Matching with Multiple Controls to Estimate Treatment Effects in Observational Studies

Matching to control for covariates in the estimation of treatment effects is not common in sociology, where multivariate data are most often analyzed using multiple regression and its generalizations. Matching can be a useful way to estimate these effects, especially when the treatment condition is comparatively rare in a population, and controls are numerous but mostly unlike the treatment cases. Matching on numerous covariates is abetted by the estimation of propensity scores, or functions of the probability that cases are treatments rather than controls. This procedure is illustrated in the estimation of the effects of an organizational innovation on Medicare mortality within hospitals; the data set is very large, but innovative hospitals few, and many of the remaining hospitals are quite unlike the hospitals constituting the treatment sub-sample. Results are based on a variance-components model that is extended to consider the effects of an additional covariate. They show effects of the organizational innovation comparable to those estimated via multiple regression models but with substantially reduced standard errors.