Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 954912, 19 pages
http://dx.doi.org/10.1155/2013/954912
Research Article

New Cancer Stochastic Models Involving Both Hereditary and Nonhereditary Cancer Cases: A New Approach

1Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA
2Department of Mathematics and Statistics, Arkansas State University, State University, AR 72467, USA

Received 24 August 2012; Accepted 10 October 2012

Academic Editors: T. LaFramboise, K. M. Page, I. Rogozin, and J. M. Starobin

Copyright © 2013 Wai-Yuan Tan and Hong Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. P. Little, “Cancer models, ionization and genomic instability: a review,” in Handbook of Cancer Models with Applications, W. Y. Tan and L. Hanin, Eds., chapter 5, World Scientific, River Edge, NJ, USA, 2008. View at Google Scholar
  2. W. Y. Tan, Stochastic Models of Carcinogenesis, Marcel Dekker, New York, NY, USA, 1991.
  3. W. Y. Tan, “Stochastic multiti-stage models of carcinogenesis as hidden Markov models: a new approach,” International Journal of Systems and Synthetic Biology, vol. 1, pp. 313–337, 2010. View at Google Scholar
  4. W. Y. Tan, L. J. Zhang, and C. W. Chen, “Stochastic modeling of carcinogenesis: state space models and estimation of parameters,” Discrete and Continuous Dynamical Systems B, vol. 4, no. 1, pp. 297–322, 2004. View at Google Scholar · View at Scopus
  5. W. Y. Tan, C. W. Chen, and L. J. Zhang, “Cancer biology, cancer models and stochastic mathematical analysis of carcinogenesis,” in Handbook of Cancer Models and Applications, W. Y. Tan and L. Hanin, Eds., chapter 3, World Scientific, River Edge, NJ, USA, 2008. View at Google Scholar
  6. R. A. Weinberg, The Biology of Human Cancer, Garland Sciences, Taylor and Frances, New York, NY, USA, 2007.
  7. Q. Zheng, “Stochastic multistage cancer models: a fresh look at an old approach,” in Handbook of Cancer Models and Applications, W. Y. Tan and L. Hanin, Eds., chapter 2, World Scientific, River Edge, NJ, USA, 2008. View at Google Scholar
  8. W. Y. Tan, L. J. Zhang, W. Chen, and J. M. Zhu, “A stochastic model of human colon cancer involving multiple pathways,” in Handbook of Cancer Models with Applications, W. Y. Tan and L. Hanin, Eds., chapter 11, World Scientific, River Edge, NJ, USA, 2008. View at Google Scholar
  9. W. Y. Tan and H. Zhou, “A new stochastic model of retinoblastoma involving both hereditary and non- hereditary cancer cases,” Journal of Carcinogenesis and Mutagenesis, vol. 2, no. 2, article 117, 2011. View at Publisher · View at Google Scholar
  10. X. W. Yan, Stochastic and State Space Models of carcinogenesis Under Complex Situation [Ph.D. thesis], Department of Mathematical Sciences, University of Memphsis, Memphis, Tenn, USA.
  11. G. L. Yang and C. W. Chen, “A stochastic two-stage carcinogenesis model: a new approach to computing the probability of observing tumor in animal bioassays,” Mathematical Biosciences, vol. 104, no. 2, pp. 247–258, 1991. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Osada and T. Takahashi, “Genetic alterations of multiple tumor suppressors and oncogenes in the carcinogenesis and progression of lung cancer,” Oncogene, vol. 21, no. 48, pp. 7421–7434, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. I. I. Wistuba, L. Mao, and A. F. Gazdar, “Smoking molecular damage in bronchial epithelium,” Oncogene, vol. 21, no. 48, pp. 7298–7306, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Landreville, O. A. Agapova, and J. W. Hartbour, “Emerging insights into the molecular pathogenesis of uveal melanoma,” Future Oncology, vol. 4, no. 5, pp. 629–636, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. H. W. Mensink, D. Paridaens, and