BACKGROUND: The answer to the question "At what age does aging begin?" is tightly related to the question "Where is the onset of mortality increase with age?" Age affects mortality rates from all diseases differently than it affects mortality rates from nonbiological causes. Mortality increase with age in adult populations has been modeled by many authors, and little attention has been given to mortality decrease with age after birth. MATERIALS AND METHODS: Nonbiological causes are excluded, and the category "all diseases" is studied. It is analyzed in Denmark, Finland, Norway, and Sweden during the period 1994-2011, and all possible models are screened. Age trajectories of mortality are analyzed separately: before the age category where mortality reaches its minimal value and after the age category. RESULTS: Resulting age trajectories from all diseases showed a strong minimum, which was hidden in total mortality. The inverse proportion between mortality and age fitted in 54 of 58 cases before mortality minimum. The Gompertz model with two parameters fitted as mortality increased with age in 17 of 58 cases after mortality minimum, and the Gompertz model with a small positive quadratic term fitted data in the remaining 41 cases. The mean age where mortality reached minimal value was 8 (95% confidence interval 7.05-8.95) years. The figures depict an age where the human population has a minimal risk of death from biological causes. CONCLUSION: Inverse proportion and the Gompertz model fitted data on both sides of the mortality minimum, and three parameters determined the shape of the age-mortality trajectory. Life expectancy should be determined by the two standard Gompertz parameters and also by the single parameter in the model c/x. All-disease mortality represents an alternative tool to study the impact of age. All results are based on published data.

Department of Economics Faculty of Informatics and Management University of Hradec Králové Hradec Králové Czech Republic

Department of Informatics and Quantitative Methods

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Gompertz B. On the nature of the function expressive of the law of human mortality. Philos Trans R Soc Lond. 1825;115:513–583. PubMed

Strehler BL, Mildvan AS. General theory of mortality and aging. Science. 1960;132:14–21. PubMed

Siler W. A competing risk model for animal mortality. Ecology. 1979;60:750–757.

Witten MT. A return to time, cells, systems, and aging – V. Further thoughts on Gompertzian survival dynamics: the geriatric years. Mech Ageing Dev. 1988;46:175–200. PubMed

Gavrilov LA, Gavrilova NS. The reliability theory of aging and longevity. J Theor Biol. 2001;213:527–545. PubMed

Lin XS, Liu X. Markov aging process and phase-type law of mortality. N Am Actuar J. 2007;11:92–109.

Arbeev KG, Ukraintseva SV, Akushevich I, et al. Age trajectories of physiological indices in relation to healthy life course. Mech Ageing Dev. 2011;132:93–102. PubMed PMC

Robine JM, Michel JP, Herrmann FR. Excess male mortality and age-specific mortality trajectories under different mortality conditions: a lesson from the heat wave of summer 2003. Mech Ageing Dev. 2012;133:378–386. PubMed

Ukraintseva S, Yashin A, Arbeev K, et al. Puzzling role of genetic risk factors in human longevity: “risk alleles” as pro-longevity variants. Biogerontology. 2016;17:109–127. PubMed PMC

Luder HU. Onset of human aging estimated from hazard functions associated with various causes of death. Mech Ageing Dev. 1993;67:247–259. PubMed

Dolejs J. The extension of Gompertz law’s validity. Mech Ageing Dev. 1997;99:233–244. PubMed

Salinari G, De Santis G. On the beginning of mortality acceleration. Demography. 2015;52:39–60. PubMed

Makeham W. On the law of mortality and the construction of annuity tables. J Inst Actuar. 1860;8:301–310.

Heligman L, Pollard JH. The age pattern of mortality. J Inst Actuar. 1980;107:49–75.

Vaupel JW, Carey JR, Christensen K, et al. Biodemographic trajectories of longevity. Science. 1998;280:855–860. PubMed

Preston SH, Heuveline P, Guillot M. Demography: Measuring and Modeling Population Processes. Oxford: Blackwell; 2001.

Bebbington M, Lai CD, Zitikis R. Modeling human mortality using mixtures of bathtub shaped failure distributions. J Theor Biol. 2007;245:528–538. PubMed

Bebbington M, Lai CD, Zitikis R. Modelling deceleration in senescent mortality. Math Popul Stud. 2011;18:18–37.

Willemse WJ, Koppelaar H. Knowledge elicitation of Gompertz’ law of mortality. Scand Actuar J. 2000;2:168–179.

World Health Organization Mortality, ICD-10. 2016. [Accessed January 27, 2015]. Available from: http://www.who.int/healthinfo/statistics/mortality_rawdata/en/index.html.

World Health Organization ICD-10: version 2010. [Accessed January 26, 2015]. Available from: http://apps.who.int/classifications/icd10/browse/2010/en.

Eurostat Population on 1 January by age and sex. 2016. [Accessed January 22, 2015]. Available from: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_pjan&lang=en.

Zheng H, Yang Y, Land KC. Heterogeneity in the Strehler-Mildvan general theory of mortality and aging. Demography. 2011;48:267–290. PubMed

Mulasso A, Roppolo M, Rabaglietti E. Physical frailty, disability, and dynamics in health perceptions: a preliminary mediation model. Clin Interv Aging. 2016;11:275–278. PubMed PMC

Wilson DL. The analysis of survival (mortality) data: fitting Gompertz, Weibull, and logistic functions. Mech Ageing Dev. 1994;74:15–33. PubMed

Kesteloot H, Huang X. On the relationship between human all-cause mortality and age. Eur J Epidemiol. 2003;18:503–511. PubMed

Bourgeois-Pichat J. De la mesure de la mortalité infantile. Population. 1946;1:53–68. PubMed

Bourgeois-Pichat J. La mesure de la mortalité infantile II: les causes de déces. Population. 1951;6:459–480.

Carnes BA, Olshansky SJ, Grahn D. The search for a law of mortality. Popul Dev Rev. 1996;22:231–264.

Knodel J, Kintner H. The impact of breast feeding patterns on biometric analysis of infant mortality. Demography. 1977;14:391–409. PubMed

Dolejs J. Analysis of mortality decline along with age and latent congenital defects. Mech Ageing Dev. 2003;124:679–696. PubMed

Dolejs J. Decrease of total activity with time at long distances from a nuclear accident or explosion. Radiat Environ Biophys. 2005;44:41–49. PubMed

Ding SL, Shen CY. Model of human aging: recent findings on Werner’s and Hutchinson-Gilford progeria syndromes. Clin Interv Aging. 2008;3:431–444. PubMed PMC

Coppedè F. The epidemiology of premature aging and associated comorbidities. Clin Interv Aging. 2013;8:1023–1032. PubMed PMC

Riggs JE, Millecchia RJ. Using the Gompertz-Strehler model of aging and mortality to explain mortality trends in industrialized countries. Mech Ageing Dev. 1992;65:217–228. PubMed

Riggs JE. Rising mortality due to Parkinson’s disease and amyotrophic lateral sclerosis: a manifestation of the competitive nature of human mortality. J Clin Epidemiol. 1992;45:1007–1012. PubMed

Vaupel JW, Manton KG, Stallard E. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography. 1979;16(3):439–454. PubMed

Vaupel JW, Manton KG, Stallard E. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography. 1979;16:439–454. PubMed

Database of age trajectories of mortality in 110 countries and web application: Data report

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