Cluster randomized trials (CRTs) with multiple unstructured mediators present significant methodological challenges for causal inference due to within-cluster correlation, interference among units, and the complexity introduced by multiple mediators. Existing causal mediation methods often fall short in simultaneously addressing these complexities, particularly in disentangling mediator-specific effects under interference that are central to studying complex mechanisms. To address this gap, we propose new causal estimands for spillover mediation effects that differentiate the roles of each individual's own mediator and the spillover effects resulting from interactions among individuals within the same cluster. We establish identification results for each estimand and, to flexibly model the complex data structures inherent in CRTs, we develop a new Bayesian nonparametric prior -- the Nested Dependent Dirichlet Process Mixture -- designed for flexibly capture the outcome and mediator surfaces at different levels. We conduct extensive simulations across various scenarios to evaluate the frequentist performance of our methods, compare them with a Bayesian parametric counterpart and illustrate our new methods in an analysis of a completed CRT.
Causal mediation in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference
It is often of interest in the health and social sciences to investigate the joint mediation effects of multiple post-exposure mediating variables. Identification of such joint mediation effects generally require no unmeasured confounding of the outcome with respect to the whole set of mediators. As the number of mediators under consideration grows, this key assumption is likely to be violated as it is often infeasible to intervene on any of the mediators. In this paper, we develop a simple two-step method of moments estimation procedure to assess mediation with multiple mediators simultaneous…
Although the exposure can be randomly assigned in studies of mediation effects, any form of direct intervention on the mediator is often infeasible. As a result, unmeasured mediator-outcome confounding can seldom be ruled out. We propose semiparametric identification of natural direct and indirect effects in the presence of unmeasured mediator-outcome confounding by leveraging heteroskedasticity restrictions on the observed data law. For inference, we develop semiparametric estimators that remain consistent under partial misspecifications of the observed data model. We illustrate the proposed …
A mediation analysis approach is proposed for multiple exposures, multiple mediators, and a continuous scalar outcome under the linear structural equation modeling framework. It assumes that there exist orthogonal components that demonstrate parallel mediation mechanisms on the outcome, and thus is named Principal Component Mediation Analysis (PCMA). Likelihood-based estimators are introduced for simultaneous estimation of the component projections and effect parameters. The asymptotic distribution of the estimators is derived for low-dimensional data. A bootstrap procedure is introduced for i…
Motivated by an imaging proteomics study for Alzheimer's disease (AD), in this article, we propose a mediation analysis approach with high-dimensional exposures and high-dimensional mediators to integrate data collected from multiple platforms. The proposed method combines principal component analysis with penalized least squares estimation for a set of linear structural equation models. The former reduces the dimensionality and produces uncorrelated linear combinations of the exposure variables, whereas the latter achieves simultaneous path selection and effect estimation while allowing the m…
Social and behavioral scientists are increasingly employing technologies such as fMRI, smartphones, and gene sequencing, which yield 'high-dimensional' datasets with more columns than rows. There is increasing interest, but little substantive theory, in the role the variables in these data play in known processes. This necessitates exploratory mediation analysis, for which structural equation modeling is the benchmark method. However, this method cannot perform mediation analysis with more variables than observations. One option is to run a series of univariate mediation models, which incorrec…
Causal indirect and direct effects provide an interpretable method for decomposing the total effect of an exposure on an outcome into the effect through a mediator and the effect through all other pathways. When the mediator is a biomarker, values can be subject to an assay lower limit. The mediator is affected by the treatment and is a putative cause of the outcome, so the assay lower limit presents a compounded problem in mediation analysis. We propose three approaches to estimate indirect and direct effects with a mediator subject to an assay limit: 1. extrapolation 2. numerical optimizatio…
Mediation analysis seeks to identify and quantify the paths by which an exposure affects an outcome. Intermediate variables which are effected by the exposure and which effect the outcome are known as mediators. There exists extensive work on mediation analysis in the context of models with a single mediator and continuous and binary outcomes. However these methods are often not suitable for multi-omic data that include highly interconnected variables measuring biological mechanisms and various types of outcome variables such as censored survival responses. In this article, we develop a genera…
Causal mediation analysis concerns the pathways through which a treatment affects an outcome. While most of the mediation literature focuses on settings with a single mediator, a flourishing line of research has examined settings involving multiple mediators, under which path-specific effects (PSEs) are often of interest. We consider estimation of PSEs when the treatment effect operates through K(\geq1) causally ordered, possibly multivariate mediators. In this setting, the PSEs for many causal paths are not nonparametrically identified, and we focus on a set of PSEs that are identified under …
Causal mediation analysis is an important statistical method in social and medical studies, as it can provide insights about why an intervention works and inform the development of future interventions. Currently, most causal mediation methods focus on mediation effects defined on a mean scale. However, in health-risk studies, such as alcohol or risky sex, outcomes are typically count data and heavily skewed. Thus, mediation effects in these setting would be natural on a rate ratio scale, such as in Poisson and negative binomial regression methods. Existing methods also mainly rely on the assu…
