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Dependent competing risks: Cause elimination and its impact on survival

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  • Dimitrova, Dimitrina S.
  • Haberman, Steven
  • Kaishev, Vladimir K.

Abstract

The dependent competing risks model of human mortality is considered, assuming that the dependence between lifetimes is modelled by a multivariate copula function. The effect on the overall survival of removing one or more causes of death is explored under two alternative definitions of removal, ignoring the causes and eliminating them. Under the two definitions of removal, expressions for the overall survival functions in terms of the specified copula (density) and the net (marginal) survival functions are given. The net survival functions are obtained as a solution to a system of non-linear differential equations, which relates them through the specified copula (derivatives) to the crude (sub-) survival functions, estimated from data. The overall survival functions in a model with four competing risks, cancer, cardiovascular diseases, respiratory diseases and all other causes grouped together, have been implemented and evaluated, based on cause-specific mortality data for England and Wales published by the Office for National Statistics, for the year 2007. We show that the two alternative definitions of removal of a cause of death have different effects on the overall survival and in particular on the life expectancy at birth and at age 65, when one, two or three of the competing causes are removed. An important conclusion is that the eliminating definition is better suited for practical use in competing risks’ applications, since it is more intuitive, and it suffices to consider only positive dependence between the lifetimes which is not the case under the alternative ignoring definition.

Suggested Citation

  • Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:464-477
    DOI: 10.1016/j.insmatheco.2013.07.008
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    References listed on IDEAS

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    Cited by:

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    3. Graziani, Rebecca & NIGRI, ANDREA, 2023. "An Age–Period–Cohort Model in a Dirichlet Framework: A Coherent Causes of Death Estimation," SocArXiv 856yw, Center for Open Science.
    4. Boumezoued, Alexandre & Hardy, Héloïse Labit & El Karoui, Nicole & Arnold, Séverine, 2018. "Cause-of-death mortality: What can be learned from population dynamics?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 301-315.
    5. Kaakaï, Sarah & Labit Hardy, Héloïse & Arnold, Séverine & El Karoui, Nicole, 2019. "How can a cause-of-death reduction be compensated for by the population heterogeneity? A dynamic approach," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 16-37.
    6. Li, Han & Li, Hong & Lu, Yang & Panagiotelis, Anastasios, 2019. "A forecast reconciliation approach to cause-of-death mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 122-133.
    7. Tickle Leonie & Booth Heather, 2014. "The Longevity Prospects of Australian Seniors: An Evaluation of Forecast Method and Outcome," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 8(2), pages 1-34, July.

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