Gompertz-Makeham law of mortality - Revision history

Dmitry Dzhagarov: /* = Mortality in people with diabetes */

2024-03-22T03:56:19Z

= Mortality in people with diabetes

← Older revision		Revision as of 03:56, 22 March 2024
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	== Gompertz models ==		== Gompertz models ==
	=== Mortality in people with diabetes ==		=== Mortality in people with diabetes ===
	Data analysis of all statutory health-insured persons (more than 47 million observations, of which over 6 million have diabetes) in in Germany in 2013 shows that mortality in people with diabetes constantly rises by 8.3% for males and 10.2% for females each year from the age of 30 (age range 30– > 95 years) and the probability that a person with diabetes dies before a person without diabetes is 61.9% for females and 63.3% for males. The survival information of the population with diabetes during a large part of the lifespan can thus be reduced to the two parameters of the Gompertz distribution.<ref>Kuss, O., Baumert, J., Schmidt, C., & Tönnies, T. (2024). Mortality of type 2 diabetes in Germany: additional insights from Gompertz models. Acta Diabetologica, 1-7. [https://pubmed.ncbi.nlm.nih.gov/38466430/ PMID: 38466430] [https://doi.org/10.1007/s00592-024-02237-w DOI: 10.1007/s00592-024-02237-w]</ref>		Data analysis of all statutory health-insured persons (more than 47 million observations, of which over 6 million have diabetes) in in Germany in 2013 shows that mortality in people with diabetes constantly rises by 8.3% for males and 10.2% for females each year from the age of 30 (age range 30– > 95 years) and the probability that a person with diabetes dies before a person without diabetes is 61.9% for females and 63.3% for males. The survival information of the population with diabetes during a large part of the lifespan can thus be reduced to the two parameters of the Gompertz distribution.<ref>Kuss, O., Baumert, J., Schmidt, C., & Tönnies, T. (2024). Mortality of type 2 diabetes in Germany: additional insights from Gompertz models. Acta Diabetologica, 1-7. [https://pubmed.ncbi.nlm.nih.gov/38466430/ PMID: 38466430] [https://doi.org/10.1007/s00592-024-02237-w DOI: 10.1007/s00592-024-02237-w]</ref>

	== References ==		== References ==

Dmitry Dzhagarov at 03:53, 22 March 2024

2024-03-22T03:53:43Z

← Older revision		Revision as of 03:53, 22 March 2024
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	[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]		[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]
	The Gompertz-Makeham law of mortality is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery>		The Gompertz-Makeham law of mortality is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery></gallery> The Gompertz law is based on the observation that biological processes in the body change with aging, resulting in a higher risk for illnesses and ultimately death. The mortality rate does not grow linearly, but exponentially, meaning that it continues to accelerate with age. This exponential change is observed virtually universally, both across regions and time.
	</gallery> The Gompertz law is based on the observation that biological processes in the body change with aging, resulting in a higher risk for illnesses and ultimately death. The mortality rate does not grow linearly, but exponentially, meaning that it continues to accelerate with age. This exponential change is observed virtually universally, both across regions and time.

	== History ==		== History ==

Dmitry Dzhagarov at 03:48, 22 March 2024

2024-03-22T03:48:30Z

← Older revision		Revision as of 03:48, 22 March 2024
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	[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]		[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]
	The Gompertz-Makeham law of mortality is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery>		The Gompertz-Makeham law of mortality is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery>
	</gallery>		</gallery> The Gompertz law is based on the observation that biological processes in the body change with aging, resulting in a higher risk for illnesses and ultimately death. The mortality rate does not grow linearly, but exponentially, meaning that it continues to accelerate with age. This exponential change is observed virtually universally, both across regions and time.

	== History ==		== History ==
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	== The Gompertz Law as an intrinsic principle of aging ==		== The Gompertz Law as an intrinsic principle of aging ==
	The neatness and simplicity of the Gompertz law (the original, simpler version of the Gompertz-Makeham law of mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>, where m<sub>t</sub> is the mortality rate, S<sub>t</sub> is the proportion of survivors of the original population, and k and c are free parameters, researchers working with the University of Groningen have suggested that k and c may represent biological characteristics. They suggest that the parameter "k" might represent the accumulation of random damage or perturbations, while "c" might represent the vitality of an organism.<ref name=":3" />		The neatness and simplicity of the Gompertz law (the original, simpler version of the Gompertz-Makeham law of mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>, where m<sub>t</sub> is the mortality rate, S<sub>t</sub> is the proportion of survivors of the original population, and k and c are free parameters, researchers working with the University of Groningen have suggested that k and c may represent biological characteristics. They suggest that the parameter "k" might represent the accumulation of random damage or perturbations, while "c" might represent the vitality of an organism.<ref name=":3" />

