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

Engelman M, Caswell H, Agree EM - Demogr Res (2014)

Bottom Line: Variation in lifespan has followed strikingly different trends for the young and old: while total lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased.Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival on the rising variability of lifespans at older ages.These findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

View Article: PubMed Central - PubMed

Affiliation: Department of Sociology and Center for Demography and Ecology, University of Wisconsin-Madison, USA.

ABSTRACT

Background: Variation in lifespan has followed strikingly different trends for the young and old: while total 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 ages at death after survival to adult ages has followed a different trend than the variation at younger ages, and aim to explain the divergence in terms of the age pattern of historical mortality changes.

Methods: Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality trajectory using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters for Swedish females from 1900 to 2010. We express mortality in terms of a Markov chain model, and apply matrix calculus to compute the sensitivity of age-specific variance trends to the changes in Siler model parameters.

Results: Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival 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.

No MeSH data available.


Trends in maximum likelihood parameter estimates for the Siler modelNotes: The child mortality parameter β1 is negative in the Siler equation, while all other parameters are positive. Based on life tables for Swedish females 1900–2010.
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Figure 3: Trends in maximum likelihood parameter estimates for the Siler modelNotes: The child mortality parameter β1 is negative in the Siler equation, while all other parameters are positive. Based on life tables for Swedish females 1900–2010.

Mentions: Figure 3 presents maximum likelihood estimates for the Siler model parameters from 1900–2010. Each parameter is represented in its own scale, to facilitate the analysis of trends. The α parameters, representing the overall levels of child, adult, and background mortality, decline over time, although α2 (the adult parameter) first increased slightly between 1900–1930 before declining. All three α parameters are negative, with α2 always less than α1 and α3. Both β slope parameters are positive, with β1 more than an order of magnitude larger than β2. The value of β1, which represents the rate of decline in childhood mortality with age, increased dramatically from 1900–1940, and then remained roughly constant — a result consistent with the known improvements in infant survival. The trend in β2, which represents the rate of increase in adult mortality with age, mirrors the α2 trend: first declining between 1900–1930, and then increasing during the latter part of the twentieth century, although the overall variation is small. Thus the slope of the adult hazard trajectory has grown slightly steeper since 1930, even as age-specific mortality hazards have declined, with mortality being increasingly compressed into the latter part of life. Overall, infant and childhood mortality declined earlier in the century, and adult survival improvement followed in subsequent decades.


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

Engelman M, Caswell H, Agree EM - Demogr Res (2014)

Trends in maximum likelihood parameter estimates for the Siler modelNotes: The child mortality parameter β1 is negative in the Siler equation, while all other parameters are positive. Based on life tables for Swedish females 1900–2010.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4326020&req=5

Figure 3: Trends in maximum likelihood parameter estimates for the Siler modelNotes: The child mortality parameter β1 is negative in the Siler equation, while all other parameters are positive. Based on life tables for Swedish females 1900–2010.
Mentions: Figure 3 presents maximum likelihood estimates for the Siler model parameters from 1900–2010. Each parameter is represented in its own scale, to facilitate the analysis of trends. The α parameters, representing the overall levels of child, adult, and background mortality, decline over time, although α2 (the adult parameter) first increased slightly between 1900–1930 before declining. All three α parameters are negative, with α2 always less than α1 and α3. Both β slope parameters are positive, with β1 more than an order of magnitude larger than β2. The value of β1, which represents the rate of decline in childhood mortality with age, increased dramatically from 1900–1940, and then remained roughly constant — a result consistent with the known improvements in infant survival. The trend in β2, which represents the rate of increase in adult mortality with age, mirrors the α2 trend: first declining between 1900–1930, and then increasing during the latter part of the twentieth century, although the overall variation is small. Thus the slope of the adult hazard trajectory has grown slightly steeper since 1930, even as age-specific mortality hazards have declined, with mortality being increasingly compressed into the latter part of life. Overall, infant and childhood mortality declined earlier in the century, and adult survival improvement followed in subsequent decades.

Bottom Line: Variation in lifespan has followed strikingly different trends for the young and old: while total lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased.Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival on the rising variability of lifespans at older ages.These findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

View Article: PubMed Central - PubMed

Affiliation: Department of Sociology and Center for Demography and Ecology, University of Wisconsin-Madison, USA.

ABSTRACT

Background: Variation in lifespan has followed strikingly different trends for the young and old: while total 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 ages at death after survival to adult ages has followed a different trend than the variation at younger ages, and aim to explain the divergence in terms of the age pattern of historical mortality changes.

Methods: Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality trajectory using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters for Swedish females from 1900 to 2010. We express mortality in terms of a Markov chain model, and apply matrix calculus to compute the sensitivity of age-specific variance trends to the changes in Siler model parameters.

Results: Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival 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.

No MeSH data available.