The standard Gompertz equation for human survival fits very poorly the survival data of the very old (age 85 and above), who appear to survive better than predicted. An alternative Gompertz model based on the number of individuals who have died, rather than the number that are alive, at each age, tracks the data more accurately. The alternative model is based on the same differential equation as in the usual Gompertz model. The standard model describes the accelerated exponential decay of the number alive, whereas the alternative, heretofore unutilized model describes the decelerated exponential growth of the number dead. The alternative model is complementary to the standard and, together, the two Gompertz formulations allow accurate prediction of survival of the older as well as the younger mature members of the population.
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Andreev KF (2004) A method for estimating size of population aged 90 and over with application to the 2000 U.S. census data. Demogr Res 11:235–262
Azbel’ MY (1999) Phenomenological theory of mortality evolution. Proc Natl Acad Sci USA 96:3303–3307
Azbel’ MY (2002) An exact law can test biological theories of mortality. Exp Gerontol 37:859–869
Barrett JC (1985) The mortality of centenarians in England and Wales. Arch Gerontol Geriatr 4:211–218
Batschelet E (1971) Introduction to mathematics for life scientists. Springer, New York
Carey JR, Liedo P, Orozco D, Vaupel JW (1992) Slowing of mortality rates at older ages in large medfly cohorts. Science 258:457–461
Depoid F (1972) La mortalité des grands vieillards. Population (Paris) 28:755–792
Easton DM (1995) Gompertz survival kinetics: fall in the number alive or growth in the number dead? Theor Popul Biol 48:1–6
Easton DM (1997) Gompertz growth in number dead confirms medflies and nematodes show excess oldster survival. Exp Gerontol 32:719–726
Faber JF (2001) Life tables for the United States: 1900–2050. US Department of Health and Human Services, Social Security Administration, SSA Pub No 11-11534, pp 11–12
Gavrilov LA, Gavrilova NS (1991) The biology of life span: a quantitative approach. Harwood, London, pp 23–28
Gompertz B (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. Philos Trans R Soc Lond, pp 313–385
Hirsch HR (1994) Can an improved environment cause lifespan to decrease? Comments on lifespan criteria and longitudinal Gompertzian analysis. Exp Gerontol 29:119–137
Jacobson PH (1964) Cohort survival for generations since 1840. Milbank Mem Fund Q 42(3):36–53
Olshansky SJ, Carnes BA (1997) Ever since Gompertz. Demography 34:1–15
Riggs JE, Millecchia RJ (1992) Mortality among the elderly in the US, 1956–1987: demonstration of the upper boundary to Gompertzian mortality. Mech Ageing Dev 62:191–199
Robine J-M (2001) A new demographic model to explain the trajectory of mortality. Exp Gerontol 36:899–914
Robine J-M, Vaupel JW (2001) Supercentenarians: slowly ageing individuals or senile elderly? Exp Gerontol 36:915–930
Schoen R, Canudas-Romo V (2005) Changing mortality and average cohort life expectancy. Demogr Res 13:117–142. http://www.demographic-research.org/Volumes/Vol13/5/default.htm
Statistical Abstracts of Sweden (1991) Official statistics of Sweden. National Central Bureau of Statistics, Stockholm
Vincent P (1951) La mortalité des vieillards. Population 6(2):181–204
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Easton, D.M., Hirsch, H.R. For prediction of elder survival by a Gompertz model, number dead is preferable to number alive. AGE 30, 311 (2008). https://doi.org/10.1007/s11357-008-9073-0
- Death rate
- Gompertz survival
- Mortality rate