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

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. 1. Introduction It is universally recognized that each cancer tumor develops through stochastic proliferation and differentiation from a single stem cell which has sustained a series of irreversible genetic and/or epigenetic changes (Little [1]; Tan [2, 3]; Tan et al. [4, 5]; Weinberg [6]; Zheng [7]). That is, carcinogenesis is a stochastic multistage model with intermediate cells subjecting to stochastic proliferation and differentiation. Furthermore, the number of stages and the number of pathways of the carcinogenesis process are significantly influenced by environmental factors underlying the individuals (Tan et al. [4, 5]; Weinberg [6]). Another important observation in human carcinogenesis is that most human cancers cluster around family members. Further, many cancer incidence data (such as SEER data of NCI/NIH, USA) have documented that some cancers develop during pregnancy before birth to give new born babies with cancer at birth. This has been referred to as pediatric cancers. Well-known examples of pediatric cancers include retinoblastoma—a pediatric eye cancer, hepatoblastoma—a pediatric liver cancer, Wilm’s tumor—a pediatric kidney cancer, and medulloblastoma—a pediatric brain tumor. Epidemiological and clinical studies on oncology have also revealed that inherited cancers are very common in many adult human cancers including lung cancer, colon cancer [8], uveal melanomas (adult eye cancer, [9]), and adult liver cancer (HCC, [10]). Given the above results from cancer biology and human cancer epidemiology, the objective of this paper is to illustrate how to develop stochastic models of carcinogenesis incorporating these biological and epidemiological