ConfoundingSHAP: Quantifying confounding strength in causal inference

Understanding the effects of interventions is central to scientific progress, with randomized controlled trials (RCTs) regarded as the gold standard for causal inference in many applied fields. However, RCTs are costly, time-consuming, and often constrained by ethical or practical limitations, motivating the need for causal methods able to draw conclusions from observational data. While such data is collected at ever larger scale, making its use for causal inference is often hindered by the fact that not all variables affecting treatment allocation and the outcome are observed: an issue known as unobserved confounding. In this paper, we introduce a new study design called confounder detection via treatment intent. The idea is to query a human expert who makes treatment decisions, and ask them to compare pairs of units proposed by a principled matching strategy, with the goal of eliciting unobserved variables that explain why treatment decisions differ. We provide a theoretical basis for such a procedure, ascertaining conditions under which such a study design may elicit unobserved confounders. Building on this newly established foundations, we study treatment effects of interventions in the intensive care unit (ICU). First, we show empirical evidence strongly indicating that electronic health records (EHRs) collected in ICUs are subject to unobserved confounding. By using clinical text notes as a proxy for physicians' knowledge and leveraging natural language processing, we provide a proof of concept for our methodology in a semi-synthetic environment with a known ground truth.

Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions, and converts those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target. In the known-truth benchmark, eight repeated primary-interaction simulations (n = 2,200 each, three actions) gave mean Local CAS MAE of 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute ATE vector. The paired advantage over one-at-a-time normalisation increased from -0.003 under additivity to 0.091 under strong interactions. On both empirical DoubleML datasets, 401(k) eligibility/net financial assets (n = 9,915) and Pennsylvania reemployment bonus/unemployment duration (n = 5,099), predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In Pennsylvania, dep1 (exactly one dependent) moved from predictive global rank 13 to Feature-CAS rank 2 and was the leading local Feature-CAS modifier. These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

Causal effect estimation from observational data requires careful adjustment for confounding. Classical estimators such as inverse probability weighting and augmented inverse probability weighting are effective under favorable model specification, but may become unstable when treatment assignment and outcome mechanisms are complex, non-linear, and high-dimensional. Machine learning and representation learning approaches improve flexibility, yet joint training can allow outcome-related information to influence treatment-side representations, which is undesirable from a causal perspective. We propose MOCA (Modular One-way Causal Attention), a transformer-based framework that separates treatment and outcome modeling through a modular design, and performs confounder adjustment using a one-way attention mechanism. A cutting-feedback strategy, implemented via gradient detachment, prevents the outcome loss from updating the treatment module. This design preserves directional information flow while retaining the representational power of transformer architectures for causal inference. Across multiple simulated scenarios, including linear, nonlinear, heavy-tailed, hidden confounding, and high-dimensional settings, MOCA shows competitive or improved performance relative to IPW, AIPW, X-learner, TARNet, and DragonNet. We further illustrate the method on the Infant Health and Development Program dataset and the Dehejia-Wahba dataset as real-world benchmarks. These results suggest that modular attention with one-way information flow provides a promising and interpretable direction for causal inference with modern deep learning models.