			== Gompertz models ==
			=== Mortality in people with diabetes ==
			Data analysis of all statutory health-insured persons (more than 47 million observations, of which over 6 million have diabetes) in in Germany in 2013 shows that mortality in people with diabetes constantly rises by 8.3% for males and 10.2% for females each year from the age of 30 (age range 30– > 95 years) and the probability that a person with diabetes dies before a person without diabetes is 61.9% for females and 63.3% for males. The survival information of the population with diabetes during a large part of the lifespan can thus be reduced to the two parameters of the Gompertz distribution.<ref>Kuss, O., Baumert, J., Schmidt, C., & Tönnies, T. (2024). Mortality of type 2 diabetes in Germany: additional insights from Gompertz models. Acta Diabetologica, 1-7. [https://pubmed.ncbi.nlm.nih.gov/38466430/ PMID: 38466430] [https://doi.org/10.1007/s00592-024-02237-w DOI: 10.1007/s00592-024-02237-w]</ref>

	== References ==		== References ==

Andrea: category change

2022-12-27T12:31:42Z

category change

← Older revision		Revision as of 12:31, 27 December 2022
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	== References ==		== References ==
	<references />		<references />
	[[Category:Longevity]]		[[Category:Main list]]
			[[Category:Longevity concepts]]

Andrea: Andrea moved page Gompertz-Makeham Law of Mortality to Gompertz-Makeham law of mortality: Changed title

2022-08-25T17:20:52Z

Andrea moved page Gompertz-Makeham Law of Mortality to Gompertz-Makeham law of mortality: Changed title

← Older revision	Revision as of 17:20, 25 August 2022
(No difference)

Andrea: /* History */

2022-08-19T11:45:27Z

History

← Older revision		Revision as of 11:45, 19 August 2022
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	== References ==		== References ==
	<references />		<references />
	~~[[Category:Drafts]]~~
	[[Category:Longevity]]		[[Category:Longevity]]

Andrea: /* Small edits and added graph */

2022-08-18T20:56:56Z

Small edits and added graph

← Older revision		Revision as of 20:56, 18 August 2022
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	[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]		[[File:Gompertz-Makeham Law of Mortality.jpg\|thumb\|143x143px\|Gompertz-Makeham Law of Mortality, where ''μ(x)'' indicates mortality rate, ''α'' and ''β'' are constants, and ''γ'' represents factors unrelated to age which contribute to mortality.]]
	The Gompertz-Makeham ~~Law~~ of ~~Mortality~~ is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery>		The Gompertz-Makeham law of mortality is an equation which shows the increase in mortality rates for organisms as they age.<ref name=":0">''Gompertz-Makeham_law_of_mortality''. (n.d.). Retrieved August 7, 2022, from <nowiki>https://www.bionity.com/en/encyclopedia/Gompertz-Makeham_law_of_mortality.html</nowiki></ref><gallery>
	</gallery>		</gallery>

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	== Description ==		== Description ==
			[[File:USGompertzCurve.svg.png\|thumb\|The Gompertz-Makeham law of mortality describes the risk of dying, which the graph depicts to exponentially increase between 30 and 80 years of age. Data from the US National Vital Statistics Report in 2003.<ref>https://www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14.pdf</ref>]]
	When solved for mortality rate, the law can be written as μ(x)=α''e''<sup>βx</sup>+γ, where "μ(x)" represents mortality rate at age x, "α" and "β" are arbitrary constants, and "γ" is a constant representing age-independent mortality.<ref name=":1" /> The term "α''e''<sup>βx</sup>" is known as the "Gompertz function" while "γ" is known as the "Makeham term" of the equation.<ref name=":0" /><ref name=":2" />		When solved for mortality rate, the law can be written as μ(x)=α''e''<sup>βx</sup>+γ, where "μ(x)" represents mortality rate at age x, "α" and "β" are arbitrary constants, and "γ" is a constant representing age-independent mortality.<ref name=":1" /> The term "α''e''<sup>βx</sup>" is known as the "Gompertz function" while "γ" is known as the "Makeham term" of the equation.<ref name=":0" /><ref name=":2" />

