Estimate Collapsibility of Causal Effects in Completed Partial DAGs via Strong d-Convex Hulls

Estimating treatment effects from observational data requires choosing an adjustment set, but valid adjustment depends on an unknown causal graph. Graph misspecification can cause under-coverage, while graph-agnostic conformal wrappers may regain nominal coverage only through large padding. We introduce CausalGuard, a structure-weighted conformal framework that calibrates after aggregating graph-conditional doubly robust pseudo-outcomes. Candidate DAGs are proposed from an LLM-derived edge prior, pruned by conditional-independence tests, and reweighted by Bayesian Information Criterion. A composite nonconformity score then calibrates the posterior-weighted pseudo-outcome. CausalGuard provides distribution-free finite-sample marginal coverage for this aggregated pseudo-outcome; under causal identification, overlap, conditional-mean nuisance stability, and concentration on target-aligned valid adjustment strategies, its conditional mean converges to the true Conditional Average Treatment Effect. Across five benchmarks, CausalGuard attains mean coverage above the nominal 90% level for the directly evaluable target and reduces width when graph-agnostic conformal baselines require large padding. Stress tests show that CausalGuard suppresses invalid collider adjustment and remains stable under misspecified priors when the retained candidate set is data-supported.

Constructing causal directed acyclic graphs (DAGs) is a core step in biomedical causal analysis, yet it remains a largely manual process. Analysts must connect study variables to prior literature, evaluate uncertain causal claims, and preserve sufficient provenance for expert review. We present EviDAG, a browser-based system for authoring causal DAGs as auditable, evidence-linked artifacts from biomedical literature. Given free-text descriptions of study concepts, EviDAG creates a reproducible literature snapshot, uses an LLM-based reasoning module to generate structured pairwise causal judgments, links literature-supported judgments to verbatim evidence excerpts, and assembles the judgments into a constraint-checked graph. Each proposed edge includes confidence estimates, provenance, and a reviewable rationale. The interface supports study specification, progress monitoring, evidence review, graph comparison, adjustment-set computation, and export. In evaluations against both compact benchmark DAGs and reference DAGs derived from published literature, EviDAG achieves high edge recall on the literature-based cohort while retaining verifiable evidence trails absent from LLM-only baselines. EviDAG thus reduces the burden of causal DAG curation while making the resulting assumptions auditable, supporting the design, analysis, and interpretation of biomedical studies.

There is a precise sense in which drawing causal inferences from observational data is hard, even when identifiability is assumed. In particular, Robins and Ritov (1997) and Robins et al. (2003) showed that causal effects can be discontinuous as a function of the data distribution: two arbitrarily close data distributions might correspond to different causal effects. This is a fact independent of the choice of estimator; however, not all estimators are equally unstable. Our contribution is to surface a second layer of instability that depends on the choice of estimator. We show that many standard point estimates can be read as point summaries of multimodal distributions over the space of structural causal models. As such, estimators can jump discontinuously in the data distribution. This defines a taxonomy of estimators that admits a decision-theoretic reading: stability depends on whether the implicit loss function an estimator optimizes is aligned with the causal effect itself. Specifically, inverse propensity weighted estimators and regression estimators are examples of discontinuous summaries, while explicit posterior means and medians are shown to be continuous.