arXiv subjects

Razieh Nabi

Publications and source records attributed to Razieh Nabi.

At least 19 recordsLinked to original sources

arXiv2026

Formulating Cross-World Mediation Estimands Through Single-World Mixtures

In causal mediation analysis, natural direct and indirect effects are defined through nested counterfactuals that combine the outcome under one exposure level with the mediator value under another and are therefore inherently cross-world. Their canonical identification additionally relies on cross-world independence assumptions. Consequently, both the estimands and their identifying assumptions remain controversial. In this paper, we ask what additional single-world structure would be required to re-express cross-world estimands as single-world quantities, identifiable under single-world assumptions. We show that these quantities can be written as mixtures of controlled single-world effects under assumptions involving a susceptibility marker, a possibly latent baseline variable that encodes the "would-be" mediator value under a reference treatment arm. If observed, the marker would make several implications of the marker restrictions empirically testable. These results provide a transparent single-world formulation of cross-world mediation effects while making explicit the assumptions required. Although these conditions clarify how cross-world estimands can be interpreted within a single-world framework, their practical relevance depends on whether such susceptibility markers can be justified in specific applications. We discuss implications for principal stratification and show in the Supplementary Material how the formulation extends to ordered mediators and settings with exposure-induced mediator-outcome confounding.

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arXiv2026

Causal Vaccine Effects on Post-infection Outcomes in the Naturally Infected

Understanding vaccine effects on post-infection outcomes is critical for evaluating the full value proposition of a vaccine. However, defining appropriate causal effects on such outcomes is challenging because infection is affected by vaccination. Existing approaches focus on the Doomed stratum, individuals who would be infected regardless of vaccine receipt. For many relevant outcomes, however, this estimand understates vaccine benefit by excluding individuals whose adverse post-infection outcomes improve because vaccination prevented infection. We therefore propose causal estimands for post-infection outcomes in the Naturally Infected, individuals who would be infected in absence of vaccine. We derive bounds under minimal assumptions and give point identification results under an exclusion restriction and/or a partial principal ignorability assumption. For point-identified settings, we develop efficient one-step estimators with robustness properties under inconsistent nuisance parameter estimation. We further show under what conditions the same identification functional can be interpreted as targeting an effect among individuals exposed to a sufficiently infectious dose of the pathogen, thereby avoiding reliance on cross-world parameters and fundamentally untestable causal assumptions. Simulations show that the bounds are valid but often wide, and that the point estimators perform well when their identifying assumptions hold. In a reanalysis of a rotavirus vaccine trial, marginal and Doomed-stratum analyses showed little evidence of an effect on antibiotic use, whereas analyses targeting the Naturally Infected suggested a protective effect under principal ignorability-based assumptions.

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arXiv2026

Toward a Semiparametric Efficiency Theory under Equality Constraints in Nested Markov Models

Probabilistic models of Directed Acyclic Graphs (DAGs) with latent variables impose equality constraints on the observed data distribution beyond ordinary conditional independencies. These so-called Verma constraints arise in nested Markov models associated with Acyclic Directed Mixed Graphs, the latent projection of latent-variable DAGs. While nested Markov models have been extensively studied from the perspectives of graphical representation and causal identification, their implications for semiparametric efficiency theory remain less understood. We develop results toward establishing a semiparametric framework for statistical models defined by Verma constraints. Our key observation is that nested Markov constraints admit weighted conditional-moment representations under post-fixing distributions induced by graphical fixing operations. We show that fixing induces weighted orthogonality relations in L2(P), thereby converting Verma constraints into explicit tangent-space restrictions. Building on this representation, we characterize the tangent-space orthocomplement for models defined by a single nested Markov constraint through residualized weighted moment functions. This geometric formulation yields Hilbert-space characterizations of semiparametric efficient influence functions and efficiency bounds via orthogonal projection and equivalent minimum-variance formulations. We further discuss extensions to models involving multiple nested Markov constraints, for which we characterize a subspace of the orthocomplement as sums of the corresponding weighted orthogonality relations, while leaving the complete tangent-space characterization open. More broadly, our results connect nested graphical structure with semiparametric Hilbert-space geometry and provide a foundation for a general efficiency theory for nested Markov models. We illustrate the framework through several latent-variable DAGs.

