Table of Contents
ISRN Biomathematics
Volume 2013, Article ID 954912, 19 pages
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.


To incorporate biologically observed epidemics into multistage models of carcinogenesis, in this paper we have developed new stochastic models for human cancers. We have further incorporated genetic segregation of cancer genes into these models to derive generalized mixture models for cancer incidence. Based on these models we have developed a generalized Bayesian approach to estimate the parameters and to predict cancer incidence via Gibbs sampling procedures. We have applied these models to fit and analyze the SEER data of human eye cancers from NCI/NIH. Our results indicate that the models not only provide a logical avenue to incorporate biological information but also fit the data much better than other models. These models would not only provide more insights into human cancers but also would provide useful guidance for its prevention and control and for prediction of future cancer cases.