IDL is the result of an effort to provide validated information on individuals who attain extreme ages. Data is collected on individuals who attained an age of 110 years or more - so called supercentenarians Data collection is performed so that age-ascertainment bias is avoided. Data from Australia, Belgium, Canada, England Wales, Switzerland, Germany, Denmark, Spain, Finland, France, Italy, Japan, Norway, Sweden, USA, with 566 supercentenarians validated at level A. Data from different time intervals for different countries, earliest death 1962, latest death 2007

GERONTOLOGY RESEARCH GROUP database The other database on supercentenarians GRG World Supercentenarian Rankings List Last Updated On: Oct 19 2017 5: 09 PM Numbers of Living Supercentenarians as of Last Update Females Males Total 40 1 41 List follows … Validated Deceased Supercentenarians (recent deaths 2008 to present in chronological order) List follows … Age-biased – not useful for statistical analysis

“Unvalidated data on ages of supercentenarians is known to be completely unreliable. ” (Summary of Poulain, M. (2010). On the age validation of supercentenarians. In H. Maier and et al. (Eds. ), Supercentenarians, Chapter 1, pp. 4– 30. Heidelberg: Springer-Verlag. ) “A significant majority of worldwide claimants to be age 110 -orover have subsequently been proven to be false (Copied from GRG webpage)

Extreme Value Statistics Block Maxima model. Not today Peaks over Thresholds (Po. T) model. Excesses (=value – threshold) of high thresholds, say excess ages after 110 -th birthdays, follow a generalized Pareto (GP) distribution; times of exceedance occur as a Poisson process. Motivation: • The GP-s are the limit distributions of excesses of higher and higher thresholds • The GP-s are threshold-stable, i. e. excesses by a GP variable of a higher threshold is again GP • The Poisson process is the limit of occurrence time of rare events • Suitably flexible models

Philosophy of EVS 1. Extreme events, e. g. survival at extreme age, are often quite different from non-extreme behavior and non-extreme behavior has little to say about extremes: so only extreme events give useful information about future extreme events. 2. Theoretically motivated models give much better possibilities to learn from experience than if everyone uses their own ad hoc method

One starting point for our analysis Gampe chapter in the book “Supercentenarians” (2010) Editors: Maier, H. , Gampe, J. , Jeune, B. , Vaupel, J. W. , Robine, J. -M. (Eds. ), Springer “The analysis confirms that human mortality after age 110 is at at a level corresponding to an annual probability of death of 50%. No sex-specific differences in mortality could be found, and no time trend in supercentenarian mortality between earlier and later cohorts could be detected. ” Based on non-parametric “life-table” methods EVS adds possibilities: to address the question of a limit for the human lifespan; make predictions about future record ages possible; to perform tests and to obtain credible confidence intervals at a much more detailed level; and a much more precise basis for further analyses and for tracking changes

GP distribution fitted to IDL data for Japan, without correction for selection bias. Life appears to have a finite limit equal to 116. 0 years Exponential distribution fitted to all IDL data with validation level A, with correction for selection bias. Life is unlimited but short. GP distribution fitted to IDL data for France, without correction for selection bias. Life appears to be unlimited Correcting the estimates from Japan and France for selection bias leads to the conclusion that also in these countries life is unlimited but short.

The data: Life lengths against year of death: blue - women, red - men, black - persons who died after December 31, 1999 in USA or in 1996 or after August 31, 2003 in Japan and which are not included in analyses. Green square is Jeanne Calment.

• No difference in mortality between men and women after age 110 (but 10 times as many women live to age 110) • No difference in mortality between first and last half of data • No difference in mortality between countries (in particular, no difference between Japan and the western countries) p-values for test of no difference in mortality between women and men after age 110.

Survival after age 110 in western Europe, north America, and Japan can be described as follows: each year a coin is tossed, and if heads comes up it means a person will live one more year. More precisely, the estimated probability to survive one more year is 47%, with 95% confidence interval (0. 44, 0. 50).

Identity link log link Yearly number of deaths of validated supercentenarians from USA, England Wales, and Italy. Line computed using Poisson regression

Identity link log link

The numbers of women aged 100+ in Sweden from 1861 to 2008 and aged 105+ in Japan from 1947 to 2007 Year of attainment of age 110 in US

Selection bias: Exponential qq-plot for IDL life lengths of supercentenarians who died 1980 -1999 in USA. Exponential qq-plot for IDL life lengths of supercentenarians who died 2000 -2003 in USA. Similar sampling plans for other countries, except Japan Contains persons who was 110 or more on first of January 2000 and died before the fall of 2003

Age-110 Not observed Beginning of study End of study Time of 110 th birthday Left and right truncated observations – this must be taken into account in inference

Age-110 Not observed Beginning of study End of study Time of 110 th birthday

LAtool

Dong, X. , B. Milholland, and J. Vijg (2016). Evidence for a limit to human lifespan. Nature 538, 257– 259. Yearly maximum reported age at death (MRAD) in France, Japan, England Wales, USA Annual average at death of supercentenarians (110 +) Ø “this strongly suggest that the duration of life is limited”

Same plot as in Dong et al. paper, but with yearly number of deaths (dashed) superimposed Same plot but for US data only Plot contains data from England Wales, France, Japan, USA, with different time periods for each country Plots for England Wales, France, Japan similar

J. W. Vaupel: Biodemography of human ageing, Nature (2010) Among very many other very interesting things discusses a frailty explanation for the exponential distribution, based on the idea that different subpopulations have different mortality, and that only those with lowest mortality will reach extreme age By EVS there are no differences between men and women or between countries. This makes the frailty explanation less likely

Oeppen & Vaupel: Broken Limits to Life Expectancy, Science (2002) Record life expectancy for females, with regression line Horizontal black lines are asserted ceilings on life expectancy. Beginning of lines are the years of pubication Dashed red lines are UN projections of female life expectancy in Japan, made in 1986, 1999, and 2001

Dong-et-al: Evidence for a limit to human lifespan. Nature letter, Oct 13, 2016 Ø “the rate of improvement of survival is slower for very high ages” Ø “the age with the most rapid gain of survival has reached a plateau”