How life expectancy varies with perturbations in age-specific mortality

Wrycza, Tomasz F.; Baudisch, Annette

doi:10.4054/demres.2012.27.13

Cited by 17 publications

(13 citation statements)

References 21 publications

(15 reference statements)

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“…Examples include the sensitivity of the intrinsic growth rate r or λ to changes in mortality and fertility, first derived by Hamilton (1966), followed by Demetrius (1969), Keyfitz (1971), and then in general form by Caswell (1978). The sensitivity of life expectancy to changes in mortality was derived by Keyfitz (1971), and investigated in more detail by Pollard (1982;1988) and more recently by Caswell (2006) and Wrycza and Baudisch (2012). Keyfitz introduced an elasticity of life expectancy in terms of life table entropy (see Keyfitz and Caswell 2 2005; chap.…”

Section: Introductionmentioning

confidence: 99%

Perturbation Analysis of Indices of Lifespan Variability

2013

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A number of indices exist to calculate lifespan variation, each with different underlying properties. Here we present new formulae for the response of seven of these indices to changes in the underlying mortality schedule (life disparity, the Gini coefficient, the standard deviation, the variance, Theil's index, the mean logarithmic deviation, and the inter-quartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity) to changes in age-specific mortality. Using empirical French and Russian male data we compare the underlying sensitivities to mortality change under different mortality regimes in order to test under which conditions the indices might differ in their conclusions about the magnitude of lifespan variation. Finally, we demonstrate how the sensitivities can be used to decompose temporal changes in the indices into contributions of age-specific mortality changes. The result is an easily computable method for calculating the properties of this important class of longevity indices.

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Section: Introductionmentioning

confidence: 99%

Perturbation Analysis of Indices of Lifespan Variability

2013

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“…Defined broadly, sensitivity analysis quantifies the change in an outcome variable in response to a change in one or more variables on which the outcome depends ( Caswell 1978 ). In demography, perturbation analysis has been used to describe the sensitivity of population growth rates to changes in the environment or in vital rates ( Demetrius 1969 ; Keyfitz 1971 ; Goodman 1971 ; Caswell 1978 , 2010 ), and the sensitivity of life expectancy to changes in age-specific mortality rates ( Keyfitz 1971 , 1977 ; Pollard 1982 ; Vaupel 1986 ; Keyfitz and Caswell 2005 ; Caswell 2006 , 2009 ; Wrycza and Baudisch 2012 ).…”

Section: Methodsmentioning

confidence: 99%

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

Engelman¹,

Caswell²,

Agree³

2014

DemRes

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BACKGROUNDVariation 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.OBJECTIVEWe 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.METHODSUsing 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.RESULTSOur 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.CONCLUSIONSThese findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

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“…More recently, changes in life expectancy due to small proportional changes in the total or cause-specific mortality have been described by Keyfitz (1977Keyfitz ( , 1985, Vaupel (1986), and Vaupel and Canudas Romo (2003). These and other results have been summarized by Wrycza and Baudisch (2012), who also present results on changes in life expectancy that are introduced by other types of perturbations in age-specific mortality. Demographers are often interested in the dynamics of populations, and their focus is therefore on describing the impact of small changes on population parameters from one calendar year to the next.…”

Section: Previous Work On the Relation Between Mortality Rate And Lifmentioning

confidence: 96%