In causal inference with ordinal outcomes, several interpretable estimands are functions of the probability that the potential outcome under one treatment is larger than that under another treatment for the same unit. This probability depends on the joint distribution of both potential outcomes and is generally not identifiable. Existing work has focused on sharp bounds of this probability based on partial identification, but bounds are often too wide to be informative. We propose a copula-based method that links the identifiable marginal distributions of the potential outcomes via a parametric copula, treating the copula association parameter as a sensitivity parameter. With a fixed copula parameter, the estimands become identified functionals of the observed data. Working under unconfoundedness, we derive the efficient influence function in the nonparametric model and construct one-step estimators that accommodate flexible nuisance estimation. The resulting procedure is rate-doubly-robust and attains the semiparametric efficiency bound under standard conditions. Varying the copula parameter yields a sensitivity curve with point-wise confidence bands that typically lie within the sharp bounds, providing an interpretable bridge between partial identification and point estimation. We further provide a comprehensive sensitivity analysis with respect to both the copula specification and the unconfoundedness assumption. We develop an associated R package \texttt{ordinalCI}.

翻译：在有序结局变量的因果推断中，几个可解释的估计量依赖于同一单位在一种处理下潜在结果大于另一种处理下潜在结果的概率。该概率取决于两种潜在结果的联合分布，通常不可识别。现有研究主要基于部分识别方法给出该概率的锐界，但边界往往过宽而缺乏信息性。我们提出一种基于copula的方法，通过参数化copula连接可识别的潜在结果边际分布，并将copula关联参数视为敏感性参数。在固定copula参数下，估计量成为观测数据的可识别泛函。基于无混杂性假设，我们推导出非参数模型中的有效影响函数，并构建能适应灵活干扰估计的一步估计量。该过程具有率双重稳健性，在标准条件下达到半参数效率界。改变copula参数可生成带有逐点置信带的敏感性曲线，该曲线通常位于锐界内，为部分识别与点估计之间提供可解释的桥梁。我们进一步针对copula设定与无混杂性假设开展全面的敏感性分析，并开发了配套的R包\texttt{ordinalCI}。