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arXiv2026

Semiparametric Efficiency Theory as Differential Calculus on a Space of Probability Distributions

Semiparametric efficiency theory provides the mathematical foundation for influence-function-based estimation, including one-step estimators, targeted minimum loss estimators, and many modern inferential methods used in causal inference and missing data analysis. Despite its widespread use, the theory is often presented through a collection of technical constructions whose geometric meaning remains opaque. As a result, influence functions are often derived and applied without an intuitive understanding of the principles connecting scores, tangent spaces, nuisance tangent spaces, and efficient influence functions. This tutorial develops a geometric exposition of semiparametric efficiency theory as a form of differential calculus on a space of probability distributions. Drawing systematic parallels with ordinary multivariable calculus, we show that paths of distributions play the role of curves, scores play the role of velocity vectors, influence functions play the role of gradients, and efficient influence functions arise as projected gradients. This perspective provides a unified explanation for several foundational questions, including why perturbation directions are represented by functions, why tangent spaces depend only on the statistical model whereas nuisance tangent spaces depend on the parameter of interest, and why efficient influence functions arise through orthogonal projection. The resulting framework offers a geometric perspective on semiparametric efficiency theory and influence-function-based inference.

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arXiv2026

Coarsening Bias from Variable Discretization in Causal Functionals

Causal identification functionals often require integration over conditional densities of continuous variables, such as those arising in nonparametric identification theory of total and mediated causal effects in DAGs with hidden variables. Estimating these densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the continuous variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even when identification is correct. Under smoothness conditions, we show that the resulting coarsening error is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple debiased coarsened functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading coarsening error term and yielding a second-order approximation error. We derive plug-in and one-step estimators for this debiased coarsened functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a simple framework for controlling the impact of variable discretization on both parameter approximation and statistical estimation.

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arXiv2026

Inferring Comprehensive Cohort Causal Effects in the Presence of Unmeasured Confounding and Missing Outcomes

This paper presents a methodological framework for estimating the comprehensive cohort causal effect (CCCE) in mixed-design clinical studies that combine randomized controlled trials (RCTs) and parallel observational study (OBS). Our approach is designed to evaluate robustness against unmeasured confounding in the OBS arm and to handle outcomes that are missing at random in either the RCT or OBS arm. By employing a semiparametric theory-based sensitivity analysis framework, we derive the efficient influence function for the CCCE, parameterized by sensitivity parameters. We propose a one-step bias-corrected estimator that allows for flexible modeling and establish conditions under which our CCCE estimator is $\sqrt{n}$-consistent. To illustrate our methods, we apply them to the TOIB study, which evaluates the efficacy and safety of oral versus topical ibuprofen in managing chronic knee pain among older adults. We also evaluate the performance of the proposed methodology in a realistic simulation study.

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arXiv2026

Causal Inference with the Napkin Graph

Unmeasured confounding can render identification strategies based on adjustment functionals invalid. We study the "Napkin" graph, a causal structure that encapsulates features of M-bias, instrumental variables, and classical back-door and front-door settings, yet identifies the average treatment effect through a nonstandard ratio of two g-formulas. We develop influence-function-based estimators for this functional, including doubly-robust one-step and targeted minimum loss-based estimators that remain asymptotically linear under slower-than-parametric nuisance estimation using machine learning. A distinguishing feature of the Napkin graph is that it imposes a generalized independence restriction, known as a Verma constraint, rather than ordinary conditional independence restrictions, on the observed data distribution. We develop semiparametric efficiency theory for causal effects under a moment restriction corresponding to this Verma constraint, characterizing the orthocomplement of the tangent space, deriving the class of influence functions, and obtaining the semiparametric efficiency bound. More broadly, our analysis provides a framework for semiparametric inference in causal models defined by Verma constraints and demonstrates how such restrictions may yield efficiency gains. Simulations confirm the estimators' theoretical properties and demonstrate substantial efficiency gains. A real-data application using the Finnish Life Course Study estimates the effect of educational attainment on income. An accompanying R package, napkincausal, implements our methods.

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arXiv2026

Bridging Predictions and Interventions: An Integrated Framework for Automated Decision-Systems

Automated decision systems (ADS) leverage predictions about individual future outcomes to inform consequential decision-making in organizational settings. Across various settings - including criminal pretrial release, clinical triage, student support, and more - it is often assumed that improved predictive accuracy is the priority consideration in determining better downstream outcomes upon the deployment of ADS. In practice, real-world case studies reveal that this is far from the case: introducing individual predictions into decision-making modifies organizational workflows, assessment, and decision-making processes in ways that require a complete re-consideration of our approach to the design, evaluation, and deployment of ADS. As a result, this Perspective develops an integrated framework for studying ADS in social systems, shifting current priorities from a purely prediction-based paradigm towards an intervention-oriented view that accounts for real-world conditions. Our aim is to improve our understanding of ADS and more meaningfully anticipate its downstream societal and organizational consequences.

