Propensity Score Matching

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What is Propensity Score Matching?

Propensity score matching is one of the most widely used methods for estimating causal effects from observational data. The core idea is to pair each treated individual with an untreated individual who has a similar propensity score.

Propensity Score Matching: A method that creates a matched sample by pairing treated and untreated individuals with similar estimated propensities for receiving treatment. The goal is to create treatment groups that are balanced on observed confounders.

If two individuals have the same propensity score, they have similar covariate profiles. By matching on propensity scores, we effectively balance all the covariates used to estimate the score.

After matching, if the matched sample is well-balanced:

$E[Y|A=1, \text{matched}] - E[Y|A=0, \text{matched}] \approx E[Y^1 - Y^0 | A=1]$

The right side is the Average Treatment Effect on the Treated (ATT).

Example: Comparing surgical vs. medical treatment for CAD
Patients who receive surgery are systematically different. By matching each surgical patient to a medically-managed patient with a similar propensity score, we create pairs where both had similar probabilities of receiving surgery.

Reference: Rosenbaum PR (2002). Observational Studies (2nd ed.). Springer.

Propensity Score Matching pairs treated individuals with untreated individuals who have similar propensity scores.

Goal: Create a matched sample where treatment groups are comparable.

Intuition: If two individuals have the same probability of treatment, they are "exchangeable" conditional on measured confounders.

After matching: $E[Y|A=1, \text{matched}] - E[Y|A=0, \text{matched}] \approx E[Y^1 - Y^0]$

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