	== Usage ==		== Usage ==
	The Gompertz-Makeham ~~Law~~ of ~~Mortality~~ is used even in modern times by insurance companies to model expected adult lifetimes, as it gives fairly accurate death rates for human populations between the ages of 30 and 80.<ref name=":0" /><ref name=":2" /> It should be noted, however, that at more advanced ages human death rates cease to increase as quickly as it predicts.<ref name=":0" /> It can also be used to predict death rates for species besides humans, though there are species to which it does not apply, and it does not necessarily describe mortality for child, infant, or extremely elderly individuals in those species for which it applies.<ref name=":1" /> In addition, several studies have found incidence curves of certain cancers to be nearly parallel to the Gompertz function, suggesting that they, and perhaps some other pathologies, depend on intrinsic aging processes. Researchers working with the University of Groningen have suggested using such similarities to distinguish between mainly intrinsically aging-associated and extrinsically caused mortality.<ref name=":3">Sas, A. A., Snieder, H., & Korf, J. (2012). Gompertz’ survivorship law as an intrinsic principle of aging. ''Medical Hypotheses'', ''78''(5), 659–663. <nowiki>https://doi.org/10.1016/j.mehy.2012.02.004</nowiki></ref>		The Gompertz-Makeham law of mortality is used even in modern times by insurance companies to model expected adult lifetimes, as it gives fairly accurate death rates for human populations between the ages of 30 and 80.<ref name=":0" /><ref name=":2" /> It should be noted, however, that at more advanced ages human death rates cease to increase as quickly as it predicts.<ref name=":0" /> It can also be used to predict death rates for species besides humans, though there are species to which it does not apply, and it does not necessarily describe mortality for child, infant, or extremely elderly individuals in those species for which it applies.<ref name=":1" /> In addition, several studies have found incidence curves of certain cancers to be nearly parallel to the Gompertz function, suggesting that they, and perhaps some other pathologies, depend on intrinsic aging processes. Researchers working with the University of Groningen have suggested using such similarities to distinguish between mainly intrinsically aging-associated and extrinsically caused mortality.<ref name=":3">Sas, A. A., Snieder, H., & Korf, J. (2012). Gompertz’ survivorship law as an intrinsic principle of aging. ''Medical Hypotheses'', ''78''(5), 659–663. <nowiki>https://doi.org/10.1016/j.mehy.2012.02.004</nowiki></ref>

	== The Gompertz Law as an ~~Intrinsic Principle~~ of ~~Aging~~ ==		== The Gompertz Law as an intrinsic principle of aging ==
	The neatness and simplicity of the Gompertz law (the original, simpler version of the Gompertz-Makeham ~~Law~~ of ~~Mortality~~) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>, where m<sub>t</sub> is the mortality rate, S<sub>t</sub> is the proportion of survivors of the original population, and k and c are free parameters, researchers working with the University of Groningen have suggested that k and c may represent biological characteristics. They suggest that the parameter "k" might represent the accumulation of random damage or perturbations, while "c" might represent the vitality of an organism.<ref name=":3" />		The neatness and simplicity of the Gompertz law (the original, simpler version of the Gompertz-Makeham law of mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>, where m<sub>t</sub> is the mortality rate, S<sub>t</sub> is the proportion of survivors of the original population, and k and c are free parameters, researchers working with the University of Groningen have suggested that k and c may represent biological characteristics. They suggest that the parameter "k" might represent the accumulation of random damage or perturbations, while "c" might represent the vitality of an organism.<ref name=":3" />

	== References ==		== References ==

Volunteer Longevity Writer 007: Expanded on "Gompertz Law as an Intrinsic Principle of Aging" section, and "Usage" section.

2022-08-15T19:25:16Z

Expanded on "Gompertz Law as an Intrinsic Principle of Aging" section, and "Usage" section.

