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.

翻译：因果归因旨在解释事件或行为发生的原因，在因果推断中至关重要，并深化了我们对科学研究中因果关系的理解。必要因果概率（PN）与充分因果概率（PS）是因果推断中最常用的两种归因度量。尽管已有许多研究探讨了PN与PS的可识别性或其边界，其高效估计问题仍未得到解决。为填补这一空白，本文聚焦于在两组可识别性假设下获得PN与PS的半参数高效估计量：强可忽略性与单调性，以及强可忽略性与条件独立性。我们分别推导了在这两组可识别性假设下PN与PS的高效影响函数及半参数效率边界。基于此，我们提出了PN与PS的高效估计量，并证明了其大样本性质。大量模拟实验验证了我们的估计量相较于现有方法的优越性。我们将所提方法应用于真实世界数据集，以评估影响脑卒中的各类风险因素。