Volume 30 - Article 48 | Pages 1367–1396  

Why do lifespan variability trends for the young and old diverge? A perturbation analysis

By Michal Engelman, Hal Caswell, Emily Agree

Abstract

Background: Variation in lifespan has followed strikingly different trends for the young and old: while overall lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased. These diverging trends reflect changes in the underlying demographic parameters determining age-specific mortality.

Objective: We ask why the variation in the adult ages at death has followed a different trend than the variation at younger ages, and aim to explain the diverging patterns in terms of historical changes in the age schedule of mortality.

Methods: Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality hazard across the full lifespan using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters over time. Finally, we express lifespan variation in terms of a Markov chain model, and apply matrix calculus perturbation analysis to compute the sensitivity of age-specific lifespan variance trends to the changing Siler model parameters.

Results: Our analysis produces a detailed quantification of the impact of changing demographic parameters on the pattern of lifespan variability at all ages, highlighting the impact of declining childhood mortality on the reduction of lifespan variability and the impact of improved survival in adulthood on the rising variability of lifespans at older ages.

Conclusions: These findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

Author's Affiliation

• Michal Engelman - University of Wisconsin–Madison, United States of America EMAIL
• Hal Caswell - Universiteit van Amsterdam, the Netherlands EMAIL
• Emily Agree - Johns Hopkins University, United States of America EMAIL

Other articles by the same author/authors in Demographic Research

The formal demography of kinship V: Kin loss, bereavement, and causes of death
Volume 49 - Article 41

The contributions of stochastic demography and social inequality to lifespan variability
Volume 49 - Article 13

How does the demographic transition affect kinship networks?
Volume 48 - Article 32

The formal demography of kinship IV: Two-sex models and their approximations
Volume 47 - Article 13

The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16

Healthy longevity from incidence-based models: More kinds of health than stars in the sky
Volume 45 - Article 13

The formal demography of kinship II: Multistate models, parity, and sibship
Volume 42 - Article 38

The formal demography of kinship: A matrix formulation
Volume 41 - Article 24

The sensitivity analysis of population projections
Volume 33 - Article 28

Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20

Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19

A matrix approach to the statistics of longevity in heterogeneous frailty models
Volume 31 - Article 19

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
Volume 23 - Article 19

Perturbation analysis of nonlinear matrix population models
Volume 18 - Article 3

Most recent similar articles in Demographic Research

The importance of education for understanding variability of dementia onset in the United States
Volume 50 - Article 26    | Keywords: dementia, education, lifespan variability, modal age, morbidity compression

Differences in mortality before retirement: The role of living arrangements and marital status in Denmark
Volume 50 - Article 20    | Keywords: inequalities, living arrangements, marital status, mortality, retirement

Racial classification as a multistate process
Volume 50 - Article 17    | Keywords: Brazil, demography, increments to life, life expectancy, life table, mortality, multistate, race/ethnicity

Measuring short-term mobility patterns in North America using Facebook advertising data, with an application to adjusting COVID-19 mortality rates
Volume 50 - Article 10    | Keywords: COVID-19, data collection, Facebook, mortality, North America, short-term mobility

Immigrant mortality advantage in the United States during the first year of the COVID-19 pandemic
Volume 50 - Article 7    | Keywords: COVID-19, immigrants, mortality