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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 lifespan variation for Swedish Females, 1900–2010Notes: Left: Trends in standard deviations of lifespan distributions for Swedish females: full population (s0) and survivors to ages 10 (s10), 50 (s50), 75 (s75), and 90 (s90).Right: Trends in standard deviations of lifespan distributions at the same ages relative to their values in 1900. Both perspectives show reduced variability in lifespan distributions containing younger people, but growing lifespan variability among survivors to older ages.Source: Human Mortality Database, 2012.
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Figure 1: Trends in lifespan variation for Swedish Females, 1900–2010Notes: Left: Trends in standard deviations of lifespan distributions for Swedish females: full population (s0) and survivors to ages 10 (s10), 50 (s50), 75 (s75), and 90 (s90).Right: Trends in standard deviations of lifespan distributions at the same ages relative to their values in 1900. Both perspectives show reduced variability in lifespan distributions containing younger people, but growing lifespan variability among survivors to older ages.Source: Human Mortality Database, 2012.

Mentions: Variation in lifespan can be measured with a number of indices, all of which are highly correlated across populations and over time (Wilmoth and Horiuchi 1999; van Raalte and Caswell 2013). Here, we measure lifespan variability by sx, the standard deviation of the age at death, conditional on survival to the index age x. Figure 1 shows that the standard deviation among newborn individuals, measured relative to its initial value, has declined since 1900, as has the variation in the distributions of ages at death conditional on survival to age 10. However, variation in the age at death among survivors to older ages is higher now than it was a century ago, when the challenges of reaching older ages may have fashioned a more highly selected group of survivors. While the figure relies on data for Swedish females to illustrate this pattern, the diverging age-specific trends have been observed for women and men across industrialized nations and appear to be a common feature of the mortality transition in contemporary high-longevity countries (Engelman et al. 2010).


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 lifespan variation for Swedish Females, 1900–2010Notes: Left: Trends in standard deviations of lifespan distributions for Swedish females: full population (s0) and survivors to ages 10 (s10), 50 (s50), 75 (s75), and 90 (s90).Right: Trends in standard deviations of lifespan distributions at the same ages relative to their values in 1900. Both perspectives show reduced variability in lifespan distributions containing younger people, but growing lifespan variability among survivors to older ages.Source: Human Mortality Database, 2012.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Trends in lifespan variation for Swedish Females, 1900–2010Notes: Left: Trends in standard deviations of lifespan distributions for Swedish females: full population (s0) and survivors to ages 10 (s10), 50 (s50), 75 (s75), and 90 (s90).Right: Trends in standard deviations of lifespan distributions at the same ages relative to their values in 1900. Both perspectives show reduced variability in lifespan distributions containing younger people, but growing lifespan variability among survivors to older ages.Source: Human Mortality Database, 2012.
Mentions: Variation in lifespan can be measured with a number of indices, all of which are highly correlated across populations and over time (Wilmoth and Horiuchi 1999; van Raalte and Caswell 2013). Here, we measure lifespan variability by sx, the standard deviation of the age at death, conditional on survival to the index age x. Figure 1 shows that the standard deviation among newborn individuals, measured relative to its initial value, has declined since 1900, as has the variation in the distributions of ages at death conditional on survival to age 10. However, variation in the age at death among survivors to older ages is higher now than it was a century ago, when the challenges of reaching older ages may have fashioned a more highly selected group of survivors. While the figure relies on data for Swedish females to illustrate this pattern, the diverging age-specific trends have been observed for women and men across industrialized nations and appear to be a common feature of the mortality transition in contemporary high-longevity countries (Engelman et al. 2010).

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.