Gompertz–Makeham life expectancies: Expressions and applications

Missov, Trifon I.; Lénárt, Ádám

doi:10.1016/j.tpb.2013.09.013

Cited by 48 publications

(27 citation statements)

References 9 publications

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“…In that analysis, heterogeneity accounted for less than 10%, and usually less than 5%, of the variance in longevity. It was based on a continuous heterogeneity model, in which a Gamma-distributed frailty term, acting as a proportional hazard on mortality, was applied to a Gompertz-Makeham mortality model (Missov 2013;Missov and Lenart 2013). The Gompertz-Makeham model is applicable to human populations only after the age of 30-40 years, so the human data corresponded to a later "adult" age than is the case for the invertebrate species studied here.…”

Section: Discussionmentioning

confidence: 99%

Variance in animal longevity: contributions of heterogeneity and stochasticity

Hartemink

Caswell

2018

Population Ecology

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Variance in longevity among individuals may arise as an effect of heterogeneity (differences in mortality rates experienced at the same age or stage) or as an effect of individual stochasticity (the outcome of random demographic events during the life cycle). Decomposing the variance into components due to heterogeneity and stochasticity is crucial for evolutionary analyses.In this study, we analyze longevity from ten studies of invertebrates in the laboratory, and use the results to partition the variance in longevity into its components. To do so, we fit finite mixtures of Weibull survival functions to each data set by maximum likelihood, using the EM algorithm. We used the Bayesian Information Criterion to select the most well supported model. The results of the mixture analysis were used to construct an age × stage-classified matrix model, with heterogeneity groups as stages, from which we calculated the variance in longevity and its components. Almost all data sets revealed evidence of some degree of heterogeneity. The median contribution of unobserved heterogeneity to the total variance was 35%, with the remaining 65% due to stochasticity. The differences among groups in mean longevity were typically on the order of 30% of the overall life expectancy. There was considerable variation among data sets in both the magnitude of heterogeneity and the proportion of variance due to heterogeneity, but no clear patterns were apparent in relation to sex, taxon, or environmental conditions.

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Section: Discussionmentioning

confidence: 99%

Variance in animal longevity: contributions of heterogeneity and stochasticity

Hartemink

Caswell

2018

Population Ecology

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“…An attractive feature for a mortality model is the possibility to compute in explicit form the life expectancy at birth (Missov 2013;Missov and Lenart 2013;Vaupel and Missov 2014). The mixture approach allows not only to compute e 0 analytically, but also to decompose the contribution to life expectancy of the three different components: infant and childhood, accidental and premature, and adult mortality.…”

Section: Life Expectancy Decompositionmentioning

confidence: 99%

A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality

2020

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Premature mortality is often a neglected component of overall deaths, and the most difficult to identify. However, it is important to estimate its prevalence. Following Pearson's theory about mortality components, a definition of premature deaths and a parametric model to study its transformations are introduced. The model is a mixture of three distributions: a Half Normal for the first part of the death curve and two Skew Normals to fit the remaining pieces. One advantage of the model is the possibility of obtaining an explicit equation to compute life expectancy at birth and to break it down into mortality components. We estimated the mixture model for Sweden, France, East Germany and Czech Republic. In addition, to the well-known reduction in infant deaths, and compression and shifting trend of adult mortality, we were able to study the trend of the central part of the distribution of deaths in detail. In general, a right shift of the modal age at death for young adults is observed; in some cases, it is also accompanied by an increase in the number of deaths at these ages: in particular for France, in the last twenty years, premature mortality increases.

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“…Second, the Gamma-Gompertz is a threeparameter model that includes the Kannisto as a special case: its hazard function has a logistic shape whose asymptote can be different than one. Also this model has gained relevant prominence during the last decades (Vaupel et al 1979;Missov and Lenart 2013;Colchero et al 2016). Finally, the Minimal and Maximal Generalized Extreme-Value models are characterized by three parameters, and for a fixed value of the third parameter (i.e.…”

Section: Other Parametric Mortality Modelsmentioning

confidence: 99%

Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models

2018

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Several parametric mortality models have been proposed to describe the age pattern of mortality since Gompertz introduced his "law of mortality" almost two centuries ago. However, very few attempts have been made to reconcile most of these models within a single framework. In this article, we show that many mortality models used in the demographic and actuarial literature can be re-parameterized in terms of a general and flexible family of models, the family of location-scale (LS) models. These models are characterized by two parameters that have a direct demographic interpretation: the location and scale parameters, which capture the shifting and compression dynamics of mortality changes, respectively. Re-parameterizing a model in terms of the LS family has several advantages over its classic formulation. In addition to aiding parameter interpretability and comparability, the statistical estimation of the LS parameters is facilitated due to their significantly lower correlation. The latter, in turn, further improves parameter interpretability and reduces estimation bias. We show the advantages of the LS family over the typical parameterization of mortality models with two illustrations using the Human Mortality Database.

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Gompertz–Makeham life expectancies: Expressions and applications

Cited by 48 publications

References 9 publications

Variance in animal longevity: contributions of heterogeneity and stochasticity

Variance in animal longevity: contributions of heterogeneity and stochasticity

A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality

Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models

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