Volume 32 - Article 36 | Pages 1031–1048  

The Gompertz force of mortality in terms of the modal age at death

By Trifon Missov, Adam Lenart, Laszlo Nemeth, Vladimir Canudas-Romo, James W. Vaupel

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


Background: The Gompertz force of mortality (hazard function) is usually expressed in terms of a, the initial level of mortality, and b, the rate at which mortality increases with age.

Objective: We express the Gompertz force of mortality in terms of b and the old-age modal age at death M, and present similar relationships for other widely-used mortality models. Our objective is to explain the advantages of using the parameterization in terms of M.

Methods: Using relationships among life table functions at the modal age at death, we express the Gompertz force of mortality as a function of the old-age mode. We estimate the correlation between the estimators of old (a and b) and new (M and b) parameters from simulated data.

Results: When the Gompertz parameters are statistically estimated from simulated data, the correlation between estimated values of b and M is much less than the correlation between estimated values of a and b. For the populations in the Human Mortality Database, there is a negative association between a and b and a positive association between M and b.

Conclusions: Using M, the old-age mode, instead of a, the level of mortality at the starting age, has two major advantages. First, statistical estimation is facilitated by the lower correlation between the estimators of model parameters. Second, estimated values of M are more easily comprehended and interpreted than estimated values of a.

Author's Affiliation

Other articles by the same author/authors in Demographic Research

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

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

Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models
Volume 24 - Article 19

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

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

Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death
Volume 50 - Article 11

Variable-r in sex ratios: Formulas in honor of Jim Vaupel
Volume 49 - Article 26

Comparative evidence of years lived with reproductive-age morbidity in sub-Saharan Africa (2010‒2019)
Volume 49 - Article 6

The role of reductions in old-age mortality in old-age population growth
Volume 44 - Article 44

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

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

Expected years ever married
Volume 38 - Article 47

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

Decomposing changes in life expectancy: Compression versus shifting mortality
Volume 33 - Article 14

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

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

Cause-specific measures of life years lost
Volume 29 - Article 41

Gamma-Gompertz life expectancy at birth
Volume 28 - Article 9

The difference between alternative averages
Volume 27 - Article 15

The crossover between life expectancies at birth and at age one: The imbalance in the life table
Volume 24 - Article 4

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

No consistent effects of prenatal or neonatal exposure to Spanish flu on late-life mortality in 24 developed countries
Volume 22 - Article 20

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

An integrated approach to cause-of-death analysis: cause-deleted life tables and decompositions of life expectancy
Volume 19 - Article 35

The modal age at death and the shifting mortality hypothesis
Volume 19 - Article 30

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

Lifesaving, lifetimes and lifetables
Volume 13 - Article 24

Changing mortality and average cohort life expectancy
Volume 13 - Article 5

Age-specific contributions to changes in the period and cohort life expectancy
Volume 13 - Article 3

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

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

Similar articles in Demographic Research

Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death
Volume 50 - Article 11    | Keywords: longevity, mathematical demography, modal age at death

Insight on 'typical' longevity: An analysis of the modal lifespan by leading causes of death in Canada
Volume 35 - Article 17    | Keywords: age-at-death distribution, Canada, cancer, cardiovascular diseases, cause of death, longevity, modal age at death, old-age mortality, Poisson P-splines, smoothing

Decomposing changes in life expectancy: Compression versus shifting mortality
Volume 33 - Article 14    | Keywords: compression of mortality, decomposition, life expectancy, modal age at death, mortality models, shifting mortality