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arXiv2026

A Law of Iterated Expectation Primer for Causal Inference

The g-formula is a foundational tool for identifying causal effects in observational data. This tool is based on the law of iterated expectation, a key mathematical identity in statistics. However, the notation with which the law of iterated expectation and the g-formula is expressed can be opaque to those with little background in statistics. We provide a primer introducing the law of iterated expectation, the integration notation used to express it, and its role for causal effect identification via the g-formula. Under the assumptions of causal consistency, positivity, and conditional exchangeability, the law of iterated expectation can be rewritten as a causal standardization formula (the g-formula) in two nonparametrically equivalent forms: a non-iterative conditional expectation (NICE) form involving a single weighted average of conditional outcome means, and an iterative conditional expectation (ICE) form involving nested expectations. We illustrate both forms using three progressively complex numerical examples: a time-fixed example with a single binary confounder, a time-fixed example with discrete and continuous confounders, and a time-varying example with two timepoints. We provide clarity on what the law of iterated expectation is, how it is related to the g-formula, and how to gain intuition of its mathematical formulations in actual data examples that can be generalized to a range of settings.

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arXiv2026

Causal Sufficient Dimension Reduction for Multiple Continuous Exposures with an Application to Environmental Mixtures

Estimating causal effects with multivariate continuous exposures is challenging because causal exposure-response surfaces can be high-dimensional, complicating estimation and interpretation of joint exposure effects. Such settings arise in environmental epidemiology, where interest centers on the health effects of chemical and pollutant mixtures. We develop causal sufficient dimension reduction (CSDR), a semiparametric framework for representing causal exposure-response surfaces through low-dimensional exposure summaries. We formalize the reduction target as the causal central mean subspace and propose a modular two-stage estimator that decouples nuisance-function estimation from subspace estimation, simplifying implementation relative to existing marginal structural model-based approaches. The reduced exposure preserves the information needed to characterize joint causal effects while enabling efficient downstream estimation. We establish a convergence rate for causal subspace recovery accounting for first-stage nuisance estimation error, show that the structural dimension can be estimated consistently, and introduce a subspace importance score that quantifies the contribution of each exposure to the reduction. In simulations, CSDR yielded more accurate estimation and uncertainty quantification of the exposure-response surface than methods using noncausal dimension reduction or the original exposure. We apply CSDR to study the effect of maternal exposure to PFAS chemical mixtures on infant birth weight in the Atlanta African American Maternal-Child Cohort.

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arXiv2026

Assessing Racial Disparities in Healthcare Expenditures via Mediator Distribution Shifts

Racial disparities in healthcare expenditures are well-documented, yet the underlying drivers remain complex. This study develops a framework to decompose such disparities through shifts in the distributions of mediating variables, rather than treating race itself as a manipulable exposure. We define disparities as differences in covariate-adjusted outcome distributions across racial groups, and decompose the total disparity into a component attributable to differences in mediator distributions, and a residual component that remains after equalizing those distributions. Using data from the Medical Expenditures Panel Survey (MEPS), we examine the extent to which expenditure disparities would persist or be reduced if mediators such as socioeconomic status (SES), insurance access, health behaviors, or health status were equalized across racial groups. To ensure valid inference, we derive asymptotically linear estimators based on influence-function techniques and flexible machine learning, including super learners and a two-part model designed for the zero-inflated, right-skewed nature of expenditure data. Applying this framework to MEPS data from 2009 and 2016, substantial disparities were observed across all pairwise racial comparisons, with the largest gaps observed between non-Hispanic Whites and Hispanics in both years. Differences in SES and health status were the largest contributors to these disparities, with insurance access also playing a meaningful role, particularly for Hispanic populations, whereas health behaviors contributed minimally. Residual disparities persisted, especially in comparisons involving non-Hispanic Whites, suggesting the influence of unmeasured or structural factors.

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arXiv2026

Flexible Nonparametric Inference for Causal Effects under the Front-Door Model

Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-n consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods.

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arXiv2026

Self-separated and self-connected models for mediator and outcome missingness in mediation analysis

Missing data is a common challenge in studying treatment effects. In the context of mediation analysis, this paper addresses missingness in the mediator and outcome, focusing on identification. We first consider self-separated missingness models where identification is achieved by conditional independence assumptions. This model class is somewhat limited as it is constrained by the need to remove a certain number of connections from the model. We then turn to self-connected missingness models where identification relies on information from shadow variables. This model class turns out to contain substantial variation, allowing models with built-in shadow variables (mediator, outcome or covariates) and models with auxiliary shadow variables at different positions in the causal structure. To improve the practical value of the missingness mechanisms, we allow where possible for dependencies due to unobserved causes of the missingness, a feature often neglected. In this exploration, we review existing models, connect to new models, and develop theory where needed. This results in templates for identification in the mediation setting, generally useful identification techniques, and perhaps most importantly a synthesis and substantial extension of shadow variable theory. Two examples relate the models to practical considerations.

