Causal mediation analysis is used to evaluate direct and indirect causal effects of a treatment on an outcome of interest through an intermediate variable or a mediator.It is difficult to identify the direct and indirect causal effects because the mediator cannot be randomly assigned in many real applications. In this article, we consider a causal model including latent confounders between the mediator and the outcome. We present sufficient conditions for identifying the direct and indirect effects and propose an approach for estimating them. The performance of the proposed approach is evaluated by simulation studies. Finally, we apply the approach to a data set of the customer loyalty survey by a telecom company.
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 analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure---an assumption frequently violated in practice. We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust semiparametric targeted minimum loss-based estimator for data-dependent stochastic direct and indirect effect…
Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence fucntion (EIF) in the non-parametric statistical model. We use the EIF to develop two asymptotically optimal, non-parametric estimators that leverage data-adaptive regression for estimation of the nuisance parameters: a one-step estimator and a…
Natural direct and indirect effects are mediational estimands that decompose the average treatment effect and describe how outcomes would be affected by contrasting levels of a treatment through changes induced in mediator values (in the case of the indirect effect) or not through induced changes in the mediator values (in the case of the direct effect). Natural direct and indirect effects are not generally point-identifiable in the presence of a treatment-induced confounder, however they may still be identified if one is willing to assume monotonicity between a treatment and the treatment-ind…
Proximal Mediation Analysis with Unmeasured Treatment-Induced Confounding
Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学统计学院与应用统计中心）；Department of Biostatistics & Medical Informatics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物统计与医学信息学系）
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…
A Bayesian semi-parametric approach to causal mediation for longitudinal mediators and time-to-event outcomes with application to a cardiovascular disease cohort study
Mediation analysis with contemporaneously observed multiple mediators is an important area of causal inference. Recent approaches for multiple mediators are often based on parametric models and thus may suffer from model misspecification. Also, much of the existing literature either only allow estimation of the joint mediation effect, or, estimate the joint mediation effect as the sum of individual mediator effects, which often is not a reasonable assumption. In this paper, we propose a methodology which overcomes the two aforementioned drawbacks. Our method is based on a novel Bayesian nonpar…
Arizona State University（亚利桑那州立大学）；City University of Hong Kong（香港城市大学）
An important problem in causal inference is to break down the total effect of a treatment on an outcome into different causal pathways and to quantify the causal effect in each pathway. For instance, in causal fairness, the total effect of being a male employee (i.e., treatment) constitutes its direct effect on annual income (i.e., outcome) and the indirect effect via the employee's occupation (i.e., mediator). Causal mediation analysis (CMA) is a formal statistical framework commonly used to reveal such underlying causal mechanisms. One major challenge of CMA in observational studies is handl…
The causal inference literature has increasingly recognized that explicitly targeting treatment effect heterogeneity can lead to improved scientific understanding and policy recommendations. Towards the same ends, studying the causal pathway connecting the treatment to the outcome can be also useful. This paper addresses these problems in the context of \emph{causal mediation analysis}. We introduce a varying coefficient model based on Bayesian additive regression trees to identify and regularize heterogeneous causal mediation effects; analogously with linear structural equation models, these …
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…
It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We propose a novel framework to nonparametrically identify causal effects with confounders subject to an outcome-independent missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal…
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 …
The goal of causal mediation analysis, often described within the potential outcomes framework, is to decompose the effect of an exposure on an outcome of interest along different causal pathways. Using the assumption of sequential ignorability to attain non-parametric identification, Imai et al. (2010) proposed a flexible approach to measuring mediation effects, focusing on parametric and semiparametric normal/Bernoulli models for the outcome and mediator. Less attention has been paid to the case where the outcome and/or mediator model are mixed-scale, ordinal, or otherwise fall outside the n…
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…
Disentangling Causal Mechanisms in Conjoint Experiments Using Mediation
College of Management, EPFL（EPFL管理学院）；Department of Government, University of Texas at Austin（德克萨斯大学奥斯汀分校政府系）；Department of Statistics, Rutgers University（罗格斯大学统计系）
The positivity assumption in causal mediation analyses? Checked!
