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Mathematical Models for Human Cancer Incidence Rates

Author

Listed:
  • Konstantin Arbeev

    (Duke University)

  • Anatoli Yashin

    (Duke University)

  • Svetlana Ukraintseva

    (Duke University)

  • Lyubov S. Arbeeva

    (Ulyanovsk State University)

Abstract

The overall cancer incidence rate declines at old ages. Possible causes of this decline include the effects of cross-sectional data which transform cohort dynamics into age pattern, population heterogeneity which selects out individuals susceptible to cancer, decline in some carcinogenic exposures in the old, effects of individual aging which slow down major physiological processes in an organism, etc. We discuss several mathematical models contributing to the explanation of this phenomenon. We extend the Strehler and Mildvan model of aging and mortality and apply it to the analysis of data on cancer incidence at old ages. The model explains time trends and age patterns of cancer incidence rates. Applications to cancer incidence data provided by the International Agency for Research on Cancer illustrate the models.

Suggested Citation

  • Konstantin Arbeev & Anatoli Yashin & Svetlana Ukraintseva & Lyubov S. Arbeeva, 2005. "Mathematical Models for Human Cancer Incidence Rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 12(10), pages 237-272.
    • Handle: RePEc:dem:demres:v:12:y:2005:i:10
    DOI: 10.4054/DemRes.2005.12.10
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    References listed on IDEAS

    as
    1. Svetlana Ukraintseva & Anatoli Yashin, 2003. "Individual Aging and Cancer Risk: How are They Related?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 9(8), pages 163-196.
    2. 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.
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    Cited by:

    1. Maxim Finkelstein, 2012. "Discussing the Strehler-Mildvan model of mortality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(9), pages 191-206.
    2. Konstantin Arbeev & Anatoli Yashin & Svetlana Ukraintseva & Lyubov S. Arbeeva, 2005. "Decline in Human Cancer Incidence Rates at Old Ages: Age-Period-Cohort Considerations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 12(11), pages 273-300.
    3. Yue, Jack C. & Wang, Hsin-Chung & Leong, Yin-Yee & Su, Wei-Ping, 2018. "Using Taiwan National Health Insurance Database to model cancer incidence and mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 316-324.
    4. Hui Zheng, 2014. "Aging in the Context of Cohort Evolution and Mortality Selection," Demography, Springer;Population Association of America (PAA), vol. 51(4), pages 1295-1317, August.

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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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