Medical Radiology and Radiation Safety. 2017. Vol. 62. No. 2. P. 35-38

DOI: 10.12737/article_58f0b9573730e4.55456538

Theoretical Estimation of Risk Function and Total Mortality Rate Based on Weibull Distribution

S.V. Osovets

Southern Urals Biophysics Institute, Ozyorsk, Chelyabinsk region, Russia, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

S.V. Osovets - senior researcher, PhD Sc. Tech.


Purpose: To estimate theoretically total mortality risk function parameters based on Weibull distribution and to calculate the average mortality rate.

Results: Lifespan distribution function takes the general form of:

where λ(t) is mortality rate function.

To obtain Weibull’s distribution mortality rate function (risk function) is represented as power equation:

where λ0 and a are power model parameters.

We provided a function for estimation of λ0 and parameters to be applied to a certain follow-up pattern using maximum likelihood technique (m deaths among N of potential outcomes during [0; T] period of time) which looks as:

As a result of minimization of the function we obtained generalized analytical λ0 and α parameter estimates for risk association during a specified period of follow-up. We developed a new technique using power man-years which may be adapted for radiation epidemiology in future. For a set period of follow-up [t1,t2] (with assumptions t2 > t1 и [t1, t2] ⊂ [0; T]) the mean mortality rate λ(t) was estimated to be:

This equation implies that λ(t) depends not only on λ0 and α parameters but also on the duration of the time line (t1, t2) during which the averaging is carried out. As a special case (with α = 1) the mean mortality rate is λ(t) = λ0 , and consistent with exponential distribution.

Conclusion: The generalized technique for estimation of the coefficient and function of total mortality risk was developed on the basis of Weibull distribution. The obtained theoretical results may be used in radiation epidemiology in future.

Key words: risk function, total mortality, Weibull distribution, power man-years, estimation technique


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For citation: Osovets SV. Theoretical Estimation of Risk Function and Total Mortality Rate Based on Weibull Distribution. Medical Radiology and Radiation Safety. 2017;62(2):35-8. Russian. DOI: 10.12737/article_58f0b9573730e4.55456538

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