Propensity Score

The propensity score is the probability that a unit (e.g., a person, patient, or subject) would receive a particular treatment or exposure, given a set of observed covariates.

The propensity score is the conditional probability of assignment to a treatment, given a vector of observed covariates:

e(x) = P(T = 1 | X = x)

where:

• T is the treatment indicator (1 = treated, 0 = untreated),
• X is the vector of observed covariates.

Propensity scores are used in observational studies to reduce selection bias when comparing outcomes between treated and untreated groups.

In randomized trials, treatment is assigned randomly. In contrast, observational studies often have confounding differences between groups. Propensity scores help balance these covariates, making groups more comparable.

• Matching: Pairing treated and untreated subjects with similar scores.
• Stratification: Dividing subjects into strata (e.g., quintiles) based on scores.
• Weighting: Applying inverse probability weights to create a pseudo-population.
• Covariate adjustment: Using the score as a covariate in a regression model.

In a study comparing surgery vs. medical therapy for a disease, patients may receive surgery based on age, comorbidities, or severity. A propensity score estimates the probability of surgery given these factors. Researchers can then compare outcomes as if the groups had been randomized.