Matching Using Estimated Propensity Scores: Relating Theory to Practice

Matched sampling is a standard technique in the evaluation of treatments in observational studies. Matching on estimated propensity scores comprises an important class of procedures when there are numerous matching variables. Recent theoretical work (Rubin, D. B. and Thomas, N., 1992, The Annals of Statistics 20, 1079-1093) on affinely invariant matching methods with ellipsoidal distributions provides a general framework for evaluating the operating characteristics of such methods. Moreover, Rubin and Thomas (1992, Biometrika 79, 797-809) uses this framework to derive several analytic approximations under normality for the distribution of the first two moments of the matching variables in samples obtained by…