Propensity Score Matching

A statistical technique pairing treated individuals with similar untreated individuals based on an estimated propensity score, balancing measured confounding variables.

Source: Rosenbaum & Rubin 1983

Propensity score matching pairs each treated patient with an untreated patient who had a similar estimated probability of receiving the treatment, given their measured characteristics. By matching on this single summary of many confounders, it builds two groups that are balanced on those measured factors, mimicking the balance randomisation would have produced. This lets an observational comparison approach the fairness of a trial, though only for the confounders that were actually measured; unmeasured differences remain. Balancing measured factors after the fact is its method. Rosenbaum and Rubin (1983) describe this technique.

Source: Rosenbaum & Rubin 1983

Propensity score matching works by first estimating each individual's propensity score, the predicted probability of receiving the treatment given their measured characteristics, usually from a model such as logistic regression; then matching treated individuals to untreated individuals with similar scores; and comparing outcomes between the matched groups. Balance on the measured covariates is checked after matching. So propensity score matching works by summarising the measured confounders into a single score and pairing treated and untreated individuals on it, so that the compared groups are similar in their measured characteristics, allowing the treatment effect to be estimated with reduced confounding by those variables.

Source: Rosenbaum & Rubin 1983

Propensity score matching is used to reduce confounding by measured variables when estimating treatment effects from observational data, where treatment is not randomised and treated and untreated groups may differ systematically. By balancing the measured covariates, it makes the groups more comparable, so that differences in outcomes can be attributed more confidently to the treatment. So propensity score matching is used to approximate the comparability that randomisation provides, for the measured characteristics, in non-randomised studies, which is valuable in real-world and pharmacoepidemiological research, though it addresses only measured confounders and not those that are unmeasured.

Source: Rosenbaum & Rubin 1983

The limitations of propensity score matching include that it balances only measured confounders, so unmeasured confounding remains and can bias the estimate; that adequate overlap between the groups' propensity scores is needed, and matching may discard unmatched individuals, affecting the population represented; and that the propensity model must be reasonably specified. So propensity score matching is used with awareness that it does not address unmeasured confounding, that its validity depends on the measured covariates capturing the important confounders, and that its results are interpreted accordingly, since, unlike randomisation, it cannot balance factors that were not measured.

Source: Rosenbaum & Rubin 1983

Propensity score matching relates to randomisation as an attempt to approximate, in observational data, the comparability that randomisation achieves. Randomisation balances both measured and unmeasured factors between groups on average, whereas propensity score matching balances only the measured covariates summarised in the score. So propensity score matching mimics randomisation for the measured characteristics but, unlike true randomisation, cannot ensure balance on unmeasured factors, which is its key limitation, meaning that while it strengthens causal inference from observational studies, it does not provide the same protection against confounding that a randomised experiment does.

Source: Hernán & Robins 2020