Volume 41 - Article 4 | Pages 83–102  

The threshold age of the lifetable entropy

By Jose Manuel Aburto, Jesús-Adrián Alvarez, Francisco Villavicencio, James W. Vaupel

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

Abstract

Background: Indicators of relative variation of lifespans are markers of inequality at the population level and of uncertainty at the time of death at the individual level. In particular, the lifetable entropy H represents the elasticity of life expectancy to a change in mortality. However, it is unknown how this measure changes over time and whether a threshold age exists, as it does for other lifespan variation indicators.

Results: The time derivative of H can be decomposed into changes in life disparity e† and life expectancy at birth eo. Likewise, changes over time in H are a weighted average of age-specific rates of mortality improvements. These weights reflect the sensitivity of H and show how mortality improvements can increase (or decrease) the relative inequality of lifespans. Further, we prove that in the assumption that mortality is reduced at all ages, H, as well as e†, has a threshold age below which saving lives reduces entropy, whereas improvements above that age increase entropy.

Contribution: We give a formal expression for changes of H over time and provide a formal proof of the existence of a unique threshold age that separates reductions and increases in lifespan variation as a result age-specific mortality improvements.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

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

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy
Volume 51 - Article 24

How lifespan and life years lost equate to unity
Volume 50 - Article 24

Subnational contribution to life expectancy and life span variation changes: Evidence from the United States
Volume 50 - Article 22

Dynamics of the coefficient of variation of the age at death distribution
Volume 49 - Article 38

Leveraging deep neural networks to estimate age-specific mortality from life expectancy at birth
Volume 47 - Article 8

Divergent trends in lifespan variation during mortality crises
Volume 46 - Article 11

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

Mexican mortality 1990‒2016: Comparison of unadjusted and adjusted estimates
Volume 44 - Article 30

Born once, die once: Life table relationships for fertility
Volume 44 - Article 2

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

Lexis fields
Volume 42 - Article 24

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

Geofaceting: Aligning small-multiples for regions in a spatially meaningful way
Volume 41 - Article 17

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

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

Symmetries between life lived and left in finite stationary populations
Volume 35 - Article 14

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

The difference between alternative averages
Volume 27 - Article 15

Attrition in heterogeneous cohorts
Volume 23 - Article 26

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

The age separating early deaths from late deaths
Volume 20 - 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

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

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

Data errors in mortality estimation: Formal demographic analysis of under-registration, under-enumeration, and age misreporting
Volume 51 - Article 9    | Keywords: age misreporting, data errors, formal demography, mortality

Socio-behavioral factors contributing to recent mortality trends in the United States
Volume 51 - Article 7    | Keywords: despair, health, mortality, National Health Interview Survey (NHIS), smoking, trends

Climate change and health transitions: Evidence from Antananarivo, Madagascar
Volume 51 - Article 6    | Keywords: climate change, health transition, historical demography, infectious diseases, mortality