Matching with Multiple Control Groups, and Adjusting for Group Differences

When estimating causal effects from observational data, it is desirable to replicate a randomized experiment as closely as possible, for example, by obtaining treated and control groups with extremely similar distributions of observed covariates. This goal can often be achieved by choosing a subsample from the original control group that matches the treatment group on the distribution of these covariates, thus reducing bias due to these covariates. However, sometimes the original sample of control units cannot provide adequate matches for the treated units. In these cases, it may be desirable to obtain matched controls from multiple control groups. Multiple control groups have been used to test for hidden biases in causal inference (e.g., Rosenbaum 2002); however, little work has been done on their use in matching or for adjusting for biases, such as potential systematic differences between the original control group and supplemental control groups beyond that which can be explained by observed covariates. Here we present a method that uses matches from multiple control groups and adjusts for potentially unobserved differences between the additional control groups and the original control group in the analysis of the outcome. The method is illustrated and evaluated using simulated data as well as data from an evaluation of a school dropout prevention program, which utilizes both local and non-local matches.