Université Laval（拉瓦尔大学）；Centre de Recherche du CHU de Québec - Université Laval（魁北克大学医院研究中心-拉瓦尔大学）；Université de Montréal（蒙特利尔大学）；Centre de recherche Azrieli, CHU Sainte-Justine（阿兹里埃研究中心，圣朱斯蒂娜大学医院）；Université du Québec à Montréal（蒙特利尔大学）；Faculté de Pharmacie, Université de Montréal（蒙特利尔大学药学院）；McGill University（麦吉尔大学）
Causal inference in observational studies can be challenging when confounders are subject to missingness. Generally, the identification of causal effects is not guaranteed even under restrictive parametric model assumptions when confounders are missing not at random. To address this, We propose a general framework to establish the identification of causal effects when confounders are subject to treatment-independent missingness, which means that the missing data mechanism is independent of the treatment, given the outcome and possibly missing confounders. We give special consideration to commo…
We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is avai…
We generalize the proximal g-formula of Miao, Geng, and Tchetgen Tchetgen (2018) for causal inference under unobserved confounding using proxy variables. Specifically, we show that the formula holds true for all causal models in a certain equivalence class, and this class contains models in which the total number of levels for the set of unobserved confounders can be arbitrarily larger than the number of levels of each proxy variable. Although straightforward to obtain, the result can be significant for applications. Simulations corroborate our formal arguments.
Gender disparities in rehospitalisations after coronary artery bypass grafting: evidence from a sparse functional causal mediation analysis of the MIMIC-IV data
It becomes increasingly popular to perform mediation analysis for complex data from sophisticated experimental studies. In this paper, we present Granger Mediation Analysis (GMA), a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The stable unit treatment assumption for causal mediation analysis is thus unrealistic for this type of…
Causal mediation analysis is widely utilized to separate the causal effect of treatment into its direct effect on the outcome and its indirect effect through an intermediate variable (the mediator). In this study we introduce a functional mediation analysis framework in which the three key variables, the treatment, mediator, and outcome, are all continuous functions. With functional measures, causal assumptions and interpretations are not immediately well-defined. Motivated by a functional magnetic resonance imaging (fMRI) study, we propose two functional mediation models based on the influenc…
An essential goal of program evaluation and scientific research is the investigation of causal mechanisms. Over the past several decades, causal mediation analysis has been used in medical and social sciences to decompose the treatment effect into the natural direct and indirect effects. However, all of the existing mediation analysis methods rely on parametric modeling assumptions in one way or another, typically requiring researchers to specify multiple regression models involving the treatment, mediator, outcome, and pre-treatment confounders. To overcome this limitation, we propose a novel…
Causal mediation analysis is a useful tool for epidemiological research, but it has been criticized for relying on a "cross-world" independence assumption that is empirically difficult to verify and problematic to justify based on background knowledge. In the present article we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and non-parametric identification of natural direct and indirect effects. In parti…
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 in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference
The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements -- effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this paper is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference…
Unobserved confounders are a long-standing issue in causal inference using propensity score methods. This study proposed nonparametric indices to quantify the impact of unobserved confounders through pseudo-experiments with an application to real-world data. The study finding suggests that the proposed indices can reflect the true impact of confounders. It is hoped that this study will lead to further discussion on this important issue and help move the science of causal inference forward.
Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For example, if $Z\rightarrow Y$ and $Z\rightarrow X$, then $X$ and $Y$ will be statistically dependent, even if there are no causal connections between the two. There are several approaches available to adjust for confounding, i.e. to remove, or reduce, the association between two variables due to the confounder. Common adjustment techniques include stratifying the a…
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…
New York University（纽约大学）；Columbia University（哥伦比亚大学）
Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting, ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these inte…
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…
In this discussion we consider why it is important to estimate causal effect parameters well even they are not identified, propose a partially identified approach for causal inference in the presence of colliders, point out an under-appreciated advantage of double robustness, discuss the relative difficulty of independence testing versus regression, and finally commend Häggström for her exploration of causal inference with high-dimensional confounding, while making a call for further research in this same vein.
Northwestern Polytechnical University（西北工业大学）；Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences（中国科学院分子细胞科学卓越创新中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；South China University of Technology（华南理工大学）；Guangdong Institute of Intelligence Science and Technology（广东智能科学技术研究院）；Fudan University（复旦大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）
Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders, while some constraint-based methods can present them. This paper proposes a causal functional model-based method called repetitive causal discovery (RCD) to discover the causal structure of observed variables affected by latent confounders. RCD repeats inferring the causal directions between a small number of observed variables and determines whether the relatio…
A Practical Introduction to Regression-based Causal Inference in Meteorology (II): Unmeasured confounders
University of Washington（华盛顿大学）；Applied Physics Laboratory, University of Washington（华盛顿大学应用物理实验室）；Climate Impacts Group, University of Washington（华盛顿大学气候影响研究组）；School of Meteorology, University of Oklahoma（俄克拉荷马大学气象学院）
Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from observational data. It is done by including them in propensity score model in so-called potential outcome framework for causal inference whereas in causal graphical modeling framework usual conditioning on them is done. However in the former framework, it is confusing when modeler finds a variable that is non-causally associated with both the treatment and th…
