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The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality

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  • Bonetti, Marco
  • Basellini, Ugofilippo
  • NIGRI, ANDREA

Abstract

In recent years, lifespan inequality has become an important indicator of population health, alongside more established longevity measures. Uncovering the statistical properties of lifespan inequality measures can provide novel insights on the study of mortality developments. We revisit the "e-dagger" measure of lifespan inequality, introduced in Vaupel and Canudas-Romo (2003). We note that, conditioning on surviving at least until age a, e-dagger(a) is equal to the covariance between the conditional lifespan random variable Ta and its transformation through its own cumulative hazard function (hence generalizing a result first noted in Schmertmann, 2020). We then derive an upper bound for e-dagger(a). Leveraging this result, we introduce the "Average Uneven Mortality" (AUM) index, a novel relative mortality index that can be used to analyze mortality patterns. We discuss some general features of the index, including its relationship with a constant ("even") force of mortality, and we study how it changes over time. The use of the AUM index is illustrated through an application to observed period and cohort death rates as well as to period life-table death rates from the Human Mortality Database. We explore the behavior of the index across age and over time, and we study its relationship with life expectancy. The AUM index at birth declined over time until the 1950s, when it reverted its trend. The index generally increases over age and reduces with increasing values of life expectancy, with differences between the period and cohort perspectives. We elaborate on Vaupel and Canudas-Romo’s e-dagger measure, deriving its upper bound. We exploit this result to introduce a novel mortality indicator, which enlarges the toolbox of available methods for the study of mortality dynamics. We also develop some new routines to compute e-dagger(a) and σ_Ta from death rates, and show that they have higher precision when compared to conventional and available functions, particularly for calculations involving older ages.

Suggested Citation

  • Bonetti, Marco & Basellini, Ugofilippo & NIGRI, ANDREA, 2023. "The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality," SocArXiv xb6vq, Center for Open Science.
    • Handle: RePEc:osf:socarx:xb6vq
    DOI: 10.31219/osf.io/xb6vq
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    References listed on IDEAS

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    1. repec:cai:popine:popu_p2001_13n1_0171 is not listed on IDEAS
    2. Vladimir Canudas-Romo, 2010. "Three measures of longevity: Time trends and record values," Demography, Springer;Population Association of America (PAA), vol. 47(2), pages 299-312, May.
    3. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    4. James Vaupel & Vladimir Romo, 2003. "Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday," Demography, Springer;Population Association of America (PAA), vol. 40(2), pages 201-216, May.
    5. Ryan D. Edwards & Shripad Tuljapurkar, 2005. "Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries," Population and Development Review, The Population Council, Inc., vol. 31(4), pages 645-674, December.
    6. James W. Vaupel & Zhen Zhang, 2012. "The difference between alternative averages," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(15), pages 419-428.
    7. Marie-Pier Bergeron-Boucher & Marcus Ebeling & Vladimir Canudas-Romo, 2015. "Decomposing changes in life expectancy: Compression versus shifting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(14), pages 391-424.
    8. Nathan Keyfitz, 1977. "What difference would it make if cancer were eradicated? An examination of the taeuber paradox," Demography, Springer;Population Association of America (PAA), vol. 14(4), pages 411-418, November.
    9. Carl Schmertmann, 2020. "Revivorship and life lost to mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(17), pages 497-512.
    10. John Wilmoth & Shiro Horiuchi, 1999. "Rectangularization revisited: Variability of age at death within human populations," Demography, Springer;Population Association of America (PAA), vol. 36(4), pages 475-495, November.
    11. Siu Cheung & Jean-Marie Robine & Edward Tu & Graziella Caselli, 2005. "Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension," Demography, Springer;Population Association of America (PAA), vol. 42(2), pages 243-258, May.
    12. Linh Hoang Khanh Dang & Carlo Giovanni Camarda & France Meslé & Nadine Ouellette & Jean-Marie Robine & Jacques Vallin, 2023. "The question of the human mortality plateau: Contrasting insights by longevity pioneers," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(11), pages 321-338.
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