Propensity Score Matching [PSM]

Propensity score matching (PSM) is a method analysts use in observational studies to reduce confounder bias when comparing groups. It addresses a fundamental problem with observational studies: researchers do not randomly assign people to treatment or control groups. Instead, people have already chosen for themselves. Their decisions about whether to receive the treatment are often driven by their characteristics, such as age, income, education, or health. This self-selection creates differences between groups at the beginning of the study that can distort the results at the end.

To account for these initial differences, researchers use a propensity score, which is the estimated probability that a person would have chosen to receive the treatment based on their observed characteristics. Researchers typically calculate these scores using a logistic regression model that includes covariates which theory suggests will influence treatment decisions.

After the study estimates propensity scores, researchers match treated and untreated individuals with similar scores. The goal is to create a treatment group that is more comparable to the control group in terms of the background variables. Participants in either group who are too different from the other group might be dropped from the study. This propensity score matching process helps reduce confounding and makes the treatment effect estimate more credible—more like what you’d get if the groups had been assigned randomly.

Alternatively, researchers can include the propensity score directly as a covariate in a regression model. This approach adjusts for differences in the likelihood of treatment without discarding data. Both strategies aim to control for bias due to observed covariates, though they cannot address bias from unmeasured factors.

PSM Example

For example, suppose researchers want to study the effect of a new educational program in an observational study. Families have already made their decisions about whether to participate in the new program. Participation isn’t random—students with higher motivation or more support at home may be more likely to enroll. Simply comparing outcomes between those who did and didn’t participate could be misleading.

Using propensity score matching, researchers estimate each student’s likelihood of enrolling in the program based on characteristics like prior grades, school type, and family income. They then match participants to similar non-participants based on those scores, creating a fairer comparison to estimate the program’s impact.