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, two untreated subjects were matched to each treated subject.

The authors recommend that, in most settings, researchers match either one or two untreated subjects to each treated subject when using propensity-score matching.