Group health risk parameters in a heterogeneous cohort. Indirect assessment as per events taken in dynamics

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57.042; 519.246.2

V.F. Obesnyuk


The Southern Urals Biophysics Institute of the RF Federal Medical and Biological Agency, 19 Ozerskoe drive, Ozersk, 456780, Russian Federation


The present work focuses on describing a procedure for assessing intensive and cumulative parameters of specific risk when observing cohorts under combined exposure to several external or internal factors.
The research goal was to reveal how to use well-known heuristic-descriptive parameters accepted in remote consequences epidemiology for analyzing dynamics of countable events in a cohort; analysis should be performed on quite strict statistic-probabilistic grounds based on Bayesian approach to explaining conditional probabilities that such countable events might occur. The work doesn’t contain any new or previously unknown epidemiologic concept or parameters; despite that, it is not a simple literature review. It is the suggested procedure itself that is comparatively new as it combines techniques used to process conventional epidemiologic information and a correct metrological approach based on process description.
The basic result is providing a reader with understanding that all basic descriptive epidemiologic parameters within cohort description framework turn out to be quantitatively interlinked in case they are considered as conditional group processes. It allows simultaneous inter-consistent assessment of annual risk parameters and Kaplan-Meier (Fleming-Harrington) and Nelson-Aalen cumulative parameters as well as other conditional risk parameters or their analogues. It is shown that when a basic descriptive characteristic of cumulative parameters is chosen as a measure for measurable long-term external exposure, it is only natural to apply such a concept as a dose of this risk factor which is surrogate in its essence. Operability of the procedure was confirmed with an example. The suggested procedure was proven to differ from its prototype that previously allowed achieving only substantially shifted estimates, up to ~100 % even in case an operation mode was normal. Application requires creating specific but quite available PC software.

