IDEAS home Printed from https://ideas.repec.org/a/spr/lsprsc/v13y2020i2d10.1007_s12076-020-00250-5.html
   My bibliography  Save this article

Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates

Author

Listed:
  • María-Dolores Huete-Morales

    (University of Granada)

  • Esteban Navarrete-Álvarez

    (University of Granada)

  • María-Jesús Rosales-Moreno

    (University of Granada)

  • María-José Del-Moral-Ávila

    (University of Granada)

  • José-Manuel Quesada-Rubio

    (University of Granada)

Abstract

This paper presents a variant of the survival function proposed by Wong and Tsui, in which we include a component reflecting heterogeneity among individuals (frailty), together with a covariate describing the influence of certain characteristics of individuals on the response variable. Using mortality statistics for the entire Spanish population, we estimated survival functions according to the variants of the model considered, also determining life expectancies and mortality ratios at each age. The advantage of the proposed variant is that it incorporates gender differences, by including sex as a covariate. Furthermore, it reflects the intrinsic randomness of individuals. With this approach, additional parameters must be considered, but all were found to be significant.

Suggested Citation

  • María-Dolores Huete-Morales & Esteban Navarrete-Álvarez & María-Jesús Rosales-Moreno & María-José Del-Moral-Ávila & José-Manuel Quesada-Rubio, 2020. "Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates," Letters in Spatial and Resource Sciences, Springer, vol. 13(2), pages 151-163, August.
    • Handle: RePEc:spr:lsprsc:v:13:y:2020:i:2:d:10.1007_s12076-020-00250-5
    DOI: 10.1007/s12076-020-00250-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12076-020-00250-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12076-020-00250-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wong, Chi Heem & Tsui, Albert K., 2015. "Forecasting life expectancy: Evidence from a new survival function," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 208-226.
    2. Permadi, Dwiko B. & Burton, Michael & Pandit, Ram & Race, Digby & Ma, Chunbo & Mendham, Daniel & Hardiyanto, Eko B., 2018. "Socio-economic factors affecting the rate of adoption of acacia plantations by smallholders in Indonesia," Land Use Policy, Elsevier, vol. 76(C), pages 215-223.
    3. Trifon Missov, 2013. "Gamma-Gompertz life expectancy at birth," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(9), pages 259-270.
    4. Feng, Xinlong & He, Guoliang & Abdurishit,, 2008. "Estimation of parameters of the Makeham distribution using the least squares method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 34-44.
    5. John Bongaarts, 2005. "Long-range trends in adult mortality: Models and projection methods," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 23-49, February.
    6. Trifon Missov & Vladimir Canudas-Romo & James W. Vaupel & Adam Lenart & Laszlo Nemeth, 2015. "The Gompertz force of mortality in terms of the modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(36), pages 1031-1048.
    7. R. Henderson & P. Oman, 1999. "Effect of frailty on marginal regression estimates in survival analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 367-379, April.
    8. Wong, Chi Heem & Tsui, Albert K, 2015. "Forecasting Life Expectancy: Evidence from a New Survival Function," CEI Working Paper Series 2015-1, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
    9. Joel E. Cohen & Roland Rau & Christina Bohk-Ewald, 2018. "Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(29), pages 773-842.
    10. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    2. Lucia Zanotto & Vladimir Canudas-Romo & Stefano Mazzuco, 2021. "A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 37(1), pages 1-27, March.
    3. Hartemink, Nienke & Missov, Trifon I. & Caswell, Hal, 2017. "Stochasticity, heterogeneity, and variance in longevity in human populations," Theoretical Population Biology, Elsevier, vol. 114(C), pages 107-116.
    4. Ugofilippo Basellini & Vladimir Canudas-Romo & Adam Lenart, 2019. "Location–Scale Models in Demography: A Useful Re-parameterization of Mortality Models," European Journal of Population, Springer;European Association for Population Studies, vol. 35(4), pages 645-673, October.
    5. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    6. Castellares, Fredy & Patrício, Silvio C. & Lemonte, Artur J. & Queiroz, Bernardo L., 2020. "On closed-form expressions to Gompertz–Makeham life expectancy," Theoretical Population Biology, Elsevier, vol. 134(C), pages 53-60.
    7. Ting Li & Yang Yang & James Anderson, 2013. "Mortality Increase in Late-Middle and Early-Old Age: Heterogeneity in Death Processes as a New Explanation," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1563-1591, October.
    8. Mathias Voigt & Antonio Abellán & Julio Pérez & Diego Ramiro, 2020. "The effects of socioeconomic conditions on old-age mortality within shared disability pathways," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-17, September.
    9. Joel E. Cohen & Roland Rau & Christina Bohk-Ewald, 2018. "Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(29), pages 773-842.
    10. Jacie Jia Liu, 2021. "A Study on Link Functions for Modelling and Forecasting Old-Age Survival Probabilities of Australia and New Zealand," Risks, MDPI, vol. 9(1), pages 1-18, January.
    11. Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    12. Paola Vazquez-Castillo & Trifon Missov & Marie-Pier Bergeron-Boucher, 2024. "Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 50(11), pages 325-346.
    13. Elizabeth Wrigley-Field, 2020. "Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don’t Act Like Frailty," Demography, Springer;Population Association of America (PAA), vol. 57(2), pages 747-777, April.
    14. Elizabeth Wrigley-Field, 2014. "Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model," Demography, Springer;Population Association of America (PAA), vol. 51(1), pages 51-71, February.
    15. Castellares, Fredy & Patrício, Silvio C. & Lemonte, Artur J., 2020. "On gamma-Gompertz life expectancy," Statistics & Probability Letters, Elsevier, vol. 165(C).
    16. Missov, Trifon I. & Lenart, Adam, 2013. "Gompertz–Makeham life expectancies: Expressions and applications," Theoretical Population Biology, Elsevier, vol. 90(C), pages 29-35.
    17. A. Roger Thatcher & Shiro Horiuchi & Siu Lan Karen Cheung & Jean-Marie Robine, 2010. "The compression of deaths above the mode," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(17), pages 505-538.
    18. Shripad Tuljapurkar & Ryan Edwards, 2011. "Variance in death and its implications for modeling and forecasting mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(21), pages 497-526.
    19. Alois Pichler & Dana Uhlig, 2023. "Mortality in Germany during the COVID-19 Pandemic," IJERPH, MDPI, vol. 20(20), pages 1-11, October.
    20. Trifon Missov & Vladimir Canudas-Romo & James W. Vaupel & Adam Lenart & Laszlo Nemeth, 2015. "The Gompertz force of mortality in terms of the modal age at death," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(36), pages 1031-1048.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:lsprsc:v:13:y:2020:i:2:d:10.1007_s12076-020-00250-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.