Exposure to other risk factors is an important consideration in assessing the role played by radiation in producing disease. A cross-sectional study of atomic-bomb survivors suggested an interaction between whole-body radiation exposure and chronic hepatitis-C viral (HCV) infection in the etiology of chronic liver disease (chronic hepatitis and cirrhosis), but did not allow determination of the joint-effect mechanism. Different estimates of probability of causation (POC) conditional on HCV status resulted from additive and multiplicative models. We therefore estimated the risk for radiation conditional on HCV status using a more general, mixture model that does not require choosing between additivity or multiplicativity, or deciding whether there is interaction, in the face of the large uncertainty. The results support the conclusion that POC increases with radiation dose in persons without HCV infection, but are inconclusive regarding individuals with HCV infection, the lower confidence bound on estimated POC for radiation with HCV infection being zero over the entire dose range. Although the mixture model may not reflect the true joint-effect mechanism, it avoids restrictive model assumptions that cannot be validated using the available data yet have a profound influence on estimated POC. These considerations apply more generally, given that the additive and multiplicative models are often used in POC related work. We therefore consider that an empirical approach may be preferable to assuming a specific mechanistic model for estimating POC in epidemiological studies where the joint-effect mechanism is in doubt.