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…
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 human microbiome can contribute to pathogeneses of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis methods are not adequate to analyze the microbiome as a mediator due to the excessive number of zero-valued sequencing reads in the data that is compounded by its compositional structure. The two main challenges raised by the zero-inflated data structure are: (a) disentangling the mediation effect induced by the point mass at zero; and (b) identifying the observed zero-valued data points that are actually not zero (i.e., false zeros). W…
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…
Brain functional connectome, the collection of interconnected neural circuits along functional networks, is one of the most cutting edge neuroimaging traits, and has a potential to play a mediating role within the effect pathway between an exposure and an outcome. While existing mediation analytic approaches are capable of providing insight into complex processes, they mainly focus on a univariate mediator or mediator vector, without considering network-variate mediators. To fill the methodological gap and accomplish this exciting and urgent application, in the paper, we propose an integrative…
In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome not through the mediator. The standard regression approach to mediation analysis assumes sequential ignorability of the mediator, that is that the mediator is effectively randomly assigned given baseline covariates and the randomized treatment. Since the experiment does not randomize the mediator, sequential ignorability is often not plausi…
Power and sample size calculations for causal mediation analysis with a binary mediator in randomized trials
Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）
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 effect estimation from observational data is one of the essential problems in causal inference. However, most estimation methods rely on the strong assumption that all confounders are observed, which is impractical and untestable in the real world. We develop a mediation analysis framework inferring the latent confounder for debiasing both direct and indirect causal effects. Specifically, we introduce generalized structural equation modeling that incorporates structured latent factors to improve the goodness-of-fit of the model to observed data, and deconfound the mediators and outcome …
Mediation analysis is a strategy for understanding the mechanisms by which treatments or interventions affect later outcomes. Mediation analysis is frequently applied in randomized trial settings, but typically assumes: a) that randomized assignment is the exposure of interest as opposed to actual take-up of the intervention, and b) no unobserved confounding of the mediator-outcome relationship. In contrast to the rich literature on instrumental variable (IV) methods to estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification st…
Recent studies suggest that the microbiome can be an important mediator in the effect of a treatment on an outcome. Microbiome data generated from sequencing experiments contain the relative abundance of a large number of microbial taxa with their evolutionary relationships represented by a phylogenetic tree. The compositional and high-dimensional nature of the microbiome mediator invalidates standard mediation analyses. We propose a phylogeny-based mediation analysis method (PhyloMed) for the microbiome mediator. PhyloMed models the microbiome mediation effect through a cascade of independent…
Interventional effects have been proposed as a solution to the unidentifiability of natural (in)direct effects under mediator-outcome confounders affected by the exposure. Such confounders are an intrinsic characteristic of studies with time-varying exposures and mediators, yet the generalization of the interventional effect framework to the time-varying case has received little attention in the literature. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator…
Mediation analysis has become an important tool in the behavioral sciences for investigating the role of intermediate variables that lie in the path between a randomized treatment and an outcome variable. The influence of the intermediate variable on the outcome is often explored using structural equation models (SEMs), with model coefficients interpreted as possible effects. While there has been significant research on the topic in recent years, little work has been done on mediation analysis when the intermediate variable (mediator) is a high-dimensional vector. In this work we present a new…
Semiparametric Mediation Analysis with Separately Observed Mediator and Outcome under Unmeasured Confounding
Department of Biostatistics, University of California, Los Angeles（加州大学洛杉矶分校生物统计系）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院生物统计系）
In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many applications involve longitudinal data, the existing causal mediation models are not directly applicable to settings where the mediators are measured on irregular time grids. In this paper, we propose a causal mediation model that accommodates longitudinal mediators on arbitrary time grids and survival outcomes simultaneously. We take a functional data analys…
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,…
Researchers are often interested in learning not only the effect of treatments on outcomes, but also the pathways through which these effects operate. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses may lead to ignoring important mediators and either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters…
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 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 dec…
Experiments often include multiple treatments, with the primary goal to compare the causal effects of those treatments. This study focuses on comparing the causal anatomies of multiple treatments through the use of causal mediation analysis. It proposes a novel set of comparative causal mediation (CCM) estimands that compare the mediation effects of different treatments via a common mediator. Further, it derives the properties of a set of estimators for the CCM estimands and shows these estimators to be consistent (or conservative) under assumptions that do not require the absence of unobserve…
