potential outcomes framework

This paper bridges the theoretical and practical gap between the potential outcomes framework and causal graphical models. Addressing core causal inference problems—including counterfactual reasoning, treatment effect identification, and estimation—the work systematically unifies potential outcomes, causal diagrams, d-separation, the backdoor criterion, single-world intervention graphs (SWIGs), and structural equation models, offering the first coherent account of their logical interconnections. Methodologically, it proposes a robust identification strategy grounded in propensity score estimation and inverse probability weighting, augmented with sandwich standard errors for valid statistical inference. The key contribution is a pedagogically transparent, operationally feasible framework that lowers the barrier to integrating these two dominant causal paradigms. By harmonizing conceptual rigor with practical applicability, the paper provides applied researchers with an accessible yet theoretically sound entry point into modern causal inference. (149 words)

Core assumptions in causal discovery and inference—such as causal sufficiency, faithfulness, and the Markov condition—are inconsistently formalized and ambiguously operationalized across methodological traditions, hindering rigorous method selection under non-ideal conditions (e.g., observational constraints, limited domain knowledge). Method: We propose the first cross-framework unification framework, employing conceptual analysis, comparative modeling, and structured meta-review to systematically map how distinct paradigms model these assumptions and align them with practical inferential goals. This yields a decision guide and reusable comparison toolkit spanning the entire causal analysis lifecycle—from problem formulation to result interpretation. Contribution: Our work achieves the first cross-paradigm integration of the formal semantics and operational logic of causal assumptions. It significantly enhances the rigor and efficiency of causal methodology selection and design, particularly when background knowledge is incomplete or data are observationally constrained.

When linear regression is used to estimate treatment effects in quasi-experiments, its causal interpretation rests on implicit assumptions—specifically, under what conditions does the regression coefficient represent a comparable contrast of individual potential outcomes? Method: We formally introduce the concept of “latent weights” to characterize regression’s implicit weighting of unobserved counterfactuals; derive necessary linear constraints on treatment assignment for causal interpretability; and define the “implicit causal design set,” unifying and extending existing theoretical frameworks. Our approach integrates design-based inference, counterfactual modeling, and linear constraint analysis. Contribution: We establish a necessary conditions framework for causal interpretation of regression, provide operational transparency diagnostics, and deliver novel theoretical justification for widely used—but previously under-justified—regression specifications, including covariate-adjusted regression.

This study systematically reconstructs Pearl’s causal hierarchy from the potential outcomes framework, mapping causal estimands at each level to distinct features of the potential outcomes distribution and analyzing their identifiability conditions and strategies. By integrating the potential outcomes model, structural causal models, and formal classification methods, this work establishes—for the first time—a comprehensive taxonomy of Pearl’s causal hierarchy from the perspective of potential outcomes. The analysis not only clarifies the identification challenges inherent to estimands at each level but also deepens understanding of Level 3 (counterfactual) estimands. Furthermore, it reveals that higher-level estimands rely on stronger identification assumptions and correspond to richer information in the potential outcomes distribution, thereby offering a novel theoretical and practical perspective for causal inference.

Counterfactual prediction under evolving intervention policies or hypothetical decision scenarios remains challenging due to unobservable potential outcomes, hindering model identifiability, evaluation, and generalization. Method: We propose the first systematic theoretical framework addressing this challenge—comprising (i) identifiability conditions for counterfactual prediction models, (ii) a performance evaluation system targeting loss, AUC, and calibration, and (iii) robust hyperparameter selection under model misspecification. Our approach integrates causal inference principles, doubly robust estimation, and loss-driven evaluation metric design. Contribution/Results: Validated via simulation studies and a real-world clinical application—cardiovascular risk prediction in statin-naïve populations—the framework significantly improves out-of-distribution generalization and clinical decision reliability in counterfactual settings.

This study addresses the identifiability of interventional effects under complex causal structures. It proposes a unified identification framework by directly interpreting single-world intervention graphs (SWIGs) as joint representations of observational and interventional distributions, thereby transcending their conventional role as mere bridges to potential outcomes. Integrating SWIGs with do-calculus and structured probabilistic modeling, the approach not only recovers classical results such as backdoor adjustment but also substantially extends the applicability of front-door criteria to more intricate scenarios. This advancement provides a more scalable theoretical foundation for identifying causal effects under general intervention structures.

This study addresses the challenge of causal inference in N-of-1 behavioral health case studies, where unobserved confounding impedes valid estimation. The authors propose the Ω causal estimator, which achieves identification without measuring or adjusting for confounders by leveraging functional contrasts over the support set of the outcome variable, requiring only the positivity assumption. This approach pioneers a support-based—rather than distribution-based—framework for causal inference, integrating de Finetti’s subjective probability interpretation with a theory of intervention–observation support consistency. A recall-baseline substitution mechanism bridges support-level contrasts to mean-level causal effects. The method’s feasibility is demonstrated in a case study on cognitive behavioral therapy for anxiety, offering clinicians a practical and robust tool for individualized causal inference.

This study addresses the lack of formal definitions in existing root cause analysis methods, which are often limited to root nodes in causal graphs or biased toward proximate causes. Within the potential outcomes framework, this work proposes the first counterfactual definition of root cause at the individual level and introduces a probabilistic measure—Probability of Root Condition (PRC)—to quantify the likelihood that a candidate set of variables constitutes a root cause for a specific outcome. Under standard causal assumptions, the authors derive an explicit identification formula for PRC by integrating causal mediation analysis with counterfactual reasoning, thereby establishing its identifiability. The effectiveness and practical utility of the proposed approach are demonstrated through two numerical examples, filling a critical gap in the formal theory of root cause analysis.

This study addresses a key limitation of traditional instrumental variable (IV) models, which assume deterministic relationships between treatment selection and potential outcomes under an instrument, thereby failing to capture stochastic decision-making in real-world settings. To overcome this restriction, the paper develops a micro-founded framework in which both potential outcomes and treatment choices exhibit individual-level randomness. Response types are redefined as state-dependent treatment probabilities coupled with distributions of potential outcomes, grounded in expected utility maximization subject to information constraints. Within this framework, conventional IV estimands are reinterpreted not merely as local average treatment effects for compliers, but as population-weighted averages of treatment effects, where weights correspond to individual changes in treatment probability induced by the instrument. This approach yields a more flexible and interpretable characterization of treatment effect heterogeneity.

A persistent methodological divide exists between the Neyman–Rubin potential outcomes framework and graphical causal models (e.g., DAGs and do-calculus), hindering principled integration and comparative assessment. Method: We systematically analyze their theoretical relationships and applicability boundaries by constructing pathological data-generating mechanisms—including cyclic dependencies, deterministic relations, M-bias, trapdoor variables, and complex front-door paths—to formally characterize the expressive and inferential limits of each framework. Contribution/Results: We establish the “complementary applicability” principle: potential outcomes excel in handling unmodeled confounding and counterfactual definition, whereas graphical models offer superior structural identifiability, computational tractability, and conditional independence reasoning. This work bridges a long-standing methodological gap, provides a rigorous theoretical foundation for hybrid causal modeling, and significantly enhances interpretability and practical applicability of cross-paradigm causal analysis.