← Older revision		Revision as of 19:25, 15 August 2022
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	== Description ==		== Description ==
	When solved for mortality rate, the law can be written as μ(x)=α''e''<sup>βx</sup>+γ, where "μ(x)" represents mortality rate at age x, "α" and "β" are arbitrary constants, and "γ" is a constant representing age-independent mortality.<ref name=":1" /> The term "α''e''<sup>βx</sup>" is known as the "Gompertz function" while "γ" is known as the "Makeham term" of the equation.<ref name=":0" /><ref name=":2" />		When solved for mortality rate, the law can be written as μ(x)=α''e''<sup>βx</sup>+γ, where "μ(x)" represents mortality rate at age x, "α" and "β" are arbitrary constants, and "γ" is a constant representing age-independent mortality.<ref name=":1" /> The term "α''e''<sup>βx</sup>" is known as the "Gompertz function" while "γ" is known as the "Makeham term" of the equation.<ref name=":0" /><ref name=":2" />

	== Usage ==		== Usage ==
	The Gompertz-Makeham Law of Mortality is used even in modern times by insurance companies to model expected adult lifetimes, as it gives fairly accurate death rates for human populations between the ages of 30 and 80.<ref name=":0" /><ref name=":2" /> It should be noted, however, that at more advanced ages human death rates cease to increase as quickly as it predicts.<ref name=":0" /> It can also be used to predict death rates for species besides humans, though there are species to which it does not apply, and it does not necessarily describe mortality for child, infant, or extremely elderly individuals in those species for which it applies.<ref name=":1" />		The Gompertz-Makeham Law of Mortality is used even in modern times by insurance companies to model expected adult lifetimes, as it gives fairly accurate death rates for human populations between the ages of 30 and 80.<ref name=":0" /><ref name=":2" /> It should be noted, however, that at more advanced ages human death rates cease to increase as quickly as it predicts.<ref name=":0" /> It can also be used to predict death rates for species besides humans, though there are species to which it does not apply, and it does not necessarily describe mortality for child, infant, or extremely elderly individuals in those species for which it applies.<ref name=":1" /> In addition, several studies have found incidence curves of certain cancers to be nearly parallel to the Gompertz function, suggesting that they, and perhaps some other pathologies, depend on intrinsic aging processes. Researchers working with the University of Groningen have suggested using such similarities to distinguish between mainly intrinsically aging-associated and extrinsically caused mortality.<ref name=":3">Sas, A. A., Snieder, H., & Korf, J. (2012). Gompertz’ survivorship law as an intrinsic principle of aging. ''Medical Hypotheses'', ''78''(5), 659–663. <nowiki>https://doi.org/10.1016/j.mehy.2012.02.004</nowiki></ref>

	== The Gompertz Law as an Intrinsic Principle of Aging ==		== The Gompertz Law as an Intrinsic Principle of Aging ==
	The neatness and simplicity of the Gompertz ~~Law~~ (the original, simpler version of the Gompertz-Makeham Law of Mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>,		The neatness and simplicity of the Gompertz law (the original, simpler version of the Gompertz-Makeham Law of Mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>, where m<sub>t</sub> is the mortality rate, S<sub>t</sub> is the proportion of survivors of the original population, and k and c are free parameters, researchers working with the University of Groningen have suggested that k and c may represent biological characteristics. They suggest that the parameter "k" might represent the accumulation of random damage or perturbations, while "c" might represent the vitality of an organism.<ref name=":3" />

	== References ==		== References ==

Volunteer Longevity Writer 007: Added a few words to "Gompertz Law as an Intrinsic Principle of Aging" section.

2022-08-15T00:53:36Z

Added a few words to "Gompertz Law as an Intrinsic Principle of Aging" section.

← Older revision		Revision as of 00:53, 15 August 2022
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	== The Gompertz Law as an Intrinsic Principle of Aging ==		== The Gompertz Law as an Intrinsic Principle of Aging ==
	The neatness and simplicity of the Gompertz Law (the original, simpler version of the Gompertz-Makeham Law of Mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" />		The neatness and simplicity of the Gompertz Law (the original, simpler version of the Gompertz-Makeham Law of Mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" /> For example, when it is written as m<sub>t</sub> = S<sub>t</sub>kc''e''<sup>kt</sup>,

	== References ==		== References ==

Volunteer Longevity Writer 007: Added to "Gompertz Law as an Intrinsic Principal of Aging" section.

2022-08-15T00:41:13Z

Added to "Gompertz Law as an Intrinsic Principal of Aging" section.

← Older revision		Revision as of 00:41, 15 August 2022
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	== The Gompertz Law as an Intrinsic Principle of Aging ==		== The Gompertz Law as an Intrinsic Principle of Aging ==
			The neatness and simplicity of the Gompertz Law (the original, simpler version of the Gompertz-Makeham Law of Mortality) has prompted some researchers to speculate that it is a fundamental law of nature, akin to some of the laws of physics.<ref name=":1" />

	== References ==		== References ==