This article presents marginal structural models with inverse propensity weighting (IPW) for assessing mediation. Generally, individuals are not randomly assigned to levels of the mediator. Therefore, confounders of the mediator and outcome may exist that limit causal inferences, a goal of mediation analysis. Either regression adjustment or IPW can be used to take confounding into account, but IPW has several advantages. Regression adjustment of even one confounder of the mediator and outcome that has been influenced by treatment results in biased estimates of the direct effect (i.e., the effect of treatment on the outcome that does not go through the mediator). One advantage of IPW is that it can properly adjust for this type of confounding, assuming there are no unmeasured confounders. Further, we illustrate that IPW estimation provides unbiased estimates of all effects when there is a baseline moderator variable that interacts with the treatment, when there is a baseline moderator variable that interacts with the mediator, and when the treatment interacts with the mediator. IPW estimation also provides unbiased estimates of all effects in the presence of nonrandomized treatments. In addition, for testing mediation we propose a test of the null hypothesis of no mediation. Finally, we illustrate this approach with an empirical data set in which the mediator is continuous, as is often the case in psychological research.
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