Propensity Score Matching (PSM)

Propensity Score Matching is a statistical technique used in observational studies to estimate the effect of a treatment, policy, or other intervention by accounting for covariates that predict receiving the treatment.

How It Works

1. Calculate Propensity Score: Estimate the probability of receiving treatment for every subject (usually via logistic regression).
2. Match Subjects: Pair treated subjects with untreated subjects who have similar propensity scores.
3. Check Balance: Ensure that after matching, the characteristics of both groups are statistically similar.
4. Estimate Effect: Compare the outcome between the matched groups.

Matching Algorithms

Method	Description	Best Use Case
Nearest Neighbor	Matches treated unit to the closest control unit.	General purpose, most common.
Caliper Matching	Matches only within a specific score distance (e.g., +/- 0.05).	When you need high precision matches.
1:k Matching	Matches one treated unit to k control units (e.g., 1:2).	When you have many controls to increase power.

Balance Diagnostics

Before analyzing the outcome, you must check if matching worked. The gold standard is the Standardized Mean Difference (SMD).

• SMD < 0.1: Excellent balance.
• SMD < 0.2: Acceptable balance.
• SMD > 0.2: Imbalanced (Need to adjust model).