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In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture “compositional” differences in the distributions of unit-level features as well as “contextual” differences in site-level features, including possible differences in program implementation. Our goal in this article is to adjust site-level estimates for differences in the distribution of observed unit-level features: If we can reweight (or “transport”) each site to have a common distribution of observed unit-level covariates, the remaining treatment effect variation captures contextual and unobserved compositional differences across sites. This allows us to make apples-to-apples comparisons across sites, parceling out the amount of cross-site effect variation explained by systematic differences in populations served. In this article, we develop a framework for transporting effects using approximate balancing weights, where the weights are chosen to directly optimize unit-level covariate balance between each site and the common target distribution. We first develop our approach for the general setting of transporting the effect of a single-site trial. We then extend our method to multisite trials, assess its performance via simulation, and use it to analyze a series of multisite trials of adult education and vocational training programs. In our application, we find that distributional differences are potentially masking cross-site variation. Our method is available in the balancer R package. 

Abstract Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to obtain weights that directly minimizes covariate imbalance. In particular, we adapt a sensitivity analysis framework using the percentile bootstrap for a broad class of balancing weights estimators. We prove that the percentile bootstrap procedure can, with only minor modifications, yield valid confidence intervals for causal effects under restrictions on the level of unmeasured confounding. We also propose an amplification—a mapping from a one-dimensional sensitivity analysis to a higher dimensional sensitivity analysis—to allow for interpretable sensitivity parameters in the balancing weights framework. We illustrate our method through extensive real data examples.