Identification and Estimation of "Probabilities of Causation" in the Presence of Confounding and Selection Bias

Probabilities of causation are valuable concepts for explainable artificial intelligence (XAI) and personalized decision-making. Pearl (2009) defined the probabilities of causation from the viewpoint of "necessity", "sufficiency", and "necessity and sufficiency" in the context of structural causal models. In addition, Tian and Pearl (2000) and Kuroki and Cai (2011) provided the identification conditions of the probabilities of causation under the monotonicity assumption. However, these identification conditions are described based on "the joint probabilities of observed random variables" and/or "causal risks" without selection biases. Thus, they are not applicable to studies in the presence of confounding and selection biases. To address this problem, this paper provides novel identification conditions for the probabilities of causation by using (i) two proxy covariates and (ii) an instrumental variable and a proxy covariate. When the probabilities of causation can be evaluated through the proposed identification conditions, new plug-in estimators for these probabilities are presented. Finally, we illustrate the application of our results on a real-world dataset.