Mediation analysis has been used in many disciplines to explain the mechanism or process that underlies an observed relationship between an exposure variable and an outcome variable via the inclusion of mediators. Decompositions of the total causal effect of an exposure variable into effects characterizing mediation pathways and interactions have gained an increasing amount of interest in the last decade. In this work, we develop decompositions for scenarios where the two mediators are causally sequential or non-sequential. Current developments in this area have primarily focused on either decompositions without interaction components or with interactions but assuming no causally sequential order between the mediators. We propose a new concept called natural counterfactual interaction effect that captures the two-way and three-way interactions for both scenarios that extend the two-way mediated interactions in literature. We develop a unified approach for decomposing the total effect into the effects that are due to mediation only, interaction only, both mediation and interaction, neither mediation nor interaction within the counterfactual framework. Finally, we illustrate the proposed decomposition method using a real data analysis where the two mediators are causally sequential.
Mediation analysis serves as a crucial tool to obtain causal inference based on directed acyclic graphs, which has been widely employed in the areas of biomedical science, social science, epidemiology and psychology. Decomposition of total effect provides a deep insight to fully understand the casual contribution from each path and interaction term. Since the four-way decomposition method was proposed to identify the mediated interaction effect in counterfactual framework, the idea had been extended to a more sophisticated scenario with non-sequential multiple mediators. However, the method ex…
Mediation analysis, which started with Baron and Kenny (1986), is used extensively by applied researchers. Indirect and direct effects are the part of a treatment effect that is mediated by a covariate and the part that is not. Subsequent work on natural indirect and direct effects provides a formal causal interpretation, based on cross-worlds counterfactuals: outcomes under treatment with the mediator set to its value without treatment. Organic indirect and direct effects (Lok 2016) avoid cross-worlds counterfactuals, using so-called organic interventions on the mediator while keeping the ini…
In causal mediation studies that decompose an average treatment effect into a natural indirect effect (NIE) and a natural direct effect (NDE), examples of post-treatment confounding are abundant. Past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due to incomplete information: it is observed under the actual treatment condition while missing under the counterfactual treatment condition. This study proposes a new sensitivity analysis strategy for handling post-treatment confounding and incorporates it into weightin…
Causal mediation in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference
With reference to a single mediator context, this brief report presents a model-based strategy to estimate counterfactual direct and indirect effects when the response variable is ordinal and the mediator is binary. Postulating a logistic regression model for the mediator and a cumulative logit model for the outcome, the exact parametric formulation of the causal effects is presented, thereby extending previous work that only contained approximated results. The identification conditions are equivalent to the ones already established in the literature. The effects can be estimated by making use…
Decomposing an exposure effect on an outcome into separate natural indirect effects through multiple mediators requires strict assumptions, such as correctly postulating the causal structure of the mediators, and no unmeasured confounding among the mediators. In contrast, interventional indirect effects for multiple mediators can be identified even when - as often - the mediators either have an unknown causal structure, or share unmeasured common causes, or both. Existing estimation methods for interventional indirect effects require calculating each distinct indirect effect in turn. This can …
With multiple potential mediators on the causal pathway from a treatment to an outcome, we consider the problem of decomposing the effects along multiple possible causal path(s) through each distinct mediator. Under Pearl's path-specific effects framework (Pearl, 2001; Avin et al., 2005), such fine-grained decompositions necessitate stringent assumptions, such as correctly specifying the causal structure among the mediators, and there being no unobserved confounding among the mediators. In contrast, interventional direct and indirect effects for multiple mediators (Vansteelandt and Daniel, 201…
Mediation analyses play important roles in making causal inference in biomedical research to examine causal pathways that may be mediated by one or more intermediate variables (i.e., mediators). Although mediation frameworks have been well established such as counterfactual-outcomes (i.e., potential-outcomes) models and traditional linear mediation models, little effort has been devoted to dealing with mediators with zero-inflated structures due to challenges associated with excessive zeros. We develop a novel mediation modeling approach to address zero-inflated mediators containing true zeros…
Given a binary treatment and a binary mediator, mediation analysis decomposes the total effect of the treatment on an outcome variable into direct and indirect effects. However, the existing decompositions are "path-dependent", and consequently, there appeared different versions of direct and indirect effects. Differently from these, this paper proposes a "path-free" decomposition of the total effect into three sub-effects: direct, indirect, and treatment-mediator interaction effects. Whereas the interaction effect has been part of the indirect effect in the existing two-effect decompositions,…
