Propensity Score

The estimated probability that an individual would receive a particular treatment given their observed characteristics, used to balance confounders in observational studies.

Source: Rosenbaum & Rubin 1983

In an observational study, patients who received a treatment often differ systematically from those who did not, confounding any comparison. A propensity score summarises each patient's measured characteristics into a single number, their estimated probability of having received the treatment, and patients with similar scores can then be matched or weighted so the treated and untreated groups look alike on those characteristics. This balances the measured confounders, mimicking on paper what randomisation achieves in fact. Crucially, it can only balance factors that were measured. Austin (2011) describes this method.

Source: Austin 2011

A propensity score is used to balance confounders through methods such as matching treated and untreated individuals with similar scores; stratifying on the score; weighting individuals by the inverse of their probability of the treatment received; or including the score in a regression. These approaches create comparisons in which the measured characteristics are balanced across treatment groups, so differences in outcome are less confounded by those characteristics. By summarising the confounders into one score and balancing on it, propensity-score methods aim to estimate the treatment effect more validly from observational data.

Source: Rosenbaum & Rubin 1983

Propensity scores are useful because they summarise many confounding variables into a single score, simplifying the task of balancing treatment groups in observational studies, and because balancing on the score can create comparable groups that approximate randomisation on the measured characteristics, reducing confounding. They also make the balance achievable and checkable, and can handle many confounders when direct adjustment is difficult. This makes propensity-score methods a widely used approach for estimating treatment effects from non-randomised data, improving comparability between treated and untreated groups on the observed confounders.

Source: Hernán & Robins 2020

The limitations of propensity scores are that they balance only measured confounders, so unmeasured confounding remains a threat, unlike randomisation, which balances unmeasured factors too; that they require the confounders influencing treatment and outcome to be measured and correctly modelled; and that balance and overlap between groups must be adequate for valid comparison. Poor overlap or omitted confounders bias the estimate. So propensity-score methods reduce but cannot eliminate confounding from observational data, and their validity depends on measuring the relevant confounders, making them weaker than randomisation for causal inference.

Source: Rosenbaum & Rubin 1983

Propensity-score adjustment balances the measured confounders between treatment groups in observational data, approximating comparability on those characteristics, whereas randomisation balances both measured and unmeasured confounders by chance, creating comparable groups on all factors. So randomisation addresses unmeasured confounding, which propensity scores cannot, since they rely on measured variables. Propensity-score methods are used when randomisation is impossible, to improve comparability from observational data, but they provide weaker causal inference because unmeasured confounding may remain. So the two differ fundamentally in their ability to control unmeasured confounders.

Source: Rosenbaum & Rubin 1983