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Applications of causally defined direct and indirect effects in mediation analysis using SEM
 University of California
"... Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a ..."
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Cited by 19 (0 self)
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Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a broader array of causal mediation analyses than previously considered in structural equation modeling practice. A new result is the ability to handle mediation by a nominal variable. Examples with a binary outcome and a binary, ordinal or nominal mediator are given using Mplus to compute the effects. The causal effects require strong assumptions even in randomized designs, especially sequential ignorability, which is presumably often violated to some extent due to mediatoroutcome confounding. To study the effects of violating this assumption, it is shown how a sensitivity analysis can be carried out. This can be used both in planning a new study and in evaluating the results of an existing study.
Principal stratification a goal or a tool? The
 International Journal of Biostatistics 7. Article
"... Principal stratification has recently become a popular tool to address certain causal inference questions particularly in dealing with postrandomization factors in randomized trials. Here we analyze the conceptual basis for this framework and invite response to clarify the value of principal strati ..."
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Cited by 18 (7 self)
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Principal stratification has recently become a popular tool to address certain causal inference questions particularly in dealing with postrandomization factors in randomized trials. Here we analyze the conceptual basis for this framework and invite response to clarify the value of principal stratification in estimating causal effects of interest.
Transportability of Causal Effects: Completeness Results
, 2012
"... The study of transportability aims to identify conditions under which causal information learned from experiments can be reused in a different environment where only passive observations can be collected. The theory introduced in [Pearl and Bareinboim, 2011] (henceforth [PB, 2011]) defines formal co ..."
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Cited by 14 (9 self)
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The study of transportability aims to identify conditions under which causal information learned from experiments can be reused in a different environment where only passive observations can be collected. The theory introduced in [Pearl and Bareinboim, 2011] (henceforth [PB, 2011]) defines formal conditions for such transfer but falls short of providing an effective procedure for deciding whether transportability is feasible for a given set of assumptions about differences between the source and target domains. This paper provides such procedure. It establishes a necessary and sufficient condition for deciding when causal effects in the target domain are estimable from both the statistical information available and the causal information transferred from the experiments. The paper further provides a complete algorithm for computing the transport formula, that is, a way of fusing experimental and observational information to synthesize an estimate of the desired causal relation.
Transportability across studies: A formal approach
, 2010
"... We provide a formal definition of the notion of “transportability, ” or “external validity, ” which we view as a license to transfer causal information learned in experimental studies to a different environment, in which only observational studies can be conducted. We introduce a formal representati ..."
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Cited by 12 (6 self)
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We provide a formal definition of the notion of “transportability, ” or “external validity, ” which we view as a license to transfer causal information learned in experimental studies to a different environment, in which only observational studies can be conducted. We introduce a formal representation called “selection diagrams ” for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we derive procedures for deciding whether causal effects in the target environment can be inferred from experimental findings in a different environment. When the answer is affirmative, the procedures identify the set of experimental and observational studies that need be conducted to license the transport. We further demonstrate how transportability analysis can guide the transfer of knowledge among nonexperimental studies to minimize remeasurement cost and improve prediction power. We further provide a causally principled definition of “surrogate endpoint ” and show that the theory of transportability can assist the identification of valid surrogates in a complex network of causeeffect relationships. 1 Introduction: Threats
The Foundations of Causal Inference
 SUBMITTED TO SOCIOLOGICAL METHODOLOGY.
, 2010
"... This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of ..."
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Cited by 11 (4 self)
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This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on nonparametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 195060s, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring the effects of potential interventions (also called “causal effects” or “policy evaluation”), as well as direct and indirect effects (also known as “mediation”), in both linear and nonlinear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and
The causal mediation formula – a guide to the assessment of pathways and mechanisms
 Prevention Science DOI: 10.1007/s1112101102701, Online
, 2012
"... Recent advances in causal inference have given rise to a general and easytouse formula for assessing the extent to which the effect of one variable on another is mediated by a third. This socalled Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and ..."
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Cited by 10 (3 self)
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Recent advances in causal inference have given rise to a general and easytouse formula for assessing the extent to which the effect of one variable on another is mediated by a third. This socalled Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of pathspecific effects with minimal assumptions regarding the datagenerating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediatedeffect ” and show how to estimate the two components in nonlinear systems with continuous and categorical variables.
A General Algorithm for Deciding Transportability of Experimental Results
, 2013
"... Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called “transportability”, defined as a license to transfer information learned in experimental studies to a diff ..."
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Cited by 10 (5 self)
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Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called “transportability”, defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim [1] derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize biasfree estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.
Econometric Mediation Analyses: Identifying the Sources of Treatment Effects from Experimentally Estimated Production Technologies with Unmeasured and Mismeasured Inputs,” NBER Working Paper No
, 2013
"... Council grant hosted by University College Dublin, DEVHEALTH 269874. The views expressed in this paper are those of the authors and not necessarily those of the funders, the persons named here, or the National Bureau of Economic Research. We thank the editor and an anonymous referee for helpful comm ..."
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Cited by 8 (6 self)
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Council grant hosted by University College Dublin, DEVHEALTH 269874. The views expressed in this paper are those of the authors and not necessarily those of the funders, the persons named here, or the National Bureau of Economic Research. We thank the editor and an anonymous referee for helpful comments. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.