As in our previous funding cycles, we propose to continue the development of two classes of statistical methods relevant to cancer epidemiology involving extended exposure histories and temporal modifying factors, one aim concerns design aspects of case-control and case-cohort studies and the other concerns the analysis of exposure-time response relationships. These two broad aims have remained unchanged since the beginning of the grant. But, as time has progressed, we have naturally narrowed our attention to particularly fruitful topics. Design and analysis methods for sampled cohort data: Much of our work in the last grant cycle was devoted to building a theoretical foundation for the analysis of a broad class of nested case-control study designs. This work has resulted in some important innovations both in the design and analysis of matched case-control and case-cohort studies. During this grant cycle, we intend to continue our work on these methods as well as extend them to unmatched case-control studies. Methods of exposure-time-response modeling: We have been developing methods for describing exposure-response relationships for extended time-dependent exposure histories, taking into account the modifying effect of time-related variables such as age at exposure and latency. During this grant cycle, we intend to develop flexible, descriptive methods for visualizing time-modifying effects and develop methods to test the "additivity of risk" assumption commonly made in models for latency.