The purpose of this project is research and development of biostatistical methods and mathematical models appropriate for the analysis of epidemiologic studies related to cancer control and prevention. The statistical problems being studied under this project are derived from the needs of other activities in the Division. This research includes the development and use of mathematical models of carcinogenesis to analyze epidemiologic studies of cancer and to help predict the effects of different intervention strategies. The Armitage-Doll model has been used to quantify the effect of cigarette smoking upon early and late stages in lung cancer development; the Moolgavkar-Venzon-Knudson (MVK) two stage model is being used to quantify two hypothesized effects of a first full-term pregnancy upon breast cancer risk; the MVK model is being extended to include two different pathways to development of a malignant tumor. A mathematical model related to carcinogenesis models is being developed to predict the effect of different time-patterns of chemotherapy treatment upon a population of malignant tumor cells which is a combination of drug-sensitive and drug-resistant cells. Research on age-period-cohort Poisson regression models is being conducted on two fronts: (1) the modeling approach has been used to disassemble the trend in lung cancer mortality into calendar period and birth cohort components; to predict the future course of lung cancer mortality in the U.S., these components have been related to past smoking behavior and the average tar content of cigarettes; and (2) a solution to the non-identifiability problem is being developed based upon use of demographic methods to decompose 5-year aggregated population age groups into single years of age. Development of a set of interactive computer programs which can be used to analyze cancer trends is also continuing.