Article
Marginal Structural Models for the Estimation of Direct and Indirect Effects
Department of Health Studies, University of Chicago, Chicago, Illinois 60637, USA.
Epidemiology (Cambridge, Mass.) (Impact Factor: 6.2). 02/2009; 20(1):1826. DOI: 10.1097/EDE.0b013e31818f69ce Source: PubMed
ABSTRACT
The estimation of controlled direct effects can be carried out by fitting a marginal structural model and using inverse probability of treatment weighting. To use marginal structural models to estimate natural direct and indirect effects, 2 marginal structural models can be used: 1 for the effects of the treatment and mediator on the outcome and 1 for the effect of the treatment on the mediator. Unlike marginal structural models typically used in epidemiologic research, the marginal structural models used to estimate natural direct and indirect effects are made conditional on the covariates.

 "The final purpose of our study is to contribute to the literature on the use of multilevel mediation analyses in randomized field trials in education settings. Mediation analyses are commonly applied in other fields to identify mechanisms through which interventions achieve their effects such as health related interventions (Stigler, Kugler, Komro, Leshabari, & Klepp, 2006), and in psychological research (MacKinnon, Fairchild, & Fritz, 2007) and epidemiological studies (VanderWeele, 2009). Fewer applications are found in experimental studies of educational interventions when three levels are present e students, classrooms, and schools e in part because this statistical technique is not widely known (Pituch, Murphy, & Tate, 2010; Raudenbush, 2011). "
Dataset: Matsumura et al JLI 2013

 "Structure equation model (SEM) is a popular approach to perform mediation analysis, which assesses the extent of the effect passing through M , see Baron and Kenny (1986) and MacKinnon et al. (2007). This topic has been studied in the statistical literature, see for example Holland (1988); Robins and Greenland (1992); Angrist et al. (1996); Ten Have et al. (2007); Jo (2008); Albert (2008); Gallop et al. (2009); VanderWeele (2009); Imai et al. (2010); Daniels et al. (2012). A popular assumption to infer causal effects is to assume the ignorability of the mediator (Imai et al., 2010). "
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ABSTRACT: Mediation analysis assesses the effect passing through a intermediate variable (mediator) in a causal pathway from the treatment variable to the outcome variable. Structure equation model (SEM) is a popular approach to estimate the mediation effect. However, causal interpretation usually requires strong assumptions, such as ignorability of the mediator, which may not hold in many social and scientific studies. In this paper, we use mediation analysis in an fMRI experiment to assess the effect of randomized binary stimuli passing through a brain pathway of two brain regions. We propose a twolayer SEM framework for mediation analysis that provides valid inference even if correlated additive errors are present. In the first layer, we use a liner SEM to model the subject level fMRI data, where the continuous mediator and outcome variables may contain correlated additive errors. We propose a constrained optimization approach to estimate the model coefficients, analyze its asymptotic properties, and characterize the nonidentifiability issue due to the correlation parameter. To address the identifiability issue, we introduce a linear mixed effects SEM with an innovation to estimate the unknown correlation parameter in the first layer, instead of sensitivity analysis. Using extensive simulated data and a real fMRI dataset, we demonstrate the improvement of our approach over existing methods. 
 "This requires estimators for the conditional mean of Y given D, M, X and the conditional density of M given D, X. In the literature, parametric methods have been most commonly used, see for instance Pearl (2011) and VanderWeele (2009). 6 They, however, appear unattractive due to their severe functional form restrictions and the potentially difficult interpretability of direct and indirect effects under nonlinear modeling (e.g., when both the outcome and the mediator are binary). "
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ABSTRACT: This paper demonstrates the identification of causal mechanisms of a binary treatment under selection on observables, (primarily) based on inverse probability weighting. I.e., we consider the average indirect effect of the treatment, which operates through an intermediate variable (or mediator) that is situated on the causal path between the treatment and the outcome, as well as the (unmediated) direct effect. Even under random treatment assignment, subsequent selection into the mediator is generally nonrandom such that causal mechanisms are only identified when controlling for confounders of the mediator and the outcome. To tackle this issue, units are weighted by the inverse of their conditional treatment propensity given the mediator and observed confounders. We show that the form and applicability of weighting depend on whether some confounders are themselves influenced by the treatment or not. A simulation study gives the intuition for these results and an empirical application to the direct andJournal of Applied Econometrics 09/2014; forthcoming:NA. DOI:10.1002/jae.2341 · 1.76 Impact Factor
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