**October 4, 2011**

The graphic on the right illustrates a standard mediation model. In this model, we hypothesize that a treatment affects a mediator that, in turn, affects an outcome. For example, in a hypothetical HIV-prevention intervention, subjects receive condom-use training (a treatment), which impacts their attitudes toward condom use (a mediator), which in turn improves their condom use (an outcome). Traditionally, mediation is assessed using multivariate regression or structural equation modeling. This traditional approach depends on the assumption that the mediator has been randomly assigned, but this is rarely possible (as in our hypothetical example, because attitudes toward condom use cannot be assigned). In this article, Methodology Center Research Associate Donna Coffman proposes and demonstrates that incorporating propensity scores into the traditional approach can remove the bias that occurs when levels of the mediator are not randomly assigned. A propensity score is the probability that an individual received a particular level of the mediator. This new approach will allow researchers to better assess the mediated effect of a treatment on an outcome.

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**Abstract: **Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, M, and the outcome, Y. This assumption holds if individuals are randomly assigned to levels of M but generally random assignment is not possible. We propose the use of propensity scores to help remove the selection bias that can result when individuals are not randomly assigned to levels of M. The propensity score is the probability that an individual receives a particular level of M. Results from a simulation study are presented to demonstrate this approach, referred to as Classical + Propensity Model (C+PM), confirming that the population parameters are recovered and that selection bias is successfully dealt with. Comparisons are made to the classical approach that does not include propensity scores. Propensity scores were estimated by a logistic regression model. If all confounders are included in the propensity model, then the C+PM is unbiased. If some, but not all, of the confounders are included in the propensity model, then the C+PM estimates are biased although not as severely as the classical approach (i.e., no propensity model is included).

Coffman, D. L. (2011). Estimating causal effects in mediation analysis using propensity scores. *Structural Equation Modeling, 18*(3), 357-369.

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