The long‐term pattern of adult mortality and the highest attained age

Recent new data on old age mortality point to a particular model for the way in which the probability of dying increases with age. The model is found to fit not only modern data but also some widely spaced historical data for the 19th and 17th centuries, and even some estimates for the early mediaeval period. The results show a pattern which calls for explanation. The model can also be used to predict a probability distribution for the highest age which will be attained in given circumstances. The results are relevant to the current debate about whether there is a fixed upper limit to the length of human life.

[1]  W. M. Makeham,et al.  On the Law of Mortality and the Construction of Annuity Tables , 1860 .

[2]  Record in longevity , 1921 .

[3]  S J Olshansky.  Forecasting Mortality , 1932, Nature.

[4]  Wilfred Perks,et al.  On Some Experiments in the Graduation of Mortality Statistics , 1932 .

[5]  E. Gumbel.  La duree extreme de la vie humaine , 1938 .

[6]  Josiah Cox Russel,et al.  British medieval population , 1949 .

[7]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[8]  P. Vincent.  La mortalité des vieillards , 1951, Population.

[9]  P. Medawar.  UNSOLVED problem of biology. , 1953, The Medical journal of Australia.

[10]  Statistics of Windfalls and Disasters , 1955, Nature.

[11]  George C. Williams,et al.  Adaptation and Natural Selection , 2018 .

[12]  J. H Pollard,et al.  Mathematical Models for the Growth of Human Populations , 1973 .

[13]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[14]  H. L. Bras.  Lois de mortalité et âge limite , 1976, Population.

[15]  R H Guember,et al.  Growing old? , 1978, Dental management.

[16]  J. H. Pollard,et al.  The age pattern of mortality , 1979 .

[17]  J F Fries,et al.  Aging, natural death, and the compression of morbidity. , 1980, The New England journal of medicine.

[18]  S. Olshansky,et al.  On forecasting mortality , 1988 .

[19]  D. Hand.  A History of Probability and Statistics and Their Applications before 1750 , 1990 .

[20]  H. Charbonneau,et al.  Vivre cent ans dans la vallée du Saint-Laurent avant 1800 , 1990 .

[21]  A. Coale,et al.  Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age. , 1990, Mathematical population studies.

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

[23]  M. Barinaga.  How long is the human life-span? , 1991, Science.

[24]  J. Robine,et al.  Healthy life expectancy: evaluation of global indicator of change in population health. , 1991, BMJ.

[25]  J. Brody,et al.  Trading Off Longer Life for Worsening Health , 1991 .

[26]  A. Thatcher.  Trends in numbers and mortality at high ages in England and Wales. , 1992, Population studies.

[27]  J. Vaupel,et al.  Demography of genotypes: failure of the limited life-span paradigm in Drosophila melanogaster. , 1992, Science.

[28]  J. Vaupel,et al.  Slowing of mortality rates at older ages in large medfly cohorts. , 1992, Science.

[29]  Ronald Lee,et al.  Modeling and forecasting U. S. mortality , 1992 .

[30]  Thatcher Ar.  Trends in numbers and mortality at high ages in England and Wales. , 1992 .

[31]  L. Gavrilov,et al.  The biology of life span: A quantitative approach: Revised and updated English edition. Originally published in Russian by Nauka, Moscow, 1986. Translated into English by John and Liliya Payne. 385 pp., 1991. Price: $40.00 US , 1992 .

[32]  S. Stearns,et al.  The Evolution of Life Histories , 1992 .

[33]  A. Edwards,et al.  A History of Probability and Statistics and Their Applications before 1750 , 1992 .

[34]  R. Illsley,et al.  Regional inequalities in mortality. , 1993, Journal of epidemiology and community health.

[35]  Samuel H. Preston,et al.  A Relational Model of Mortality at Older Ages in Low Mortality Countries , 1994 .

[36]  L. de Haan,et al.  On the maximal life span of humans. , 1994, Mathematical population studies.

[37]  R. Lee,et al.  Stochastic population forecasts for the United States: beyond high, medium, and low. , 1994, Journal of the American Statistical Association.

[38]  S. Preston,et al.  The Elderly and Their Kin: Patterns of Availability and Access , 1994 .

[39]  A. Yashin,et al.  A duality in aging: the equivalence of mortality models based on radically different concepts , 1994, Mechanisms of Ageing and Development.

[40]  James W. Vaupel,et al.  Reductions in mortality at advanced ages: several decades of evidence from 27 countries. , 1994 .

[41]  M. Murphy.  Methods for forecasting mortality and their performance , 1995 .

[42]  James W. Vaupel,et al.  Exceptional Longevity: From Prehistory to the Present , 1995 .

[43]  J. Wilmoth,et al.  Extreme longevity in five countries , 1996, European journal of population = Revue europeenne de demographie.

[44]  M R Rose,et al.  Evolutionary theory predicts late-life mortality plateaus. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[45]  R. Cardenas,et al.  [Reductions in mortality]. , 1996, Demos.

[46]  J. Wilmoth,et al.  Development of Oldest-Old Mortality, 1950-1990: Evidence from 28 Developed Countries , 1996 .

[47]  M. Murphy,et al.  The health of adult Britain 1841-1994. , 1997 .

[48]  The health of adult Britain 1841-1994 , 1997 .

[49]  R. Ecob,et al.  Has regional variation in mortality rates declined since 1931, and in all age groups, in Britain? A re-analysis using formal statistical modelling. , 1997, Journal of epidemiology and community health.

[50]  K. Manton,et al.  Chronic disability trends in elderly United States populations: 1982-1994. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Richard L. Smith,et al.  Statistics for Exceptional Athletics Records , 1997 .

[52]  R. S. Davies,et al.  English population history from family reconstitution 1580–1837: Adjusting mortality rates taken from the four groups to form a single series , 1997 .

[53]  P. Johnson.  Fiscal implications of population ageing. , 1997, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[54]  K. Wachter.  Kinship resources for the elderly. , 1997, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[55]  Population data at a glance : shaded contour maps of demographic surfaces over age and time , 1997 .

[56]  M. Whitehead,et al.  Health Inequalities Decennial Supplement , 1997 .

[57]  A. Yashin,et al.  Effects of Unobserved and Partially Observed Covariate Processes on System Failure: A Review of Models and Estimation Strategies , 1997 .

[58]  James W. Vaupel,et al.  The force of mortality at ages 80 to 120 , 1998 .

[59]  J. Curtsinger,et al.  MORTALITY PLATEAUS AND THE EVOLUTION OF SENESCENCE: WHY ARE OLD‐AGE MORTALITY RATES SO LOW? , 1998, Evolution; international journal of organic evolution.

[60]  Margaret Thomas.  Living in Britain : results from the 1996 General Household Survey , 1998 .