Mediation analysis is concerned with the decomposition of the total effect of an exposure on an outcome into the indirect effect through a given mediator, and the remaining direct effect. This is ideally done using longitudinal measurements of the mediator, as these capture the mediator process more finely. However, longitudinal measurements pose challenges for mediation analysis. This is because the mediators and outcomes measured at a given time-point can act as confounders for the association between mediators and outcomes at a later time-point; these confounders are themselves affected by …
In mediation analysis, the effect of an exposure (or treatment) on an outcome variable is decomposed into two components: a direct effect, which pertains to an immediate influence of the exposure on the outcome, and an indirect effect, which the exposure exerts on the outcome through a third variable called mediator. Our motivating example concerns the relationship between maternal smoking (the exposure, $X$), birthweight (the mediator, $M$), and infant mortality (the outcome, $Y$), which has attracted the interest of epidemiologists and statisticians for many years. We introduce new causal es…
Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. With multiple mediators, which are potentially causally dependent, the possible decomposition of pathway effects grows exponentially with the number of mediators. Huang and Pan (2016) introduced a principal component analysis (PCA) based approach to address this challenge, in which the transformed mediators are conditionally independent given the orthogonality of the PCs. However, the transformed mediator PCs, which are linear combinations of original mediators, are…
A parametric expression for causal natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator. The proposed effect decomposition does not require the outcome to be rare and generalizes the existing ones, allowing for interactions between both the exposure and the mediator and confounding covariates. Further, it outlines the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, in parallel with results derived under the rare outcome assumption. Formulae for standard errors, obtained via the d…
The Wisconsin Smoker's Health Study (WSHS2) was a longitudinal trial conducted to compare the effectiveness of two commonly used smoking cessation treatments, varenicline and combination nicotine replacement therapy (cNRT) with the less intense standard of care, nicotine patch. The main outcome of the WSHS2 study was that all three treatments had equivalent treatment effects. However, in-depth analysis of the compliance data collected via ecological momentary assessment (EMA) were not analyzed. Compliance to the treatment regimens may represent a confounder as varenicline and cNRT are more int…
In causal mediation analysis, nonparametric identification of the pure (natural) direct effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called "cross-world-counterfactuals" independence and (ii) no exposure- induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data fro…
The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator, the outcome, and possibly also the exposure can be modeled by an underlying latent variable giving rise to a growth curve. Settings are also considered in which the exposure is instead fixed at a single point in time.
Judea Pearl's insight that, when errors are assumed independent, the Pure (aka Natural) Direct Effect (PDE) is non-parametrically identified via the Mediation Formula was `path-breaking' in more than one sense! In the same paper Pearl described a thought-experiment as a way to motivate the PDE. Analysis of this experiment led Robins \& Richardson to a novel way of conceptualizing direct effects in terms of interventions on an expanded graph in which treatment is decomposed into multiple separable components. We further develop this novel theory here, showing that it provides a self-contained f…
Causal mediation analysis aims at disentangling a treatment effect into an indirect mechanism operating through an intermediate outcome or mediator, as well as the direct effect of the treatment on the outcome of interest. However, the evaluation of direct and indirect effects is frequently complicated by non-ignorable selection into the treatment and/or mediator, even after controlling for observables, as well as sample selection/outcome attrition. We propose a method for bounding direct and indirect effects in the presence of such complications using a method that is based on a sequence of l…
Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. In this paper we present an analogous decomposition of the \textit{population intervention effect}, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct an…
Mediation analysis allows one to use observational data to estimate the importance of each potential mediating pathway involved in the causal effect of an exposure on an outcome. However, current approaches to mediation analysis with multiple mediators either involve assumptions not verifiable by experiments, or estimate the effect when mediators are manipulated jointly which precludes the practical design of experiments due to curse of dimensionality, or are difficult to interpret when arbitrary causal dependencies are present. We propose a method for mediation analysis for multiple manipulab…
