Biomaterial Database

To use or not to use? Backward equations in stochastic carcinogenesis models. 1998

Q Zheng

Division of Biometry and Risk Assessment, National Center for Toxicological Research, Jefferson, Arkansas 72079, USA. qzheng@nctr.fda.gov

The method based on the Kolmogorov backward equations of Little (1995, Biometrics 51, 1278-1291) for computing hazard functions for the multistage carcinogenesis models fails when model parameters are time-dependent. In addition to suggesting an alternative method based on the Kolmogorov forward equation, this note highlights the interplay of the forward equation, the backward equation, and the characteristic method. Advantages and disadvantages of the forward and backward equations are discussed.

UI	MeSH Term	Description	Entries
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
D009154	Mutation	Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.	Mutations
D002470	Cell Survival	The span of viability of a cell characterized by the capacity to perform certain functions such as metabolism, growth, reproduction, some form of responsiveness, and adaptability.	Cell Viability,Cell Viabilities,Survival, Cell,Viabilities, Cell,Viability, Cell
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
D001699	Biometry	The use of statistical and mathematical methods to analyze biological observations and phenomena.	Biometric Analysis,Biometrics,Analyses, Biometric,Analysis, Biometric,Biometric Analyses
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
D016016	Proportional Hazards Models	Statistical models used in survival analysis that assert that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time.	Cox Model,Cox Proportional Hazards Model,Hazard Model,Hazards Model,Hazards Models,Models, Proportional Hazards,Proportional Hazard Model,Proportional Hazards Model,Cox Models,Cox Proportional Hazards Models,Hazard Models,Proportional Hazard Models,Hazard Model, Proportional,Hazard Models, Proportional,Hazards Model, Proportional,Hazards Models, Proportional,Model, Cox,Model, Hazard,Model, Hazards,Model, Proportional Hazard,Model, Proportional Hazards,Models, Cox,Models, Hazard,Models, Hazards,Models, Proportional Hazard