risk, parameter, epidemiology, risk factor, competition, indirect estimate, mortality, process, cohort, strata, model
Obesnyuk V.F. Group health risk parameters in a heterogeneous cohort. indirect assessment as per events taken in dynamics. Health Risk Analysis, 2021, no. 2, pp. 17–32. DOI: 10.21668/health.risk/2021.2.02.eng
  1. Onishchenko G.G., Zaitseva N.V., May I.V. [et al.]. Health risk analysis in the strategy of state social and economical development: monograph. In: G.G. Onishchenko, N.V. Zaitseva eds. Мoscow, Perm, Publishing house of the Perm National Research Polytechnic University Publ., 2014, 738 p. (in Russian).
  2. Commonwealth of Australia, 2012. Environmental Health Risk Assessment. Guideline for assessing human health risk from environmental hazards: Glossary. Commonwealth of Australia, 2012, 244 p.
  3. Publikatsiya 103 Mezhdunarodnoi Komissii po radiatsionnoi zashchite (MKRZ) [Publication No. 103 issued by the International Commission on Radiological Protection (ICRP 103)]. In: M.F. Kiselev, N.K. Shandala eds. Moscow, OOO PKF «Alana» Publ., 2009, 344 p. (in Russian).
  4. Zlokachestvennye novoobrazovaniya v Rossii v 2018 godu (zabolevaemost' i smertnost') [Malignant neoplasms in Russia in 2018 (morbidity and mortality)]. In: A.D. Kaprin, V.V. Starinskii, G.V. Petrova eds. Moscow, MNIOI im. P.A. Gertsena Publ., 2019, 250 p. (in Russian).
  5. Handbook of epidemiology. In: W. Ahrens, I. Pigeot eds. Switzerland, Springer Publ., 2005, 1617 p. DOI: 10.1007/978-3-540-26577-1
  6. Newman J.R. Mathematics of a lady tasting tea by Sir Ronald Fisher. The World of mathematics. Vol. III, Part VIII. New-York, Simon and Schuster Publ., 1956, pp. 1514‒1521.
  7. Vaupel J.W., Manton K.G., Stallard E. The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality. Demography, 1979, vol. 16, no. 3, pp. 439. DOI: 10.2307/2061224
  8. Mikhal'skii A.I., Petrovskii A.M., Yashin A.I. Teoriya otsenivaniya neodnorodnykh populyatsii [Theory of heterogeneous population estimation]. Moscow, Nauka Publ., 1989, 128 p. (in Russian).
  9. Preston D.L., Kato H., Kopecky K.J., Fujita S. Technical Report No. 1-86. Life span study report 10. Part 1. Cancer mortality among A-bomb survivors in Hiroshima and Nagasaki, 1950‒1982. RERF, 1987, no. 111, pp. 151‒178.
  10. Preston D.L., Cullings H., Suyama A., Funamoto S., Nishi N., Soda M., Mabuchi K., Kodama K. [et al.]. Solid cancer incidence in atomic bomb survivors exposed in utero or as young children. Journal of the National Cancer Institute, 2008, vol. 100, no. 6, pp. 428–436. DOI: 10.1093/jnci/djn045
  11. Epicure. The premiere software for risk regression and person-year tabulation. «EPICURE» Risk Sciences International. Available at: (21.04.2021).
  12. Gauss K.F. Izbrannye geodezicheskie sochineniya [Selected geodesic works]. In: G.V. Bagratun, S.G. Sudakov eds. Moscow, IGL Publ., 1957, vol. 1, 153 p. (in Russian).
  13. Vaeth M., Pearce D. Calculating excess lifetime risk in relative risk models. Environmental Health Perspectives, 1990, vol. 87, pp. 83–94. DOI: 10.1289/ehp.908783
  14. Thomas D., Darby S., Fagnani F., Hubert P., Vaeth M., Weiss K. Definition and estimation of lifetime detriment from radiation exposures: principles and methods. Health Physics, 1992, vol. 63, no. 3, pp. 259–272. DOI: 10.1097/00004032-199209000-00001
  15. Ulanowski A., Kaiser J.C., Schneider U., Walsh L. Lifetime radiation risk of stochastic effects – prospective evaluation for space flight or medicine. Ann. ICRP, 2020, vol. 49, no. 1, pp. 200‒212. DOI: 10.1177/0146645320956517
  16. Ulanowski A., Kaiser J.C., Schneider U., Walsh L. On prognostic estimates of radiation risk in medicine and radiation protection. Radiat. Environ. Biophys, 2019, vol. 58, no. 3, pp. 305‒319. DOI: 10.1007/s00411-019-00794-1
  17. Esteve J., Benhamou E., Raymond L. Statistical methods in cancer research. Descriptive epidemiology. IARC Scientific Publication, 1994, vol. IV, no. 128, pp. 313.
  18. Sasieni P.D., Shelton J., Ormiston-Smith N., Thomson C.S., Silcocks P.B. What is the lifetime risk of developing cancer? The effect of adjusting for multiple primaries. Br. J. Cancer, 2011, vol. 105, no. 3, pp. 460–465. DOI: 10.1038/bjc.2011.250
  19. Aalen O., Andersen P.K., Borgan Ø., Gill R.D., Keiding N. History of application of martingales in survival analysis. Electronic Journal of History of Probability and Statistic, 2009, vol. 5, no. 1, pp. 1‒28.
  20. Aalen O., Borgan Ø., Gjessing H. Survival and Event history analysis: A process point of view. New-York, Springer Science + Business Media B.V. Publ., 2008, pp. 539.
  21. Grunkemeier G.L., Jin R., Eijkemans M.J.C., Takkenberg J.J.M. Actual and actuarial probabilities of competing risks: apples and lemons. The Annals of Thoracic Surgery, 2007, vol. 83, no. 5, pp. 1586–1592. DOI: 10.1016/j.athoracsur.2006.11.044
  22. Kaplan E.L., Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 1958, vol. 53, no. 282, pp. 457–481. DOI: 10.1007/978-1-4612-4380-9_25
  23. Nelson W. Theory and applications of hazard plotting for censored failure data. Technometrics, 1972, vol. 14, no. 4, pp. 945‒966. DOI: 10.1080/00401706.2000.10485975
