IDEAS home Printed from https://ideas.repec.org/a/dem/demres/v12y2005i10.html
   My bibliography  Save this article

Mathematical Models for Human Cancer Incidence Rates

Author

Listed:
  • Konstantin Arbeev

    (Duke University)

  • Svetlana Ukraintseva

    (Duke University)

  • Lyubov S. Arbeeva

    (Ulyanovsk State University)

  • Anatoli Yashin

    (Duke 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 & Svetlana Ukraintseva & Lyubov S. Arbeeva & Anatoli Yashin, 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
    as

    Download full text from publisher

    File URL: https://www.demographic-research.org/volumes/vol12/10/12-10.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/DemRes.2005.12.10?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
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 & Svetlana Ukraintseva & Lyubov S. Arbeeva & Anatoli Yashin, 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.

    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. Belzunce, Felix & Ortega, Eva-Maria & Ruiz, Jose M., 2007. "On non-monotonic ageing properties from the Laplace transform, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 1-14, January.
    2. Svetlana V. Ukraintseva & Anatoli I. Yashin, 2005. "Economic progress as cancer risk factor. I: Puzzling facts of cancer epidemiology," MPIDR Working Papers WP-2005-021, Max Planck Institute for Demographic Research, Rostock, Germany.
    3. Bagdonavicius, Vilijandas & Nikulin, Mikhail, 2000. "On goodness-of-fit for the linear transformation and frailty models," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 177-188, April.
    4. Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    5. Filipe Costa Souza & Wilton Bernardino & Silvio C. Patricio, 2024. "How life-table right-censoring affected the Brazilian social security factor: an application of the gamma-Gompertz-Makeham model," Journal of Population Research, Springer, vol. 41(3), pages 1-38, September.
    6. K. Motarjem & M. Mohammadzadeh & A. Abyar, 2020. "Geostatistical survival model with Gaussian random effect," Statistical Papers, Springer, vol. 61(1), pages 85-107, February.
    7. Xu, Linzhi & Zhang, Jiajia, 2010. "An EM-like algorithm for the semiparametric accelerated failure time gamma frailty model," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1467-1474, June.
    8. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    9. James W. Vaupel, 2002. "Post-Darwinian longevity," MPIDR Working Papers WP-2002-043, Max Planck Institute for Demographic Research, Rostock, Germany.
    10. Maxim S. Finkelstein, 2005. "Shocks in homogeneous and heterogeneous populations," MPIDR Working Papers WP-2005-024, Max Planck Institute for Demographic Research, Rostock, Germany.
    11. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    12. Yeo, Keng Leong & Valdez, Emiliano A., 2006. "Claim dependence with common effects in credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 609-629, June.
    13. 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.
    14. Graziella Caselli & Franco Peracchi & Elisabetta Barbi & Rosa Maria Lipsi, 2003. "Differential Mortality and the Design of the Italian System of Public Pensions," LABOUR, CEIS, vol. 17(s1), pages 45-78, August.
    15. Enrique Acosta & Alain Gagnon & Nadine Ouellette & Robert R. Bourbeau & Marilia R. Nepomuceno & Alyson A. van Raalte, 2020. "The boomer penalty: excess mortality among baby boomers in Canada and the United States," MPIDR Working Papers WP-2020-003, Max Planck Institute for Demographic Research, Rostock, Germany.
    16. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    17. Hess Wolfgang & Tutz Gerhard & Gertheiss Jan, 2016. "A Flexible Link Function for Discrete-Time Duration Models," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(4), pages 455-481, August.
    18. Bas Klaauw & Limin Wang, 2011. "Child mortality in rural India," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(2), pages 601-628, April.
    19. Xian Liu, 2000. "Development of a Structural Hazard Rate Model in Sociological Research," Sociological Methods & Research, , vol. 29(1), pages 77-117, August.
    20. Hsieh Fushing, 2012. "Semiparametric efficient inferences for lifetime regression model with time-dependent covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 1-25, February.

    More about this item

    Keywords

    aging; models; cancer; heterogeneity; incidence rate; model;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    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:dem:demres:v:12:y:2005:i:10. 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: Editorial Office (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    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.