Example: Causal Mediation Using Propensity Scores | The Methodology Center

Example: Causal Mediation Using Propensity Scores

Causal Inference & Mediation

Many research questions involve behaviors that cannot be randomized

Causal inference means inferring a causal relationship between a treatment T and an outcome Y. (Note: T could also be an exposure.) This is straightforward when individuals are randomly assigned to treatment, but it becomes more complicated when randomization is impossible. In the study of behaviors and health, many topics of interest can never be randomized, such as drug use, parenting behavior, beliefs, and risky sexual activity. For this reason much of The Methodology Center's work focuses on causal mediation, which can accommodate non-randomized treatments and/or mediators. In causal mediation the treatment causes a change in a mediator, which in turn causes a change in the outcome. See the example below for more details. 

Introductory Example: Causal Mediation-Impact of HIV Intervention on Unprotected Sex

Data Set

  • 243 incarcerated, adult women re-entering the community (69.1% White, 24.3% African American; 4.5% Hispanic; 6.6% Other).
  • Scheduled to go before parole board within 6 weeks
  • Used illegal substances at least weekly before incarceration
  • Willing to be randomized to study condition 

Mediation Model

Mediation ModelOur research relies on the standard mediation model that is commonly used in social sciences.


Treatment is sometimes referred to as an exposure, because exposure to an event or life circumstance could be considered a treatment in this model. In this example, the treatment is randomly assigned, but the model described here can also work when treatment is not random.


Most health interventions work through a mediator. The mediator in this study is a set of thoughts about relationships. Here the intervention was randomly assigned, but it is impossible to randomly assign beliefs. If this mediator could be randomized, every woman would be assigned to accurate and healthy thoughts. Researchers asked subjects to answer the following questions about risky relationship thoughts:

  • Does having unprotected sex strengthen a relationship?
  • Do you only feel good about yourself when you are in a relationship, even a risky relationship?
  • Does your partner look, talk, and/or act in a way that makes you feel safe?
  • Do you feel that you will not get HIV because you are not really at risk?
  • Is practicing safe sex unimportant because you’ve been with your partner for a long time?
  • Do you have to use sex as a way to get what you want in a relationship?


The independent variable or exposure



Sometimes a treatment impacts the outcome through an intermediate variable, called a mediator.



The dependent variable


Note: The study measured women's thoughts about the items above. The accuracy of these thoughts was not under consideration. The beliefs act as a mediator because the RRR-HIV intervention impacts them, and they impact the outcome.


The outcome is sex without a condom.


Through this model, we can understand the impact of the RRR-HIV intervention on beliefs, the impact of beliefs on risky sex, and the impact of RRR-HIV on risky sex through other mechanisms. Several questions naturally arise:

  • Did beliefs about risky relationships change?
  • Did risky sex decrease? These first two questions can be answered in a traditional manner, because the treatment was randomized.
  • Is the decrease in risky sex attributable to changes in the individuals' beliefs about risky relationships, and are those changes attributable to the intervention? Because the beliefs were not randomized, answering this question requires new analytic methods.


Other Factors (Confounders) That May Impact Risky Sexual Behavior

In this example, researchers were unable to randomly assign participants to levels of the mediator (risky thoughts). Because there is no random assignment, other factors (called confounders) could bias the estimates of the relationships between the mediator and outcome. To eliminate potential bias, the researchers selected factors based on a review of literature about and risky relationships and risky sexual behavior, which included the following items.


Any of these factors could impact the relationship between a woman's risky relationship thoughts (the mediator) and her willingness to have sex without a condom (the outcome). For example, a woman who is financially dependent on her partner might harbor riskier thoughts about relationships than somebody who is not financially dependent. At the same time, her odds of engaging in unprotected sex may increase. 

Propensity Scores


Variable that influences both the treatment and the outcome

The confounders are included in the model using propensity scores. Generally, the more potential confounders that are included, the better, with a few exceptions: confounders that could be influenced by the mediator should NOT be included in the model, and confounders that strongly influence the mediator but only weakly influence the outcome should not be included. No study will successfully identify all confounders, but the more that are identified, the closer researchers come to the truth. Including some is much better than including none.


Propensity scores allow a non-randomized treatment or mediator to be evaluated as though it were randomized.

Conceptually, a propensity score is the probability that an individual received the treatment. If the people who have high levels of risky relationship thoughts are different from those who do not have these thoughts, then we need to understand the differences. We cannot simply compare the results for people who harbored risky thoughts to the results for those people who did not harbor risky thoughts, because the groups are not equivalent. At the most basic level, by accounting for the different circumstances between study participants, propensity scores allow researchers to compare results as though participants were similar. This allows us to know whether the mediator was the true reason for any change we observe on the outcome. In other words, propensity scores allow a non-randomized mediator (or using slightly different methods, a non-randomized treatment) to be evaluated as though it were randomized.



Causal Mediation Using Propensity ScoresAfter the data are adjusted, the average causal effect can be estimated. We fit the model for risky sex and incorporated inverse propensity weights. See the recommended reading for examples using the different estimation methods. The results indicated that the intervention resulted in a significant decrease in risky relationship beliefs, and lower risky relationship beliefs resulted in a decrease in instances of sex without a condom. 

What are Methodology Center researchers working on?

Center researchers are working on extending mediation models so that they can be used to improve substance use interventions and on developing software for the application of these methods. For more information, see our research topics in causal inference. The field of causality is exciting, dynamic and filled with competing ideas; this debate advances the science of causal inference. For some key readings in the field, see the recommended reading list. Please note that this list relates to Methodology Center research and to research closely related to ours. It is not meant to be comprehensive.



Coffman, D. L., & Kugler, K. C. (2012). Causal mediation of a human immunodeficiency virus preventive intervention. Nursing Research, 61(3), 224-230. PMCID: PMC3377683

Havens, J. R., Leukefeld, C. G., Oser, C. B., Staton-Tindall, M., Knudsen, H.K., Mooney, J., ... Inciardi, J. A. (2009). Examination of an interventionist-led HIV intervention among criminal justice-involved female prisoners. Journal of Experimental Criminology, 5, 245-272.

Staton-Tindall, M., Leukefeld, C., Palmer, J., Oser, C., Kaplan, A., Krietemeyer, J., ..., Surratt, H. L. (2007). Relationships and HIV risk among incarcerated women. The Prison Journal, 87, 143-165.

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