Biomaterial Database

Calculating tumor incidence rates in stochastic models of carcinogenesis. 1996

C J Portier, and A Kopp-Schneider, and C D Sherman

National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina, USA.

Multistage models of carcinogenesis are increasingly used in the estimation of risks from exposure to environmental agents. The two-stage model of carcinogenesis is routinely used because it agrees with much of the existing tumor incidence data, parallels the biological two-stage model, and has much of its mathematical details derived. However, recent findings on the mechanisms of carcinogenesis has led researchers to believe that there are a greater number of stages and a more complex structure to these models than a single pathway. In this paper, a method for readily computing tumor incidence rates for arbitrarily complex multistage models is derived. The formulas for the two-stage model with time-varying rates are given explicitly. Simple rules for more complicated models are given, and computer code able to implement these formulas are provided.

UI	MeSH Term	Description	Entries
D008433	Mathematics	The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)	Mathematic
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D009369	Neoplasms	New abnormal growth of tissue. Malignant neoplasms show a greater degree of anaplasia and have the properties of invasion and metastasis, compared to benign neoplasms.	Benign Neoplasm,Cancer,Malignant Neoplasm,Tumor,Tumors,Benign Neoplasms,Malignancy,Malignant Neoplasms,Neoplasia,Neoplasm,Neoplasms, Benign,Cancers,Malignancies,Neoplasias,Neoplasm, Benign,Neoplasm, Malignant,Neoplasms, Malignant
D003043	Cocarcinogenesis	The combination of two or more different factors in the production of cancer.	Cocarcinogeneses
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D013269	Stochastic Processes	Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.	Process, Stochastic,Stochastic Process,Processes, Stochastic