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Means and Variances in Stochastic Multistage Cancer Models

  • Aidan Sudbury (a1)

Abstract

A widely used model of carcinogenesis assumes that cells must go through a process of acquiring several mutations before they become cancerous. This implies that at any time there will be several populations of cells at different stages of mutation. In this paper we give exact expressions for the expectations and variances of the number of cells in each stage of such a stochastic multistage cancer model.

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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, VIC 3800, Australia. Email address: aidan.sudbury@monash.edu

References

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Armitage, P. and Doll, R. (1957). A two-stage theory of carcinogenesis in relation to the age distribution of human cancer. British J. Cancer 11, 161169.
Connolly, R. B. and Kimbell, J. S. (1994). Simulation of cell growth governed by stochastic processes: application to clonal growth cancer models. Toxicology Appl. Pharmacology 124, 284295.
Kingman, J. F. C. (1975). The first birth problem for an age-dependent branching process. Ann. Prob. 3, 790801.
Portier, C. J., Kopp-Schneider, A. and Sherman, C. D. (1996). Calculating tumor incidence rates in stochastic models. Math. Biosci. 135, 129146.
Portier, C. J., Sherman, C. D. and Kopp-Schneider, A. (2000). Multistage stochastic models of the cancer process: a general theory for calculating tumor incidence. Stoch. Environ. Res. Risk Assess. 14, 173179.
Zheng, Q. (2008). Stochastic multistage cancer models: a fresh look at an old approach. In Handbook of Cancer Models with Applications, World Scientific, Singapore, pp. 2544.

Keywords

MSC classification

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Means and Variances in Stochastic Multistage Cancer Models

  • Aidan Sudbury (a1)

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