This is a multi-investigator project that applies mathematical and statistical methods to the study of clinical and experimental cancer and of biological mechanisms relevant to cancer. (1) Data on human cancer incidence are being compared to a mathematical model that incorporates cell kinetics as well as transition rates for each two stages. The role of smoking in the origin of various human cancers is also being studied. (2) Statistical methods are being developed and utilized in the analysis of individuals infected with hepatitis B virus, their rates of conversion to the carrier state, and their acquisition of primary hepatocellular cancer. Mathematical models are also being applied to the study of cancer in rats as a function of early diet and growth. (3) Stochastic methods are being employed to analyze such diverse problems as the incidence of cancer in families and local communities, the estimation of numbers of cell surfaces, and the structures of proteins and nucleic acids. (4) Mathematical analysis is being performed on the mitotic cycle of cells, utilizing data obtained by time-lapse microcinematography and by two-parameter flow cytometry.