Skip to main content
Log in

On identification of morbidity parameters in a heterogeneous model: The cases of complete and incomplete information

  • Large Scale Systems Control
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper suggests a methodology to estimate morbidity parameters in a three-state model, which includes the heterogeneity factor modeled by a gamma-distributed random variable. The cases of complete and incomplete information are considered and various risk estimation methods are discussed. We give estimates of morbidity radiation risks in four classes of diseases based on data from the Russian National Radiation Epidemiological Registry. The methodology can be used during the development of radiation protection systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gradshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Fizmatlit, 1963.

    Google Scholar 

  2. Ivanov, V.K., Tsyb, A.F., Gorsky, A.I, et al., Cancer Morbidity and Mortality among Chernobyl Emergency Workers: Estimation of Radiation Risks, Radiats. Biol. Radioekol., 2006, vol. 46, no. 2, pp. 159–166.

    Google Scholar 

  3. International Statistical Classification of Diseases and Related Health Problems, Geneva: IHO, 1995.

  4. Miller, B.M. and Pankov, A.R., Teoriya sluchainykh protsessov (Theory of Random Processes), Moscow: Fizmatlit, 2002.

    Google Scholar 

  5. Mikhalskii, A.I., Metody analiza geterogennykh struktur i populyatsii (Analysis Methods for Heterogeneous Structures and Populations), Moscow: Inst. Probl. Upravlen., 2002.

    Google Scholar 

  6. Mikhalskii, A.I. et al., Accounting of Heterogeneity in the Estimation of Radiation Risks, Autom. Remote Control, 2008, vol. 69, no. 6, pp. 1045–1050.

    Article  MathSciNet  MATH  Google Scholar 

  7. Mikhalskii, A.I., Petrovskii, A.M., and Yashin, A.I., Teoriya otsenivaniya neodnorodnykh populyatsii (Theory of Estimation of Heterogeneous Populations), Moscow: Nauka, 1989.

    Google Scholar 

  8. Annals of the ICRP. ICRP Publication 103. The 2007 Recommendations of the International Commission on Radiological Protection, 2007, vol. 37, nos. 2–4. Translated under the title Publikatsiya 103 Mezhdunarodnoi komissii po radiatsionnoi zashchite, Moscow: Alana, 2009.

  9. Brauer, F., Epidemic Models with Heterogeneous Mixing and Treatment, Bull. Mathem. Biol., 2008, vol. 70, pp. 1869–1885.

    Article  MathSciNet  MATH  Google Scholar 

  10. Statistical Methods in Cancer Research, vol. 2: The Design and Analysis of Cohort Studies, Breslow, N.E. and Day, N.E., Eds., Lyon: IARC, 1987.

  11. Cook, R.J. and Lawless, J.F., Statistical Issues in Modeling Chrohic Disease in Cohort Studies, Stat. Biosci., 2014, no. 6, pp. 127–221.

    Article  Google Scholar 

  12. Finkelstein, M. and Cha, J.H., Stochastic Modeling for Reliability, Springer Series in Reliability Engineering, London: Springer-Verlag, 2013.

    Book  MATH  Google Scholar 

  13. Ivanov, V.K., Maksioutov, M.A., Chekin, S.Y., et al., The Risk of Radiation-Induced Cerebrovascular Disease in Chernobyl Emergency Workers, Health Phys., 2006, vol. 90, no. 3, pp. 199–207.

    Article  Google Scholar 

  14. Ivanov, V.K., Tsyb, A.F., Ivanov, S.I., et al., Medical Radiological Consequences of the Chernobyl Catastrophe in Russia: Estimation of Radiation Risks, St. Petersburg: Nauka, 2004.

    Google Scholar 

  15. Madan, D., Bakshi, G., and Panayotov, G., Heterogeneity in Beliefs and Volatility Tail Behavior, J. Finan. Quantit. Anal., 2015, vol. 50, no. 6, pp. 1389–1414.

    Article  Google Scholar 

  16. Meira-Machado, L., de Una-Alvarez, J., and Datta, S., Nonparametric Estimation of Conditional Transition Probabilities in a Non-Markov Illness-Death Model, Comput. Stat., 2015, vol. 30, no. 2, pp. 377–397.

    Article  MathSciNet  MATH  Google Scholar 

  17. Norberg, R., Life Insurance Mathematics. Encyclopedia of Actuarial Science, New York: Wiley, 2004.

    Google Scholar 

  18. Vaupel, J.W., Manton, K.G., and Stallard, E., The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality, Demography, 1979, vol. 16, pp. 439–454.

    Article  Google Scholar 

  19. Vaupel, J.W. and Yashin, A.I., Heterogeneity’s Ruses: Some Surprising Effects of Selection on Population Dynamics, Am. Stat., 1985, vol. 39, pp. 176–182.

    MathSciNet  Google Scholar 

  20. Yashin, A.I., Akushevich, I., Arbeev, K., et al. Studying Health Histories of Cancer: A New Model Connecting Cancer Incidence and Survival, Math. Biosci., 2009, vol. 218, no. 2, pp. 88–97.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. V. Ivanov.

Additional information

Original Russian Text © R.V. Ivanov, A.I. Mikhalskii, V.K. Ivanov, S.Yu. Chekin, M.A. Maksyutov, V.V. Kashcheev, 2015, published in Upravlenie Bol’shimi Sistemami, 2015, No. 57, pp. 138–157.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ivanov, R.V., Mikhalskii, A.I., Ivanov, V.K. et al. On identification of morbidity parameters in a heterogeneous model: The cases of complete and incomplete information. Autom Remote Control 78, 1329–1340 (2017). https://doi.org/10.1134/S0005117917070141

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117917070141

Navigation