Title: New bounds for the Probability of Causation in Mediation Analysis,
Abstract: 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. Under appropriate assumptions, these
bounds can be tightened if we can make other observations (e.g., on
non-experimental cases), measure additional variables (e.g., covariates) or
measure complete mediators. In this work we propose new bounds for the case
that a third variable mediates partially the effect of the exposure on the
outcome.