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arXiv2026

MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data

Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To address this gap, we propose MissNODAG, a differentiable framework for learning both the underlying cyclic causal graph and the missingness mechanism from partially observed data, including data missing not at random. Our framework integrates an additive noise model with an expectation-maximization procedure, alternating between imputing missing values and optimizing the observed data likelihood, to uncover both the cyclic structures and the missingness mechanism. We establish consistency guarantees under exact maximization of the score function in the large sample setting. Finally, we demonstrate the effectiveness of MissNODAG through synthetic experiments and an application to real-world gene perturbation data.

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arXiv2026

Controllable Generative Sandbox for Causal Inference

Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal controllability, including explicit control over overlap, unmeasured confounding, and treatment effect heterogeneity. We introduce CausalMix, a variational generative framework that closes this gap by coupling a mixture of Gaussian latent priors with data-type-specific decoders for continuous, binary, and categorical variables. The model incorporates explicit causal controls: an overlap regularizer shaping propensity-score distributions, alongside direct parameterizations of confounding strength and effect heterogeneity. This unified objective preserves fidelity to the observed data while enabling factorial manipulation of causal mechanisms, allowing overlap, confounding strength, and treatment effect heterogeneity to be varied independently at design time. Across benchmarks, CausalMix achieves state-of-the-art distributional metrics on mixed-type tables while providing stable, fine-grained causal control. We demonstrate practical utility in a comparative safety study of metastatic castration-resistant prostate cancer treatments, using CausalMix to compare estimators under calibrated data-generating processes, tune hyperparameters, and conduct simulation-based power analyses under targeted treatment effect heterogeneity scenarios.

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arXiv2026

Weighting-Based Identification and Estimation in Graphical Models of Missing Data

We propose a constructive algorithm for identifying complete data distributions in graphical models of missing data. The complete data distribution is unrestricted, while the missingness mechanism is assumed to factorize according to a conditional directed acyclic graph. Our approach follows an interventionist perspective in which missingness indicators are treated as variables that can be intervened on. A central challenge in this setting is that sequences of interventions on missingness indicators may induce and propagate selection bias, so that identification can fail even when a propensity score is invariant to available interventions. To address this challenge, we introduce a tree-based identification algorithm that explicitly tracks the creation and propagation of selection bias and determines whether it can be avoided through admissible intervention strategies. The resulting tree provides both a diagnostic and a constructive characterization of identifiability under a given missingness mechanism. Building on these results, we develop recursive inverse probability weighting procedures that mirror the intervention logic of the identification algorithm, yielding valid estimating equations for both the missingness mechanism and functionals of the complete data distribution. Simulation studies and a real-data application illustrate the practical performance of the proposed methods. An accompanying R package, flexMissing, implements all proposed procedures.

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arXiv2026

Causal Inference for Preprocessed Outcomes with an Application to Functional Connectivity

In biomedical research, repeated measurements within each subject are often processed to remove artifacts and unwanted sources of variation. The resulting data are used to construct derived outcomes that act as proxies for scientific outcomes that are not directly observable. Although intra-subject processing is widely used, its impact on inter-subject statistical inference has not been systematically studied, and a principled framework for causal analysis in this setting is lacking. In this article, we propose a semiparametric framework for causal inference with derived outcomes obtained after intra-subject processing. This framework applies to settings with a modular structure, where intra-subject analyses are conducted independently across subjects and are followed by inter-subject analyses based on parameters from the intra-subject stage. We develop multiply robust estimators of causal parameters under rate conditions on both intra-subject and inter-subject models, which allows the use of flexible machine learning. We specialize the framework to a mediation setting and focus on the natural direct effect. For high dimensional inference, we employ a step-down procedure that controls the exceedance rate of the false discovery proportion. Simulation studies demonstrate the superior performance of the proposed approach. We apply our method to estimate the impact of stimulant medication on brain connectivity in children with autism spectrum disorder.

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arXiv2026

Bridging Prediction and Intervention Problems in Social Systems

Many automated decision systems (ADS) are designed to solve prediction problems -- where the goal is to learn patterns from a sample of the population and apply them to individuals from the same population. In reality, these prediction systems operationalize holistic policy interventions in deployment. Once deployed, ADS can shape impacted population outcomes through an effective policy change in how decision-makers operate, while also being defined by past and present interactions between stakeholders and the limitations of existing organizational, as well as societal, infrastructure and context. In this work, we consider the ways in which we must shift from a prediction-focused paradigm to an intervention-oriented paradigm when considering the impact of ADS within social systems. We argue this requires a new default problem setup for ADS beyond prediction, to instead consider predictions as decision support, final decisions, and outcomes. We highlight how this perspective unifies modern statistical frameworks and other tools to study the design, implementation, and evaluation of ADS systems, and point to the research directions necessary to operationalize this paradigm shift. Using these tools, we characterize the limitations of focusing on isolated prediction tasks, and lay the foundation for a more intervention-oriented approach to developing and deploying ADS.

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