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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.


Sensitivity of each age-specific (conditional) standard deviation in the distribution of lifespans to unit changes in Siler model parameters for selected agesNotes: Sensitivity is measured in the same units as the standard deviation.
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Figure 5: Sensitivity of each age-specific (conditional) standard deviation in the distribution of lifespans to unit changes in Siler model parameters for selected agesNotes: Sensitivity is measured in the same units as the standard deviation.

Mentions: For a more detailed longitudinal perspective on the relationship between the Siler parameters and conditional variability for selected ages, Figure 5 presents the trends in the sensitivity of the standard deviation of the lifespan distribution for survivors to selected ages (0, 10, 50, and 75) to each Siler model parameter. The sensitivities of s0 to each parameter have changed dramatically over the course of the twentieth century. For example, while the childhood mortality parameters α1 and β1 were quite influential for s0 in 1900, its sensitivity to them declined steeply after that. Another steep decline, followed by stable lower rate, is apparent in the sensitivity of s0 to α3, the background mortality component. The sensitivity of s0 to the two adult mortality parameters, α2 and β2, also shows two distinct phases: it rapidly moves towards less negative values during the first part of the century, and then stabilizes (or continues to decline very slowly) during the latter part of the time series. Trends for the sensitivity of s10 to the same parameters follow a similar pattern, consistent with the reductions in early-life mortality which took place in the first half of the twentieth century.


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

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

Sensitivity of each age-specific (conditional) standard deviation in the distribution of lifespans to unit changes in Siler model parameters for selected agesNotes: Sensitivity is measured in the same units as the standard deviation.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Sensitivity of each age-specific (conditional) standard deviation in the distribution of lifespans to unit changes in Siler model parameters for selected agesNotes: Sensitivity is measured in the same units as the standard deviation.
Mentions: For a more detailed longitudinal perspective on the relationship between the Siler parameters and conditional variability for selected ages, Figure 5 presents the trends in the sensitivity of the standard deviation of the lifespan distribution for survivors to selected ages (0, 10, 50, and 75) to each Siler model parameter. The sensitivities of s0 to each parameter have changed dramatically over the course of the twentieth century. For example, while the childhood mortality parameters α1 and β1 were quite influential for s0 in 1900, its sensitivity to them declined steeply after that. Another steep decline, followed by stable lower rate, is apparent in the sensitivity of s0 to α3, the background mortality component. The sensitivity of s0 to the two adult mortality parameters, α2 and β2, also shows two distinct phases: it rapidly moves towards less negative values during the first part of the century, and then stabilizes (or continues to decline very slowly) during the latter part of the time series. Trends for the sensitivity of s10 to the same parameters follow a similar pattern, consistent with the reductions in early-life mortality which took place in the first half of the twentieth century.

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.