MATCHING USING ESTIMATED PROPENSITY SCORES - RELATING THEORY TO PRACTICE

Matched sampling is a standard technique in the evaluation of treatmen ts in observational studies. Matching on estimated propensity scores c omprises an important class of procedures when there are numerous matc hing variables. Recent theoretical work (Rubin, D. B. and Thomas, N., 1992, The Annals of Statistics 20, 1079-1093) on affinely invariant ma tching methods with ellipsoidal distributions provides a general frame work for evaluationg the operating characteristics of such methods. Mo reover, Rubin and Thomas (1992, Biometrika 79, 797-809) uses this fram ework to derive several analytic approximations under normality for th e distribution of the first two moments of the matching variables in s amples obtained by matching on estimated linear propensity scores. Her e we provide a bridge between these theoretical approximations and act ual practice. First, we complete and refine the nomal-based analytic a pproximations, thereby making it possible to apply these results to pr actice. Second, we perform Monte Carlo evaluations of the analytic res ults under normal and nonnormal ellipsoidal distributions, which confi rm the accuracy of the analytic approximations, and demonstrate the pr edictable ways in which the approximations deviate from simulation res ults when normal assumptions are violated within the ellipsoidal famil y. Third, we apply the analytic approximations to real data with clear ly nonellipsoidal distributions, and show that the thoretical expressi ons, although derived under artificial distributional conditions, prod uce useful guidance for practice. Our results delineate the wide range of settings in which matching on estimated Linear propensity scores p erforms well, thereby providing useful information for the design of m atching studies. When matching with a particular data set, our theoret ical approximations provide benchmarks for expected performance under favorable conditions, thereby identifying matching variables requiring special treatment. After matching is complete and data analysis is at hand, our results provide the variances required to compute valid sta ndard errors for common estimators.