Causal Mediation Analysis

A central goal when designing treatment policies is often to "do no harm", that is, to avoid interventions that improve average outcomes while worsening outcomes for some individuals. A widely used notion for harm is the fraction of negatively affected (FNA), defined as the probability that an intervention decreases an individual's outcome. However, in many applications, treatments operate through mediators, and a single "total" FNA can obscure whether harm arises primarily through direct pathways or indirect (mediator-induced) pathways. In this work, we introduce a path-specific analogue of the FNA. For this, we disentangle total harm into direct and indirect harm in causal mediation settings. However, these quantities depend on joint distributions of potential outcomes that are not point-identified even in randomised controlled trials. As a remedy, we develop a novel partial identification framework for direct and indirect FNA. In our framework, we (i) derive sharp Makarov bounds for the FNA, and (ii) propose a semiparametrically efficient estimator with valid confidence intervals for these bounds under mild margin conditions. We demonstrate our framework across various numerical experiments. To the best of our knowledge, we are the first to study path-specific decomposition of causal harm and to develop an orthogonal inference framework for its analysis.

We propose a two-stage estimator for structural mediation parameters that combines deep representation learning with G-estimation under the "no essential heterogeneity" (NEH) assumption. We call the method UNIT. In the first stage,TARNet estimates the heterogeneous effect of a randomized treatment on a mediator by learning a shared covariate representation across treatment arms.The resulting conditional average treatment effect (CATE) estimate provides a plug-in approximation to the heterogeneity-dependent component of the weight function entering the G-estimating equation of Zheng and Zhou (2015), which identifies the structural parameters even in the presence of unmeasured mediator-outcome confounding. We show that more accurate first-stage representation learning can yield a more informative plug-in weight and thereby improve the precision of the structural parameter estimator. In simulations with non-Gaussian covariates and nonlinear mediator effects, TARNet weights reduce the Stage-2 standard error of the mediation coefficient by a factor of $1.45$ to $1.51$ (median across replications, $n \ge 2000$) relative to the classical approach, at no cost to bias or coverage.

Diabetic retinopathy (DR) is a local retinal lesion process and a visible manifestation of systemic microvascular injury. Modern retinal AI can grade images accurately, but often leaves unanswered how local lesion evidence, retinal vascular structure, and systemic disease pathways are connected. This paper introduces \emph{Causal-RetiGraph}, a compact biomedical informatics framework that links retinal graph phenotypes with NHANES-anchored pathway modelling. The retinal-image fold constructs an interpretable $X1234$ phenotype from vessel maps, lesion evidence, image embeddings, and AutoMorph biomarkers through spatial $X_{12}$ and Jacobian $X_{34}$ branches. The NHANES fold models systemic exposures, covariates, a same-subject retinal mediator family $R^*$, and downstream outcome families. $X1234$ is used for retinal support and pathway prioritisation, while $R^*$ is used for participant-level pathway summaries. On the retinal fold, $X1234$ achieves 0.9055 binary DR accuracy and 0.9711 AUROC, with graded DR QWK of 0.8312. The results show that lesion and biomarker streams improve contextual retinal representation under scarce and imbalanced data. In NHANES, HbA1c, urine albumin, pulse pressure, fasting glucose, and systolic blood pressure are the strongest binary DR anchors. Participant-level pathway analysis identifies glycaemic--renal and glycaemic--haemodynamic pathways as the clearest mediator-style signals. These results suggest that retinal graph phenotypes can help prioritise systemic pathways in DR while preserving the distinction between image-derived support and same-subject mediation.

This paper studies the problem of identifying the treatment that maximizes the expected natural direct potential outcome (NDPO), which captures the potential outcome of an intervention while excluding the pathway transmitted through a mediator that researchers may wish to remove from evaluation. We first establish population-level identification of the expected NDPO in a causal bandit setting using observable interventional distributions. We then develop a fixed-confidence best-arm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, employing a cutting-set method to solve the resulting semi-infinite optimization problem. The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee. We prove that it satisfies $δ$-correctness and asymptotic optimality. Finally, we validate the approach through empirical evaluations on a large-scale real-world advertising dataset (IPinYou).

Learning causal models from fragmented biomedical data is challenging because clinical, molecular, and imaging variables are often incomplete or not jointly observed. We propose RetiSEM, a domain-constrained structural equation modelling (SEM) framework for causal graph recovery and mediation analysis under limited multimodal resources. This proposed work organises variables into biologically informed blocks, applies forbidden-edge constraints, and decomposes pathway-level effects into TE, NDE, and NIE components. We evaluate RetiSEM across ten synthetic benchmark scenarios that vary in dimensionality, nonlinearity, causal depth, and pathway structure, together with a fragmented real-world setting that combines NHANES clinical variables with externally derived retinal representations. This approach achieves lower structural error and higher causal accuracy than unconstrained baselines across the synthetic benchmarks. In the real-data analysis, retinal variables behave mainly as downstream biomarker-like indicators, with smaller but detectable indirect effects. These findings support our strategy as an interpretable framework for testing structured causal hypotheses in limited-resource biomedical AI. The code and resources for this work are publicly available at: https://github.com/Inamullah-Colab/ReitSEM.

