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Illness-death model: statistical perspective and differential equations

Author

Listed:
  • Ralph Brinks

    (University Hospital Duesseldorf)

  • Annika Hoyer

    (German Diabetes Center)

Abstract

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Suggested Citation

  • Ralph Brinks & Annika Hoyer, 2018. "Illness-death model: statistical perspective and differential equations," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 743-754, October.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:4:d:10.1007_s10985-018-9419-6
    DOI: 10.1007/s10985-018-9419-6
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    References listed on IDEAS

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    1. Brinks, Ralph & Landwehr, Sandra, 2014. "Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany," Theoretical Population Biology, Elsevier, vol. 92(C), pages 62-68.
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    Cited by:

    1. Abdel-Haleem Abdel-Aty & Mostafa M. A. Khater & Raghda A. M. Attia & Hichem Eleuch, 2020. "Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells," Mathematics, MDPI, vol. 8(5), pages 1-11, May.

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