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Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes

Author

Listed:
  • Gisou Díaz-Rojo

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad del Tolima, Barrio Santa Helena Parte Alta, 730006 Ibagué, Tolima, Colombia)

  • Ana Debón

    (Centro de Gestión de la Calidad y del Cambio, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

  • Jaime Mosquera

    (School of Statistic, Universidad del Valle, Calle 13 No. 100-00, 760001 Cali, Colombia)

Abstract

The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T 2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.

Suggested Citation

  • Gisou Díaz-Rojo & Ana Debón & Jaime Mosquera, 2020. "Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2093-:d:449474
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    References listed on IDEAS

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    1. Laurent Callot & Niels Haldrup & Malene Kallestrup-Lamb, 2016. "Deterministic and stochastic trends in the Lee–Carter mortality model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(7), pages 486-493, May.
    2. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    3. Debón, A. & Montes, F. & Puig, F., 2008. "Modelling and forecasting mortality in Spain," European Journal of Operational Research, Elsevier, vol. 189(3), pages 624-637, September.
    4. Edviges Coelho & Luis C. Nunes, 2011. "Forecasting mortality in the event of a structural change," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(3), pages 713-736, July.
    5. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    6. Gaviria, Alejandro, 2000. "Increasing returns and the evolution of violent crime: the case of Colombia," Journal of Development Economics, Elsevier, vol. 61(1), pages 1-25, February.
    7. Lee, Ronald & Rofman, Rafael, 1994. "Modelación y proyección de la mortalidad en Chile," Notas de Población, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL), June.
    8. Angelos Alexopoulos & Petros Dellaportas & Jonathan J. Forster, 2019. "Bayesian forecasting of mortality rates by using latent Gaussian models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 689-711, February.
    9. Duolao Wang & Pengjun Lu, 2005. "Modelling and forecasting mortality distributions in England and Wales using the Lee-Carter model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 873-885.
    10. Marcos Postigo-Boix & Ramón Agüero & José L Melús-Moreno, 2019. "An alternative procedure to obtain the mortality rate with non-linear functions: Application to the case of the Spanish population," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-16, October.
    11. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
    12. Carfora, M.F. & Cutillo, L. & Orlando, A., 2017. "A quantitative comparison of stochastic mortality models on Italian population data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 198-214.
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