Human mortality at extreme age

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.

[1]  L. Haan,et al.  Extreme value theory , 2006 .

[2]  M. Sibuya,et al.  Estimating the Upper Limit of Lifetime Probability Distribution, Based on Data of Japanese Centenarians. , 2016, The journals of gerontology. Series A, Biological sciences and medical sciences.

[3]  Evon M. O. Abu-Taieh,et al.  Comparative Study , 2020, Definitions.

[4]  A. Thatcher.  The long‐term pattern of adult mortality and the highest attained age , 1999, Journal of the Royal Statistical Society. Series A,.

[5]  Ørnulf Borgan,et al.  Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties , 1986 .

[6]  J. Vaupel,et al.  Broken Limits to Life Expectancy , 2002, Science.

[7]  Jon A. Wellner,et al.  Confidence bands for a survival curve from censored data , 1980 .

[8]  M. Poulain.  On the age validation of supercentenarians , 2010 .

[9]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[10]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[11]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[12]  L. Gavrilov,et al.  Late-life mortality is underestimated because of data errors , 2019, PLoS biology.

[13]  H. Rootzén,et al.  Human life is unlimited – but short , 2017, Extremes.

[14]  Richard L. Smith.  Approximations in Extreme Value Theory. , 1987 .

[15]  Vijayan N. Nair,et al.  Confidence Bands for Survival Functions With Censored Data: A Comparative Study , 1984 .

[16]  Bruce W. Turnbull,et al.  Probability Plotting With Censored Data , 1992 .

[17]  K. Wachter,et al.  The plateau of human mortality: Demography of longevity pioneers , 2018, Science.

[18]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[19]  Limits to Human Life Span Through Extreme Value Theory , 2019, Journal of the American Statistical Association.

[20]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[21]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[22]  Thomas B. L. Kirkwood,et al.  Deciphering death: a commentary on Gompertz (1825) ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’ , 2015, Philosophical Transactions of the Royal Society B: Biological Sciences.

[23]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[24]  H. Rootzén,et al.  Rejoinder to discussion of the paper “Human life is unlimited—but short” , 2018, Extremes.

[25]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[26]  Paul J. Northrop,et al.  Improved threshold diagnostic plots for extreme value analyses , 2014 .

[27]  Nicholas P. Jewell,et al.  A note on the product-limit estimator under right censoring and left truncation , 1987 .

[28]  Jan Vijg,et al.  Puzzles, promises and a cure for ageing , 2008, Nature.

[29]  A. Davison.  ‘The life of man, solitary, poore, nasty, brutish, and short’: Discussion of the paper by Rootzén and Zholud , 2018, Extremes.

[30]  Carl Scarrott,et al.  A Review of Extreme Value Threshold Estimation and Uncertainty Quantification , 2012 .

[31]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[32]  J. Gampe.  Human mortality beyond age 110 , 2010 .

[33]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[34]  Jennifer L. Wadsworth,et al.  Exploiting Structure of Maximum Likelihood Estimators for Extreme Value Threshold Selection , 2016, Technometrics.

[35]  Pao-Sheng Shen,et al.  Nonparametric analysis of doubly truncated data , 2010 .