Statistical Criteria for Selecting the Optimal Number of Untreated Subjects Matched to Each Treated Subject When Using Many-to-One Matching on the Propensity Score

Propensity-score matching is increasingly being used to estimate the effects of treatments using observational data. In many-to-one (M:1) matching on the propensity score, M untreated subjects are matched to each treated subject using the propensity score. The authors used Monte Carlo simulations to examine the effect of the choice of M on the statistical performance of matched estimators. They considered matching 1–5 untreated subjects to each treated subject using both nearest-neighbor matching and caliper matching in 96 different scenarios. Increasing the number of untreated subjects matched to each treated subject tended to increase the bias in the estimated treatment effect; conversely, increasing the number of untreated subjects matched to each treated subject decreased the sampling variability of the estimated treatment effect. Using nearest-neighbor matching, the mean squared error of the estimated treatment effect was minimized in 67.7% of the scenarios when 1:1 matching was used. Using nearest-neighbor matching or caliper matching, the mean squared error was minimized in approximately 84% of the scenarios when, at most, 2 untreated subjects were matched to each treated subject. The authors recommend that, in most settings, researchers match either 1 or 2 untreated subjects to each treated subject when using propensity-score matching.