Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding

Abstract: Causal mediation analysis provides techniques for defining and estimating effects that may be endowed with mechanistic interpretations. With many scientific investigations seeking to address mechanistic questions, causal direct and indirect effects have garnered much attention. The natural direct and indirect effects, the most widely used among such causal mediation estimands, are limited in their practical utility due to stringent identification requirements. Accordingly, considerable effort has been invested in developing alternative direct and indirect effect decompositions with relaxed identification requirements. Such efforts often yield effect definitions with nuanced and challenging interpretations. By contrast, relatively limited attention has been paid to relaxing the identification assumptions of the natural direct and indirect effects. Motivated by a secondary aim of a recent non-randomized vaccine prospective cohort study (NCT05168813), we present a set of relaxed conditions under which the natural direct effect is identifiable in spite of unobserved baseline confounding of the exposure-mediator pathway; we use this result to investigate the effect mediated by putative immune correlates of protection. Relaxing the commonly used but restrictive cross-world counterfactual independence assumption, we discuss strategies for evaluating the natural direct effect in non-randomized settings that arise in the analysis of vaccine studies. We revisit prior studies of semi-parametric efficiency theory to demonstrate the construction of flexible, multiply robust estimators of the natural direct effect and discuss efficient estimation strategies that do not place restrictive modeling assumptions on nuisance functions.

• The paper derives relaxed identification conditions that enable inference on natural direct effects despite unmeasured confounding between the exposure and mediator.
• It develops efficient, multiply robust estimators, including one-step and targeted maximum likelihood methods, that leverage modern machine learning techniques.
• Simulation studies in vaccine research demonstrate that the proposed methods maintain unbiasedness and valid coverage even with significant confounding.

Identification and Estimation of Causal Direct Effects under Unmeasured Confounding

Overview

"Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding" (2604.01501) addresses the identification and estimation of the natural direct effect (NDE) in the presence of unmeasured confounding of the exposure–mediator relationship—a critical scenario in applied causal mediation analysis. The work derives a set of relaxed identification conditions that enable inference on the NDE without requiring absence of unmeasured confounding between exposure and mediator. The framework is motivated by and applied to mechanistic questions in vaccine studies, specifically analyzing mediators of COVID-19 vaccine efficacy.

Background and Problem Context

Causal mediation analysis aims to disentangle the total effect of an exposure into direct and indirect (mediated) components, often providing mechanistic insights in biomedical research. Standard identification of natural (in)direct effects (NDE/NIE) relies on strong ignorability conditions: no unmeasured confounding of the exposure–outcome, exposure–mediator, and mediator–outcome pairs; no intermediate confounders affected by exposure; and a form of cross-world independence. These assumptions are generally unattainable in observational settings and can be logically problematic (cross-world independence cannot be falsified by experiment).

The setting motivating the developments is common in vaccine research: inferring the direct effect of vaccination (or hybrid immunity) on infection outcomes, not mediated by quantifiable immune responses, where pre-exposure immune status or infection history is typically unmeasured and can confound the exposure–mediator relationship. The inability to assume full knowledge of exposure–mediator confounders challenges conventional mediation analysis.

Methodological Innovations

Relaxed Identification of the NDE

The central contribution is an identification result for the NDE under unmeasured exposure–mediator confounding, provided these unmeasured confounders affect the outcome only through the mediator (i.e., absence of a direct path from confounder to outcome). Expressed in structural causal model (SCM) terms, this is: $f_Y(W, V, A, Z, U_Y) \equiv f_Y(W, A, Z, U_Y)$—the unmeasured confounder $V$ does not directly enter the outcome model. A weaker requirement is also introduced: conditional expectation equivalence,

$E[Y \mid W, V, A=1, Z] = E[Y \mid W, A=1, Z]$

which is shown to hold under weak restrictions on the exogenous error structure. This identification scenario is particularly relevant for vaccine studies with nonrandomized exposures.

Efficient, Multiply Robust Estimation

Building on this identification result, the authors revisit semiparametric efficiency theory for the NDE, emphasizing flexible, multiply-robust estimation. Both one-step and targeted maximum likelihood (TML) estimators are provided, implementing efficient influence function (EIF)-based inference. These estimators accommodate machine learning for nuisance function estimation and are compatible with outcome-dependent sampling designs (e.g., two-phase, case-cohort samples), bolstered by accessible software implementations.

Extension to Stochastic Interventions

The identification and estimation strategy is naturally extended to stochastic interventions, drawing post-intervention mediators from observed conditional distributions rather than static levels. This aligns with modern definitions of the NDE that avoid ill-defined cross-world counterfactuals.

Empirical Demonstrations

Strong numerical support is presented through simulation studies that vary the magnitude of unmeasured exposure–mediator confounding. The proposed estimators maintain unbiasedness, valid coverage, and only modest reductions in asymptotic efficiency as confounding strength increases, provided the pathway from confounders to outcomes is correctly blocked by the mediator. Application to simulated vaccine cohort data further validates the robustness and efficiency of the estimation procedures under case-cohort sampling.

In the motivating real-world analysis (the CoVPN 3008 nonrandomized vaccine study), the proposed method enables inference on the direct effect of hybrid versus vaccine immunity on COVID-19 incidence, decomposing the effect relative to neutralizing antibody titers. Despite incomplete measurement of prior infection (IgG N-protein concentrations), the methodology justifies inference under plausible structural assumptions.

Implications and Theoretical Significance

The key theoretical implication is a substantial relaxation of previously standard identification conditions for direct effects in mediation analysis. It demonstrates that—contrary to earlier dogma—direct effects along non-mediated pathways can remain identifiable, without measurement or control of confounders of the exposure–mediator link, so long as these confounders do not directly affect the outcome. This extends the array of analyses possible in domains where mechanistic understandings are hampered by limited covariate measurement, such as cohort studies, electronic health record analyses, and vaccine efficacy trials with imperfect immunological data.

Practically, these findings inform the design and analysis of mediation studies under partial confounder control, offering guidance for mechanistic hypothesis testing in settings where exhaustive confounder measurement is infeasible or cost-prohibitive. The efficient, multiply robust estimators provided facilitate valid inference with modern regression adjustment and machine learning methods, as well as in outcome-dependent sampling schemes.

Future Directions

Future research can extend the framework in several directions:

• Mediation with multiple mediators: Adapting the identification result to settings with complex mediator structures or high-dimensional mediators.
• Time-varying exposures and mediators: Developing analogous identification and estimation theory for longitudinal mediation questions.
• Partial identification: Characterizing bounds when even weaker assumptions may hold, or in the presence of direct confounder–outcome links of known magnitude.
• Sensitivity analysis: Formalizing the robustness of the identification result to plausible violations of the pathway-blocking assumption, potentially integrating E-values or bounding techniques.

Conclusion

This work advances causal mediation analysis by deriving and operationalizing identification results for direct effects under unmeasured exposure–mediator confounding, relaxing a class of restrictive and often untestable assumptions. The approach leverages semiparametric efficiency theory for robust inference in observational and semi-experimental settings, augments the toolbox for mechanism-oriented analysis in epidemiology and biostatistics, and enhances the interpretability of mediation results in complex applied studies.

Reference:

"Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding" (2604.01501)