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A bivariate limiting distribution of tumor latency time
S T Rachev1, C Wu, Yakovlev AYu
1Department of Statistics and Applied Probability, University of California, Santa Barbara 93106, USA.
Mathematical Biosciences
|June 1, 1995
Summary
This study extends radiation carcinogenesis models to account for multiple cancer sites using generalized distributions. Findings introduce Weibull-Marshall-Olkin and bivariate Pareto-Marshall-Olkin distributions for advanced risk assessment.
Area of Science:
- Stochastic modeling
- Radiation carcinogenesis
- Survival analysis
Background:
- The Klebanov, Rachev, and Yakovlev model for radiation carcinogenesis uses limiting latent time distributions at high doses.
- This model, based on random minima, includes the two-parameter Weibull distribution but does not address multiple cancer sites.
Purpose of the Study:
- To generalize the existing radiation carcinogenesis model to incorporate multi-site carcinogenesis.
- To explore new distributional forms arising from randomized minima schemes.
Main Methods:
- Developed a two-dimensional generalization using the Weibull-Marshall-Olkin distribution.
- Investigated a randomized model variant employing the negative binomial minima scheme, leading to a bivariate Pareto-Marshall-Olkin distribution.
Main Results:
- Introduced the Weibull-Marshall-Olkin distribution as a natural extension for multi-site radiation carcinogenesis.
- Derived the bivariate Pareto-Marshall-Olkin distribution from a randomized model.
- Provided an estimate for the rate of convergence to the limiting distribution in the bivariate Pareto-Marshall-Olkin case.
Conclusions:
- The generalized models offer a framework for analyzing radiation-induced multi-site carcinogenesis.
- These advanced distributions provide more comprehensive tools for cancer risk assessment in radiation exposure scenarios.