propensityscore

Propensity score is the probability of receiving a treatment given observed covariates. Introduced by Rosenbaum and Rubin in 1983, it serves as a balancing score intended to help observational studies mimic some aspects of randomized experiments by making treated and untreated groups comparable on measured covariates.

In practice, the propensity score is estimated from data using models for the treatment indicator, most commonly logistic regression, though machine learning methods can also be used. After estimating the score, several strategies use it to reduce confounding: matching treated and untreated units with similar scores, stratifying the sample into balance groups (for example, quintiles of the score), weighting observations by inverse probability of treatment, or including the score as a covariate in outcome analysis.

Common approaches include propensity score matching (nearest-neighbor or caliper matching), stratification into score-based strata, inverse probability weighting to create a pseudo-population, and using the score in outcome models for covariate adjustment. After applying these methods, balance diagnostics—such as standardized mean differences and variance ratios—are used to assess whether covariates are similar across treatment groups.

Assumptions and limitations: the key assumption is no unmeasured confounding given the observed covariates (strong ignorability). There must be sufficient overlap in propensity scores between treatment and control groups (positivity). Validity depends on correct model specification and comprehensive covariate measurement; sensitivity analyses are recommended for potential hidden bias.

Related concepts: propensity score methods are part of causal inference approaches and are often complemented by techniques such as doubly robust estimation and targeted maximum likelihood estimation.