This paper proposes a new two-stage network mediation method based on the use of a latent network approach -- model-based eigenvalue decomposition -- for analyzing social network data with nodal covariates. In the decomposition stage of the observed network, no assumption on the metric of the latent space structure is required. In the mediation stage, the most important eigenvectors of a network are used as mediators. This method further offers an innovative way for controlling for the conditional covariates and it only considers the information left in the network. We demonstrate this approac…
Emission control technologies installed on power plants are a key feature of many air pollution regulations in the US. While such regulations are predicated on the presumed relationships between emissions, ambient air pollution, and human health, many of these relationships have never been empirically verified. The goal of this paper is to develop new statistical methods to quantify these relationships. We frame this problem as one of mediation analysis to evaluate the extent to which the effect of a particular control technology on ambient pollution is mediated through causal effects on power…
Causal variance decompositions for a given disease-specific quality indicator can be used to quantify differences in performance between hospitals or health care providers. While variance decompositions can demonstrate variation in quality of care, causal mediation analysis can be used to study care pathways leading to the differences in performance between the institutions. This raises the question of whether the two approaches can be combined to decompose between-hospital variation in an outcome type indicator to that mediated through a given process (indirect effect) and remaining variation…
Causal decomposition analysis provides a way to identify mediators that contribute to health disparities between marginalized and non-marginalized groups. In particular, the degree to which a disparity would be reduced or remain after intervening on a mediator is of interest. Yet, estimating disparity reduction and remaining might be challenging for many researchers, possibly because there is a lack of understanding of how each estimation method differs from other methods. In addition, there is no appropriate estimation method available for a certain setting (i.e., a regression-based approach …
In randomized trials, once the total effect of the intervention has been estimated, it is often of interest to explore mechanistic effects through mediators along the causal pathway between the randomized treatment and the outcome. In the setting with two sequential mediators, there are a variety of decompositions of the total risk difference into mediation effects. We derive sharp and valid bounds for a number of mediation effects in the setting of two sequential mediators both with unmeasured confounding with the outcome. We provide five such bounds in the main text corresponding to two diff…
Causal decomposition has provided a powerful tool to analyze health disparity problems, by assessing the proportion of disparity caused by each mediator. However, most of these methods lack \emph{policy implications}, as they fail to account for all sources of disparities caused by the mediator. Besides, their estimations \emph{pre-specified} some covariates set (\emph{a.k.a}, admissible set) for the strong ignorability condition to hold, which can be problematic as some variables in this set may induce new spurious features. To resolve these issues, under the framework of the structural causa…
It is common in the internet industry to use offline-developed algorithms to power online products that contribute to the success of a business. Offline-developed algorithms are guided by offline evaluation metrics, which are often different from online business key performance indicators (KPIs). To maximize business KPIs, it is important to pick a north star among all available offline evaluation metrics. By noting that online products can be measured by online evaluation metrics, the online counterparts of offline evaluation metrics, we decompose the problem into two parts. As the offline A/…
A key objective of decomposition analysis is to identify a factor (the 'mediator') contributing to disparities in an outcome between social groups. In decomposition analysis, a scholarly interest often centers on estimating how much the disparity (e.g., health disparities between Black women and White men) would be reduced/remain if we set the mediator (e.g., education) distribution of one social group equal to another. However, causally identifying disparity reduction and remaining depends on the no omitted mediator-outcome confounding assumption, which is not empirically testable. Therefore,…
Causal mediation analysis has historically been limited in two important ways: (i) a focus has traditionally been placed on binary treatments and static interventions, and (ii) direct and indirect effect decompositions have been pursued that are only identifiable in the absence of intermediate confounders affected by treatment. We present a theoretical study of an (in)direct effect decomposition of the population intervention effect, defined by stochastic interventions jointly applied to the treatment and mediators. In contrast to existing proposals, our causal effects can be evaluated regardl…
Greater understanding of the pathways through which an environmental mixture operates is important to design effective interventions. We present new methodology to estimate natural direct and indirect effects and controlled direct effects of a complex mixture exposure on an outcome through a mediator variable. We implement Bayesian Kernel Machine Regression (BKMR) to allow for all possible interactions and nonlinear effects of (1) the co-exposures on the mediator, (2) the co-exposures and mediator on the outcome, and (3) selected covariates on the mediator and/or outcome. From the posterior pr…
