Volume 23 - Article 26 | Pages 737–748  

Attrition in heterogeneous cohorts

By James W. Vaupel, Zhen Zhang

This article is part of the ongoing Special Collection 8 "Formal Relationships"

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 - Syddansk Universitet, Denmark EMAIL
• Zhen Zhang - Fudan University, China EMAIL

Other articles by the same author/authors in Demographic Research

The difference between alternative averages
Volume 27 - Article 15

The age separating early deaths from late deaths
Volume 20 - Article 29

Outsurvival as a measure of the inequality of lifespans between two populations
Volume 44 - Article 35

Population aging caused by a rise in the sex ratio at birth
Volume 43 - Article 32

Onset of the old-age gender gap in survival
Volume 42 - Article 25

The impact of the choice of life table statistics when forecasting mortality
Volume 41 - Article 43

The threshold age of the lifetable entropy
Volume 41 - Article 4

Life lived and left: Estimating age-specific survival in stable populations with unknown ages
Volume 39 - Article 37

Coherent forecasts of mortality with compositional data analysis
Volume 37 - Article 17

In Memoriam: Professor Jan M. Hoem
Volume 36 - Article 24

Demographic characteristics of Sardinian centenarian genealogies: Preliminary results of the AKeA2 study
Volume 32 - Article 37

The Gompertz force of mortality in terms of the modal age at death
Volume 32 - Article 36

Maternal longevity is associated with lower infant mortality
Volume 31 - Article 42

Unobserved population heterogeneity: A review of formal relationships
Volume 31 - Article 22

Senescence vs. sustenance: Evolutionary-demographic models of aging
Volume 23 - Article 23

Total daily change with age equals average lifetime change
Volume 22 - Article 36

Survival as a Function of Life Expectancy
Volume 21 - Article 29

Life lived and left: Carey’s equality
Volume 20 - Article 3

Formal Relationships: Introduction and Orientation
Volume 20 - Article 1

The relative tail of longevity and the mean remaining lifetime
Volume 14 - Article 7

Lifesaving, lifetimes and lifetables
Volume 13 - Article 24

Oldest Old Mortality in China
Volume 8 - Article 7

Life Expectancy at Current Rates vs. Current Conditions: A Reflexion Stimulated by Bongaarts and Feeney’s "How Long Do We Live?"
Volume 7 - Article 8

Decomposing demographic change into direct vs. compositional components
Volume 7 - Article 1

Dr. Väinö Kannisto: A Reflexion
Volume 6 - Article 5

Most recent similar articles in Demographic Research

Excess mortality associated with HIV: Survey estimates from the PHIA project
Volume 51 - Article 38    | Keywords: excess mortality, HIV/AIDS, mortality

A Bayesian model for age at death with cohort effects
Volume 51 - Article 33    | Keywords: age at death, Bayesian approach, cohort effects, Italy, mortality

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy
Volume 51 - Article 24    | Keywords: Gompertz law, life expectancy, lifespan variation, longevity, mode, mortality

Makeham mortality models as mixtures: Advancing mortality estimations through competing risks frameworks
Volume 51 - Article 18    | Keywords: background mortality, competing risks, Makeham, mixture model, mortality models, senescent mortality

The role of sex and age in seasonal mortality – the case of Poland
Volume 51 - Article 17    | Keywords: mortality, Poland, seasonality, sex differences