Propensity scores are a very useful tool for inferring causality when a mediator is present. When individuals are not randomly assigned to levels of the mediator (which is often the case), propensity scores can be used to account for confounding.
For example, in an HIV-prevention intervention, subjects receive condom-use training (a treatment), which impacts their belief that they can successfully use condoms (a mediator), which in turn improves their condom use (an outcome). Because the mediator (condom-use self-efficacy) cannot be randomly assigned, the use of propensity scores can enable much more accurate causal inference than the traditional approach of using multivariate regression alone.
In the article, "Estimating causal effects in mediation analysis using propensity scores" (2011) 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.
Coffman, D. L. (2011). Estimating causal effects in mediation analysis using propensity scores. Structural Equation Modeling, 18(3), 357-369. PMCID: PMC3212948
Inferring Causality in the Presence of a Moderator
In a recent paper, boredom with leisure activities is hypothesized to influence whether or not teens start smoking (Coffman, Caldwell, & Smith, 2012). The moderator in the model is teen's level of smoking initiation risk. Researchers found that for teens with high levels of risk, leisure boredom did not impact their rates of smoking initiation. However, for teens with low levels of risk, leisure boredom did increase their rates of smoking initiation.
Almirall, D., McCaffrey, D. F., Ramchand, R., & Murphy, S. A. (2011). Subgroups analysis when treatment and moderators are time-varying. Prevention Science. Advance online publication. doi: 10.1007/s11121-011-0208-7 PMCID: PMC3135740
Almirall, D., Ten Have, T., & Murphy, S. A. (2010). Structural nested mean models for assessing time-varying effect moderation. Biometrics, 66(1), 131-139. PMCID: PMC2875310
Coffman, D. L., Caldwell, L. L., & Smith, E. A. (2012). Introducing the at-risk average causal effect with application to HealthWise South Africa. Prevention Science. Advance online publication. doi:10.1007/s11121-011-0271-0 PMCID: PMC3405190
Inferring Causality in the Presence of Moderated Mediation
Methodology Center researchers have found that the effect of a treatment on an outcome through the mediator can be different for different subgroups of people. For example, in boys, condom-use self-efficacy impacts condom use, but in girls condom-use self-efficacy has no impact.
Coffman, D. L., & Zhong, W. (2012). Assessing mediation using marginal structural models in the presence of confounding and moderation. Psychological Methods, 17,(4), 342-664. PMCID: PMC3553264 doi: 10.1037/a0029311
Methods for Estimating Propensity Scores
This work demonstrates and expands the use of propensity score methods. An article by Debashis Ghosh (2011) shows that certain conditional independence assumptions from dimension-reduction procedures can be used to justify the validity of causal inference modeling. The author studies links between the two fields in this article.The methods are illustrated with simulated data and are applied to a medical study.
In the article, "A boosting algorithm for estimating generalized propensity scores with continuous treatments," the authors propose a stopping criterion, the absolute average correlation coefficient, to determine the optimal number of trees.
Ghosh, D. (2011). Propensity score modeling in observational studies using dimension reduction methods. Statistics & Probability Letters, 81(7), 813-820. doi:10.1016/j.spl.2011.03.002 PMCID: PMC3099445
Zhu, Y., Coffman, D. L., & Ghosh, D. (in press). A boosting algorithm for estimating generalized propensity scores with continuous treatments. Journal of Causal Inference.