Using Bayesian propensity score analysis in testing causal mechanisms
Mediation analysis helps identify and understand the underlying mechanism of a phenomenon. As an example, a simple mediated effect occurs when an intervention changes a mediator (i.e., the a path) and that mediator changes the outcome (i.e., the b path). The mediated effect is then the product of α and β paths, ab, which estimates the part of the total program effect transmitted through the mediator.
 
Current use in conventional mediation analysis follows a linear regression approach (Baron & Kenny, 1986; MacKinnon, 2008) and relies on the following assumptions:
 
(i) No unmeasured confounders for the relationship between X and Y and  X and M.
(ii) No unmeasured confounder for the relationship between M and Y.
 
Assumption (i) is formally known as sequential ignorability I assumption. It refers to the ignorability of treatment assignment (i.e., being independent of mediator and outcome) given the observed pretreatment confounders. This assumption is usually satisfied with randomization of X.  Assumption (ii) is called the sequential ignorability II assumption. It refers to the ignorability of the mediator given the observed treatment and pretreatment confounders. This assumption is hard to meet because randomization of M is usually not plausible for many studies (i.e., the mediator status is not randomly assigned, but rather self-selected by participants). One of the methods to deal with the causal inference problem for the b path is the use of propensity scores.
 
Bayesian methods have also been used to assess mediation, giving an advantage over frequentist mediation analysis by using prior information to improve efficiency of estimates and giving more exact estimates in small samples (Yuan & MacKinnon, 2009). This study illustrates the use of Bayesian propensity score analysis in testing indirect effects.
 


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Reference:
Kisbu-Sakarya, Y., O’Rourke, H., & MacKinnon, D., (June, 2012). Causal inference in Bayesian mediation analysis: Implications of prior information use. Presented at the Annual Meeting of Society of Prevention Research, Washington DC.