One or more rates of ageing? The extended gamma-Gompertz model (EGG)

Salinari, Giambattista; Santis, Gustavo De

doi:10.1007/s10260-019-00471-z

Cited by 9 publications

(3 citation statements)

References 39 publications

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“…Observation of improvements in life expectancy and the availability of better datasets on mortality (especially for advanced ages) put the overall validity of the Gompertz law into question since mortality increases appear to slow down (or stagnate) in advanced ages, rather than being constant as in the Gompertz model (BARBI et al, 2018;BÖHNSTEDT;GAMPE, 2019;SALINARI;DE SANTIS, 2020;LI et al, 2021). Formally, this evidence of mortality deceleration can be addressed with a multiplicative frailty model (VAUPEL; MANTON; STALLARD, 1979).…”

Section: The Case Of a Gamma-heterogeneous Populationmentioning

confidence: 99%

“…This formula is now known as the Gompertz-Makeham (or simply Makeham) mortality law. Throughout the 20th century and to this day, Gompertz and Makeham's contributions to actuarial science have inspired scientists in a variety of fields, such as Demography, Biodemography, Evolutionary Biology (OLSHANSKY; CARNES, 1997;OLSHANSKY, 2010;FINKELSTEIN, 2011;MISSOV, 2014;DAŃKO, 2016;MISSOV, 2018), Statistics and Applied Mathematics (JODRÁ, 2009DEY;MOALA;KUMAR, 2018;BÖHNSTEDT;GAMPE, 2019;SALINARI;DE SANTIS, 2020), Business (BEMMAOR; GLADY, 2012; MILEVSKY; SALISBURY; ALEXANDER, 2016) and, evidently, Actuarial Science (PITACCO, 2004;BUTT;HABERMAN, 2004;LI et al, 2021), among others.…”

Section: Introductionmentioning

confidence: 99%

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Closed-form expressions to Gompertz-Makeham life expectancies: a historical note

Souza

2022

Rev. bras. estud. popul.

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Results well known in the actuarial community about closed-form expressions to Gompertz and Gompertz-Makeham life expectancies for a person aged x are still being independently rediscovered to this day. This note seeks to acknowledge previous results about closed-form expressions to Gompertz-Makeham life expectancies, especially in the actuarial science field, hoping to stimulate interdisciplinarity and provide the background for further developments, especially since the derivation of closed-form expressions for life expectancy (and annuities) based on particular mortality laws are matters of interest for multiple fields such as actuarial science, biology, demography, statistics among others.

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Section: The Case Of a Gamma-heterogeneous Populationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Closed-form expressions to Gompertz-Makeham life expectancies: a historical note

Souza

2022

Rev. bras. estud. popul.

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“…90 years when the numbers of people aged so much became high enough to provide for reliable estimated of mortality rates. The predominant approaches to explaining this phenomenon are based on the assumption that the populations under consideration are heterogenous, and the organisms that are frailer initially and/or become frailer more rapidly during aging die out earlier thus increasing the proportions of those whose dying out is slower (Vaupel, Carey et al 1998, Németh and Missov 2018, Salinari and De Santis 2019. The possibility that the real deceleration of the biological aging may take place at the latest periods of lifespans is most often not considered.…”

Section: Introductionmentioning

confidence: 99%

Invariances in relations between the rates of mortality and aging captured by a generalization of the Gompertz-Makeham law: Lessons from Caucasus

Golubev

2024

Preprint

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Among scarce biological relations qualifiable as laws, the Gompertz-Makeham law (GML) stands out being directly related to life-and-death issues. GML may be written as: -[dn(t)/n(t)]/dt≡µ(t) = e^(-v + γt) + C = e^(-v)*e^(gt) + C = µ0*e^(gt) + C, where µ(t) is mortality rate (MR), v captures vitality (resistance to mortality), g captures aging-associated v decrease, µ0 = 1/e^v is the initial MR, and C captures the MR part attributable to external (background) hazards irresistible at any age. GML status is questionable since, upon the common assumptions that vitality decreases linearly and C is constant, MR-vs-age trajectories violate GML, especially at later ages. A generalized GML (GGML) µ(t) = C(t)+µ0*e^[f(t)] suggests that MR increases exponentially IF vitality decreases linearly, i.e. IF f(t) = gt, and C = 0. GGML produces µ(t) changes from any vitality changes by exponentiation and, from any background hazardousness changes, in a linear way. Thus, f(t) may be deduced from µ(t), provided C(t) is treated properly. Based on this, it may be shown that a hump of the biological aging rate revealed through the lens of GGML at ages 65 to 90 years in low C(t) countries featuring high life expectancies may be discerned also in high C(t) countries by taking into account that C(t) there is increased mostly in the middle of age span, as in the North Caucasus and some other Russian Federation regions. Thus, GGML captures relational invariants inherent in the animate nature and discernable even beneath such multifactorial phenomena as human mortality and its such diverse manifestations as mortality kinetics. These invariants constrain advances in human life expectancy.

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An underappreciated peculiarity of late-life human mortality kinetics assessed through the lens of a generalization of the Gompertz-Makeham law

Golubev

2023

Biogerontology

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One or more rates of ageing? The extended gamma-Gompertz model (EGG)

Cited by 9 publications

References 39 publications

Closed-form expressions to Gompertz-Makeham life expectancies: a historical note

Closed-form expressions to Gompertz-Makeham life expectancies: a historical note

Invariances in relations between the rates of mortality and aging captured by a generalization of the Gompertz-Makeham law: Lessons from Caucasus

An underappreciated peculiarity of late-life human mortality kinetics assessed through the lens of a generalization of the Gompertz-Makeham law

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