DESCRIPTION In this proposal we address the problems of estimating and predicting carcinogenic risks from exposure to mixtures of carcinogens. Our approach to this problem will be based on the two mutation clonal expansion (TMCE) model of carcinogenesis. This model can explicitly accommodate both initiators and promoters in the risk assessment process. In this proposal, we make a distinction between simple and complex mixtures. Complex mixtures, such as diesel exhaust, emissions from coke oven batteries, and cigarette smoke, contain hundreds of cancer causing chemicals. Often, however, complex mixtures can be treated as single carcinogens when good data on exposure to the entire mixture are available. Thus, the first objective addresses the problem of estimating cancer risk when a small number of component carcinogens is involved. Questions regarding the roles of the carcinogen type (mode of action), exposure pattern, dose-protraction, and dependency on start and stop of exposures are formulated and their impact on cancer risk explored. Specifically, we focus on human exposures to low and high LET radiation and lung cancer (or death from lung cancer) as the endpoint. Three large data sets will serve to illustrate the usefulness and effectiveness of our approach: the Colorado Plateau Uranium Miners cohort, with detailed individual information on joint exposure to cigarette smoking and exposure to radon; the Chinese Tin Miners data set, with detailed individual information on three lung carcinogens: tobacco smoke, radon progeny and arsenic; and the Life Span Study of the atomic bomb survivors. The second objective concerns the development of appropriate methods for analyzing case-control data using biologically-based models. This provides another tool for assessing the carcinogenic potential of mixtures. The third objective concerns the toxicity equivalency factor (TEF) approach for complex mixtures that may contain numerous chemical components like those mentioned above. To evaluate the usefulness of the TEF approach we propose to analyze the Allegheny/non-Allegheny coke oven cohort data, as an example.