The probability of causation under a stochastic model for individual risk.

In this paper we offer a mathematical definition for the probability of causation that formalizes the legal and ordinary-language meaning of the term. We show that, under this definition, even the average probability of causation among exposed cases is not identifiable from epidemiologic data. This is because the probability of causation depends both on the unknown mechanisms by which exposure affects disease risk and competing risks, and on the unknown degree of heterogeneity in the background disease risk of the exposed population. We derive the maximum and minimum values for the probability of causation consistent with the observable population quantities. We also derive the relationship of the "assigned share" (excess incidence rate as a proportion of total incidence rate) to the probability of causation.