Causal inference with ordinal outcomes: copula-based identification, estimation and sensitivity analysis

2026-05-11

AI Summary

In causal inference with ordinal outcomes, the joint distribution of potential outcomes is generally non-identifiable, hindering precise estimation of key causal effects. This work proposes a copula-based sensitivity analysis framework that leverages identifiable marginal distributions and links potential outcomes via a parametric copula, treating the copula association parameter as a sensitivity parameter to achieve point identification and estimation of causal effects under unconfoundedness. The approach integrates partial identification with point estimation, yielding interpretable sensitivity curves accompanied by confidence bands, and enables joint assessment of copula specification and the unconfoundedness assumption. The proposed estimator enjoys double robustness and semiparametric efficiency, with sensitivity curves typically residing within sharp bounds. An accompanying R package, ordinalCI, is made publicly available.

Abstract

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}.

Problem

• causal inference
• ordinal outcomes
• partial identification
• sensitivity analysis
• copula

Innovation

• copula-based causal inference
• ordinal outcomes
• sensitivity analysis
• double robustness
• semiparametric efficiency