The research project proposes to implement and investigate stochastic compartment model methodology as a tool in modeling and estimating epidemiological risk due to environmental stresses. Although not all modeling of risk factors can be accomplished using a compartment model formulation, most epidemiological models of assessing risk currently in use can be quite simply put into this framework. In this setting, both an empirical and a theoretical investigation will be made of the current methods of risk estimation including bias, robustness and statistical power of the tests. Which kinds of hypotheses can and cannot be examined using the various methods will particularly be studied. The model proposed is easily generalized to represent more complex survival-death processes. This generalization lends itself to the estimation of risk when more specific mechanisms regarding possible environmental hypotheses are proposed. One such example is the estimation of latency in cancer studies. A second example is in extending the definition of risk to multiple cause mortality data incorporating intermediate as well as underlying causes of death in assessing disease linkage (correlations and causal sequencing). Thus the second aim is to develop a methodology which will expand the family of risk estimable models from epidemiological data. As in all compartment formulations, however, problems of parameter identifiability are present. Which parameters of these more complex models can be practically identified and the robustness of these estimates under model fluctuations is also to be examined.