Matching (statistics)

Matching pairs or groups treated units with similar untreated units using observed characteristics, then compares outcomes to estimate treatment effects in observational data.

Propensity score: The probability of receiving a treatment given observed characteristics. Matching often uses this probability to summarize many covariates when pairing treated and comparison units.
Potential outcomes: A framework that represents each unit's outcomes under alternative treatment conditions. Matching estimates causal effects by comparing observed outcomes as proxies for unobserved potential outcomes.
Randomized controlled trial: An experiment that assigns units to treatment conditions by random allocation. Random assignment balances measured and unmeasured causes in expectation, unlike observational matching.
Case-control study: An observational study that selects participants by outcome status and compares prior exposures. Matching cases to controls can balance selected characteristics in this study design.
Unmeasured confounding: Confounding caused by variables that are absent or inadequately measured in the data. Matching cannot balance causes of treatment and outcome that were not measured.
Nearest neighbor algorithm: An algorithm that assigns each item to the closest item under a chosen distance measure. Nearest-neighbor matching pairs units with the smallest covariate distance.
Confounding: A distortion of an exposure–outcome association by a common cause of both. Matching aims to reduce confounding from measured characteristics.
Inverse probability weighting: An estimator that weights units by the inverse of their treatment-assignment probabilities. Weighting adjusts the comparison population without selecting explicit pairs.
Propensity score matching: A matching method that pairs units using their estimated probabilities of treatment. It is a widely used implementation of matching for observational treatment-effect studies.
Sensitivity analysis: Methods that assess how conclusions change under departures from modeling assumptions or data conditions. Sensitivity analyses examine how strong hidden bias would need to be to alter a matched estimate.

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