Probability of causation: Bounds and identification for partial and complete mediation analysis

An individual has been subjected to some exposure and has developed some outcome. Using data on similar individuals, we wish to evaluate, for this case, the probability that the outcome was in fact caused by the exposure. Even with the best possible experimental data on exposure and outcome, we typically can not identify this “ probability of causation” exactly, but we can provide information in the form of bounds for it. Here, using the potential outcome framework, we propose new bounds for the case that a third variable mediates partially or completely the e↵ect of the exposure on the outcome.