James W. Vaupel
Zhen Zhang

http://www.demographic-research.org/volumes/vol23/26/

doi:10.4054/DemRes.2010.23.26

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Abstract

In a heterogeneous cohort, the change with age in the force of mortality or some other kind of hazard or intensity of attrition depends on how the hazard changes with age for the individuals in the cohort and on how the composition of the cohort changes due to the loss of those most vulnerable to attrition. Here we prove that the change with age for the cohort equals the average of the change in the hazard for the individuals in the cohort minus the variance in the hazard across individuals. The variance captures the compositional change. This very general and remarkably elegant relationship can be applied to understand and to analyze changes with age in many kinds of demographic hazards, including, e.g., the lifetable aging rate or the intensity of first births.

Author's affiliation
James W. Vaupel
Max Planck Institute for Demographic Research, Germany
Zhen Zhang
Max Planck Institute for Demographic Research, Germany

Keywords
attrition, frailty, gamma distribution, Gompertz, heterogeneity, Makeham, mortality

Related links

All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/

Word count (Main text)
1779

Other articles by the same author/authors (in Demographic Research)

	[23-23] Senescence vs. sustenance: Evolutionary-demographic models of aging
	[22-36] Total daily change with age equals average lifetime change
	[21-29] Survival as a Function of Life Expectancy
	[20-29] The age separating early deaths from late deaths
	[20-3] Life lived and left: Carey’s equality
	[20-1] Formal Relationships: Introduction and Orientation
	[14-7] The relative tail of longevity and the mean remaining lifetime
	[13-24] Lifesaving, lifetimes and lifetables
	[8-7] Oldest Old Mortality in China
	[7-8] Life Expectancy at Current Rates vs. Current Conditions: A Reflexion Stimulated by Bongaarts and Feeney’s "How Long Do We Live?"
	[7-1] Decomposing demographic change into direct vs. compositional components
	[6-5] Dr. Väinö Kannisto: A Reflexion

Similar articles in Demographic Research

	[14-7] The relative tail of longevity and the mean remaining lifetime (heterogeneity, frailty)
	[7-8] Life Expectancy at Current Rates vs. Current Conditions: A Reflexion Stimulated by Bongaarts and Feeney’s "How Long Do We Live?" (heterogeneity, frailty)

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