A. De Klein, “Genetics of uveal melanoma,” Expert Review of Ophthalmology, vol. 4, no. 6, pp. 607–616, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Y. Tan and X. W. Yan, “A new stochastic and state space model of human colon cancer incorporating multiple pathways,” Biology Direct, vol. 5, article 26, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. L. B. Klebanov, S. T. Rachev, and A. Y. Yakovlev, “A stochastic model of radiation carcinogenesis: latent time distributions and their properties,” Mathematical Biosciences, vol. 113, no. 1, pp. 51–75, 1993. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Y. Yakovlev and A. D. Tsodikov, Stochastic Models of Tumor Latency and Their Biostatistical Applications, World Scientific, River Edge, NJ, USA, 1996.
  19. H. Fakir, W. Y. Tan, L. Hlatky, P. Hahnfeldt, and R. K. Sachs, “Stochastic population dynamic effects for lung cancer progression,” Radiation Research, vol. 172, no. 3, pp. 383–393, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. A. G. Knudson, “Mutation and cancer: statistical study of retinoblastoma,” Proceedings of the National Academy of Sciences of the United States of America, vol. 68, no. 4, pp. 820–823, 1971. View at Google Scholar · View at Scopus
  21. J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory, Harper and Row, New York, NY, USA, 1970.
  22. W. Y. Tan, Stochastic Models With Applications to Genetics, Cancers, AIDS and Other Biomedical Systems, World Scientific, River Edge, NJ, USA, 2002.
  23. W. Y. Tan, C. W. Chen, and L. J. Zhang, “Cancer risk assessment by state space models,” in Handbook of Cancer Models and Applications, W. Y. Tan and L. Hanin, Eds., Chapter 13, World Scientific, River Edge, NJ, USA, 2008. View at Google Scholar
  24. W. Y. Tan and C. W. Chen, “Stochastic modeling of carcinogenesis: some new insights,” Mathematical and Computer Modelling, vol. 28, no. 11, pp. 49–71, 1998. View at Publisher · View at Google Scholar · View at Scopus
  25. W. Y. Tan and C. W. Chen, “Cancer stochastic models,” in Encyclopedia of Statistical Sciences, Revised edition, John Wiley and Sons, New York, NY, USA, 2005. View at Google Scholar
  26. E. G. Luebeck and S. H. Moolgavkar, “Multistage carcinogenesis and the incidence of colorectal cancer,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 23, pp. 15095–15100, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. R. Durrett, J. Mayberry, S. Moseley, and D. Schmidt, “Probability models for cancer development and progression,” Google Search, Google 2012.
  28. G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, Mass, USA, 1973.
  29. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm (with discussion),” Journal of the Royal Statistical Society B, vol. 39, pp. 1–38, 1977. View at Google Scholar
  30. A. F. M. Smith and A. E. Gelfand, “Bayesian statistics without tears: a samplingresampling perspective,” American Statistician, vol. 46, pp. 84–88, 1992. View at Google Scholar
  31. A. E. Loercher and J. W. Harbour, “Molecular genetics of uveal melanoma,” Current Eye Research, vol. 27, no. 2, pp. 69–74, 2003. View at Publisher · View at Google Scholar · View at Scopus
  32. C. S. Potten, C. Booth, and D. Hargreaves, “The small intestine as a model for evaluating adult tissue stem cell drug targets,” Cell Proliferation, vol. 36, no. 3, pp. 115–129, 2003. View at Publisher · View at Google Scholar · View at Scopus
  33. C. J. Lynch and J. Milner, “Loss of one p53 allele results in four-fold reduction of p53 mRNA and protein: a basis for p53 haplo-insufficiency,” Oncogene, vol. 25, no. 24, pp. 3463–3470, 2006. View at Publisher · View at Google Scholar · View at Scopus