The concept of the marginal subject in propensity-score matched analyses
Propensity-score matching is increasingly being used to reduce the impact of treatment-selection bias when estimating causal treatment effects using observational data. Matching on the propensity-score creates sets of treated and untreated subjects who have a similar distribution of baseline covariates. Propensity-score matching frequently relies upon calipers, such that matched treated and untreated subjects must have propensity scores that lie within a specified caliper distance of each other. We define the “marginally-matched” subject as a subject who would be matched using the specified caliper width, but who would not have been matched had calipers with a narrower width been employed. Using patients hospitalized with an acute myocardial infarction (or heart attack) and with exposure to a statin prescription at discharge, we demonstrate that the inclusion of marginally-matched subjects can have both a quantitative and qualitative impact upon the estimated treatment effect. Furthermore, marginally-matched treated subjects can differ from marginally matched untreated subjects to a substantially greater degree than the differences between non-marginally matched treated and untreated subjects in the propensity-score matched sample. The concept of the marginally-matched subject can be used as a sensitivity analysis to examine the impact of the matching method on the estimates of treatment effectiveness.
Peter C. Austin and Douglas S. Lee. "The concept of the marginal subject in propensity-score matched analyses" Pharmacoepidemiology and Drug Safety 18 (2009): 469-482.