Semiparametric Efficient Inference for the Probability of Necessary and Sufficient Causation

Causal attribution, which aims to explain why events or behaviors occur, is crucial in causal inference and enhances our understanding of cause-and-effect relationships in scientific research. The probabilities of necessary causation (PN) and sufficient causation (PS) are two of the most common quantities for attribution in causal inference. While many works have explored the identification or bounds of PN and PS, efficient estimation remains unaddressed. To fill this gap, this paper focuses on obtaining semiparametric efficient estimators of PN and PS under two sets of identifiability assumptions: strong ignorability and monotonicity, and strong ignorability and conditional independence. We derive efficient influence functions and semiparametric efficiency bounds for PN and PS under the two sets of identifiability assumptions, respectively. Based on this, we propose efficient estimators for PN and PS, and show their large sample properties. Extensive simulations validate the superiority of our estimators compared to competing methods. We apply our methods to a real-world dataset to assess various risk factors affecting stroke.