A Two-Stage Propensity Score Matching Strategy for Treatment Effect Estimation in a Multisite Observational Study

When nonrandom treatments occur across sites, within-site matching (WM) is often desirable. This approach, however, can significantly reduce treatment group sample size and exclude substantively important subgroups. To limit these drawbacks, we extend a matching approach developed by Stuart and Rubin to a multisite study. We demonstrate the proposed method through a multisite analysis of algebra enrollment effects in 50 middle schools, where within each school students are assigned to algebra or pre-algebra and test the utility of the proposed method with a simulation study. The results document the method's conceptual appeal and indicate that two-stage matching is a viable alternative to strict WM or matching that ignores the nested data structure (pooled matching).