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

In the data-driven era, large-scale datasets are routinely collected and analyzed using machine learning (ML) and artificial intelligence (AI) to inform decisions in high-stakes domains such as healthcare, employment, and criminal justice, raising concerns about the fairness behavior of these systems. Existing works in fair ML cover tasks such as bias detection, fair prediction, and fair decision-making, but largely focus on static settings. At the same time, fairness in temporal contexts, particularly survival/time-to-event (TTE) analysis, remains relatively underexplored, with current approaches to fair survival analysis adopting statistical fairness definitions, which, even with unlimited data, cannot disentangle the causal mechanisms that generate disparities. To address this gap, we develop a causal framework for fairness in TTE analysis, enabling the decomposition of disparities in survival into contributions from direct, indirect, and spurious pathways. This provides a human-understandable explanation of why disparities arise and how they evolve over time. Our non-parametric approach proceeds in four steps: (1) formalizing the necessary assumptions about censoring and lack of confounding using a graphical model; (2) recovering the conditional survival function given covariates; (3) applying the Causal Reduction Theorem to reframe the problem in a form amenable to causal pathway decomposition; (4) estimating the effects efficiently. Finally, our approach is used to analyze the temporal evolution of racial disparities in outcome after admission to an intensive care unit (ICU).

Mediation analysis has traditionally focused on outcome-level summary contrasts, such as mean effects, which may obscure substantial distributional changes induced by complex and nonlinear causal mechanisms. We propose Distributional Causal Mediation Analysis (DCMA), a generative learning framework for identifying and estimating treatment effects on entire outcome distributions transmitted through multiple mediators. DCMA learns conditional generative models for the mediators and the outcome, recovering the relevant conditional distributions from observational data. Leveraging the identification formulas, it reconstructs interventional outcome distributions via Monte Carlo forward simulation by noise resampling, enabling the capture of both classical summary effects and rich distributional contrasts such as energy distance and the Wasserstein distance. Analytical error bounds are derived to decompose how estimation errors in the learned conditional models propagate to the reconstructed interventional outcome distributions. The empirical effectiveness of DCMA is demonstrated through numerical experiments and real-world data applications.

Latent visual reasoning aims to mimic human's imagination process by meditating through hidden states of Multimodal Large Language Models. While recognized as a promising paradigm for visual reasoning, the underlying mechanisms driving its effectiveness remain unclear. Motivated to demystify the true source of its efficacy, we investigate the validity of latent reasoning using Causal Mediation Analysis. We model the process as a causal chain: the input as the treatment, the latent tokens as the mediator, and the final answer as the outcome. Our findings uncover two critical disconnections: (a) Input-Latent Disconnect: dramatic perturbations on the input result in negligible changes to the latent tokens, suggesting that latent tokens do not effectively attend to the input sequence. (b) Latent-Answer Disconnect: perturbations on the latent tokens yield minimal impact on the final answer, indicating the limited causal effect latent tokens imposing on the outcome. Furthermore, extensive probing analysis reveals that latent tokens encode limited visual information and exhibit high similarity. Consequently, we challenge the necessity of latent reasoning and propose a straightforward alternative named CapImagine, which teaches the model to explicitly imagine using text. Experiments on vision-centric benchmarks show that CapImagine significantly outperforms complex latent-space baselines, highlighting the superior potential of visual reasoning through explicit imagination.

In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.

Statistical fairness metrics in AI-driven credit decisions conflate two causally distinct mechanisms: discrimination operating directly from a protected attribute to a credit outcome, and structural inequality propagating through legitimate financial features. We formalise this distinction using Pearl's framework of natural direct and indirect effects applied to the credit decision setting. Our primary theoretical contribution is an identification strategy for natural direct and indirect effects under treatment-induced confounding -- the prevalent setting in which protected attributes causally affect both financial mediators and the final decision, violating standard sequential ignorability. We show that interventional direct and indirect effects (IDE/IIE) are identified under the weaker Modified Sequential Ignorability assumption, and prove that IDE/IIE provide conservative bounds on the unidentified natural effects under monotone indirect treatment response. We propose a doubly-robust augmented inverse probability weighted (AIPW) estimator for IDE/IIE with semiparametric efficiency properties, implemented via cross-fitting. An E-value sensitivity analysis addresses residual confounding on the direct pathway. Empirical evaluation on 89,465 real HMDA conventional purchase mortgage applications from New York State (2022) demonstrates that approximately 77% of the observed 7.9 percentage-point racial denial disparity operates through financial mediators shaped by structural inequality, while the remaining 23% constitutes a conservative lower bound on direct discrimination. The open-source CausalFair Python package implements the full pipeline for deployment at resource-constrained financial institutions.