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 Pearl's nonparametric structural equation model. These PSEs are defined as contrasts between the expectations of 2^{K+1} potential outcomes and identified via what we call the generalized mediation functional (GMF). We introduce an array of regression-imputation, weighting, and "hybrid" estimators, and, in particular, two K+2-robust and locally semiparametric efficient estimators for the GMF. The latter estimators are well suited to the use of data-adaptive methods for estimating their nuisance functions. We establish the rate conditions required of the nuisance functions for semiparametric efficiency. We also discuss how our framework applies to several estimands that may be of particular interest in empirical applications. The proposed estimators are illustrated with a simulation study and an empirical example.
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 …
Causal mediation in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference
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）
University of Hong Kong（香港大学）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Columbia University（哥伦比亚大学）
Causal mediation analysis can unpack the black box of causality and is therefore a powerful tool for disentangling causal pathways in biomedical and social sciences, and also for evaluating machine learning fairness. To reduce bias for estimating Natural Direct and Indirect Effects in mediation analysis, we propose a new method called DeepMed that uses deep neural networks (DNNs) to cross-fit the infinite-dimensional nuisance functions in the efficient influence functions. We obtain novel theoretical results that our DeepMed method (1) can achieve semiparametric efficiency bound without imposi…
Causally Interpretable Meta-Mediation Analysis With Missing At Random Mediator and Outcome Data
EPILOGY, Institut Mondor of Biomedical Research, INSERM U955（INSERM U955 蒙多尔生物医学研究所 EPILOGY）；Université Paris-Est Créteil（巴黎东克雷泰伊大学）；Mines Paris, Université Paris Sciences Lettres（巴黎矿业学院，巴黎文理研究大学）；Department of Mathematics, Université du Québec à Montréal（蒙特利尔大学数学系）
While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon evaluating the total effect of the exposure, investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure, through a mediator variable or not, that occurs subsequently to the exposure and prior to the outcome. Although powerful…
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…
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）
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…
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…
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…
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…
E-commerce companies have a number of online products, such as organic search, sponsored search, and recommendation modules, to fulfill customer needs. Although each of these products provides a unique opportunity for users to interact with a portion of the overall inventory, they are all similar channels for users and compete for limited time and monetary budgets of users. To optimize users' overall experiences on an E-commerce platform, instead of understanding and improving different products separately, it is important to gain insights into the evidence that a change in one product would i…
We implement Ananke: an object-oriented Python package for causal inference with graphical models. At the top of our inheritance structure is an easily extensible Graph class that provides an interface to several broadly useful graph-based algorithms and methods for visualization. We use best practices of object-oriented programming to implement subclasses of the Graph superclass that correspond to types of causal graphs that are popular in the current literature. This includes directed acyclic graphs for modeling causally sufficient systems, acyclic directed mixed graphs for modeling unmeasur…
Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal models in use resulted in a fragmented view of identification. This fragmentation makes it unnecessarily…
In many medical studies, an ultimate failure event such as death is likely to be affected by the occurrence and timing of other intermediate clinical events. Both event times are subject to censoring by loss-to-follow-up but the nonterminal event may further be censored by the occurrence of the primary outcome, but not vice versa. To study the effect of an intervention on both events, the intermediate event may be viewed as a mediator, but conventional definition of direct and indirect effects is not applicable due to semi-competing risks data structure. We define three principal strata based …
Causal identification of treatment effects for infectious disease outcomes in interconnected populations is challenging because infection outcomes may be transmissible to others, and treatment given to one individual may affect others' outcomes. Contagion, or transmissibility of outcomes, complicates standard conceptions of treatment interference in which an intervention delivered to one individual can affect outcomes of others. Several statistical frameworks have been proposed to measure causal treatment effects in this setting, including structural transmission models, mediation-based partne…
Stanford University（斯坦福大学）；Hoover Institution（胡佛研究所）；Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院）；Princeton University（普林斯顿大学）
The empirical practice of using factor models to adjust for shared, unobserved confounders, $\mathbf{Z}$, in observational settings with multiple treatments, $\mathbf{A}$, is widespread in fields including genetics, networks, medicine, and politics. Wang and Blei (2019, WB) formalizes these procedures and develops the "deconfounder," a causal inference method using factor models of $\mathbf{A}$ to estimate "substitute confounders," $\hat{\mathbf{Z}}$, then estimating treatment effects by regressing the outcome, $\mathbf{Y}$, on part of $\mathbf{A}$ while adjusting for $\hat{\mathbf{Z}}$. WB cl…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. However, it becomes unstable to fit such models with high dimensional mediators, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown. This paper proposes a sparse mediation model using a regularized SEM a…
Split flow models, in which a physician rather than a nurse performs triage, are increasingly being used in hospital emergency departments (EDs) to improve patient flow. Before deciding whether such interventions should be adopted, it is important to understand how split flows causally impact patient flow and outcomes. We employ causal inference methodology to estimate average causal effects of a split flow model on time to be roomed, time to disposition after being roomed, admission decisions, and ED revisits at a large tertiary teaching hospital that uses a split flow model during certain ho…
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,…
Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause specific or subdistribution hazards, are fundamentally hard to be interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both th…
