Journal of Applied Probability

Means and variances in stochastic multistage cancer models

Aidan Sudbury

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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 .

Article information

Source
J. Appl. Probab., Volume 49, Number 2 (2012), 590-594.

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1339878807

Digital Object Identifier
doi:10.1239/jap/1339878807

Mathematical Reviews number (MathSciNet)
MR2977816

Zentralblatt MATH identifier
1243.92035

Subjects
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 92B05: General biology and biomathematics

Keywords
Multistage cancer model mutation chain

Citation

Sudbury, Aidan. Means and variances in stochastic multistage cancer models. J. Appl. Probab. 49 (2012), no. 2, 590--594. doi:10.1239/jap/1339878807. https://projecteuclid.org/euclid.jap/1339878807


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References

  • 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, 161–169.
  • 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, 284–295.
  • Kingman, J. F. C. (1975). The first birth problem for an age-dependent branching process. Ann. Prob. 3, 790–801.
  • Portier, C. J., Kopp-Schneider, A. and Sherman, C. D. (1996). Calculating tumor incidence rates in stochastic models. Math. Biosci. 135, 129–146.
  • 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, 173–179.
  • 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. 25–44. \endharvreferences