  24. Bure V.M., Parilina E.M., Rubsha A.I., Svirkina L.V. Survival analysis of medical databaseof patients with prostate cancer. Vestnik SPbGU. Seriya 10, 2014, vol. 10, no. 2, pp. 27–35 (in Russian).
  25. Fisher R.A. On the mathematical foundations of theoretical statistics. Phil. Trans. of the Royal Soc. of London. Series A, 1922, vol. 222, pp. 309–368. DOI: 10.1098/rsta.1922.0009
  26. Wilks S.S. The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 1938, vol. 9, no. 1, pp. 60–62. DOI: 10.1214/aoms/1177732360
  27. Fan J., Hung H., Wong W. Geometric understanding of likelihood ratio statistics. JASA, 2000, vol. 95, no. 451, pp. 836–841.
  28. Gelfand А.Е., Smith A. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 1990, vol. 85, no. 410, pp. 398–409. DOI: 10.1080/01621459.1990.10476213
  29. Sources and effects of ionizing radiation. UNSCEAR 1994 report to General Assembly. New-York, United Nations Scientific Committee on the Effects of Atomic Radiation Publ., 1994, 272 p.
  30. Effect on ionizing radiation. UNSCEAR 2006. Report to General Assembly. New-York, United Nations Scientific Committee on the Effects of Atomic Radiation Publ., 2008, vol. 1A, 16 p.
  31. Finashov L.V., Kuznetsova I.S., Sokol'nikov M.E., Skukovskii S.G. Radiation risk of prostate cancer incidence due to external gamma-exposure in the cohort of «Mayak» PA workers occupationally subjected to prolonged radiation exposure. Voprosy radiatsionnoi bezopasnosti, 2020, no. 2, pp. 37–48 (in Russian).
  32. Tukov A.R., Shafranskii I.L., Prokhorova O.N., Ziyatdinov M.N. The incidence of cataracts and the radiation risk of their occurrence in liquidators of the Chernobyl accident, workers in the nuclear industry. Radiatsiya i risk, 2019, vol. 28, no. 1, pp. 37–46 (in Russian).
  33. Kreisheimer M., Sokolnikov M.E., Koshurnikova N.A., Khokhryakov V.F., Romanow S.A., Shilnikova N.S., Okatenko P.V., Nekolla E.A., Kellerer A.M. Lung cancer mortality among nuclear workers of the Mayak facilities in the former Soviet Union. Radiat. Environ. Biophys, 2003, vol. 42, no. 2, pp. 129–135. DOI: 10.1007/s00411-003-0198-3
  34. Zöllner S., Sokolnikov M.E., Eidemüller M. Beyond two-stage models for lung carcinogenesis in the Mayak workers: implications for plutonium risk. PLoS ONE, 2015, vol. 10, no. 5, pp. e0126238. DOI: 10.1371/journal.pone.0126238
  35. Demin V.F., Ivanov S.I., Novikov S.M. Common methodology of health risk assessment for impact of different harm sources. Meditsinskaya radiologiya i radiatsionnaya bezopasnost', 2009, vol. 54, no. 1, pp. 5–15 (in Russian).
  36. Ivanov V.K, Gorsky A.I., Kashcheev V.V., Maksioutov M.A., Tumanov K.A. Latent period in induction of radiogenic solid tumors in the cohort of emergency workers. Radiation and Environmental Biophysics, 2009, vol. 48, no. 3. DOI: 10.1007/s00411-009-0223-2
  37. Ivanov V.K., Tsyb A.F., Panfilov A.P., Agapov A.M. Optimizatsiya radiatsionnoi zashchity: «dozovaya matritsa» [How to optimize radiological protection: «dose matrix»]. Moscow, Meditsina Publ., 2006, 304 p. (in Russian).
  38. Jacob P., Meckbach R., Sokolnikov M., Khokhryakov V.V., Vasilenko E. Lung cancer risk of Mayak workers: modeling of carcinogenesis and bystander effect. Radiat. Environ. Biophys, 2007, vol. 46, no. 4, pp. 383–394. DOI: 10.1007/s00411-007-0117-0
  39. Chen M., Ibrahim J., Sinha D. A new bayesian model for survival data with a surviving fraction. Journal of the American Statistical Association, 1999, vol. 94, no. 447, pp. 909–919. DOI: 10.1080/01621459.1999.10474196
  40. Rodrigues J., Balakrishnan N., Cordeiro G., de Castro M. A unified view on lifetime distributions arising from selection mechanisms. Computational Statistics and Data Analysis, 2011, vol. 55, no. 12, pp. 3311–3319. DOI: 10.1016/j.csda.2011.06.018
  41. Tsodikov A.D., Ibrahim J.G., Yakovlev A.Y. Estimating cure rates from survival data: an alternative to two-component mixture models. Journal of the American Statistical Association, 2003, vol. 98, no. 464, pp. 1063–1067. DOI: 10.1198/01622145030000001007
  42. Moher D., Hopewell S., Schulz K.F., Montori V., Gøtzsche P.C., Devereaux P.J., Elbourne D., Douglas M.E., Altman G. CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomized trials. International Journal of Surgery, 2012, vol. 10, no. 1, pp. 28–55. DOI: 10.1016/j.ijsu.2011.10.001
  43. Health risks from exposure to low levels of ionizing radiation. BEIR VII, phase 2. Washington D.C., Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation Publ., 2006, 406 p.
  44. Timofeev-Resovskii N.V., Tsimmer K.G. Teoriya misheni radiobiologicheskogo deistviya (v izlozhenii) [Theory of radiological-biological effects targeting (a presentation)]. Biosfera, 2010, vol. 2, no. 3, pp. 432–450 (in Russian).
  45. Zimmer K.G. Ergebnisse und Grenzen der treffertheoretischem Deutung von strahlenbiologischen Dosis-Effekt kurven. Biol. Zent, 1941, no. 63, pp. 72‒107.
  46. Jacobi W. The concept of the effective dose ‒ a proposal of the combination of the organ doses. Radiat. And Environm. Biophys, 1975, vol. 12, no. 2, pp. 101‒109. DOI: 10.1007/BF01328971

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