Entropy Balancing for Generalizing Causal Estimation with Summary-level Information

In this paper, we focus on estimating the average treatment effect (ATE) of a target population when individual-level data from a source population and summary-level data (e.g., first or second moments of certain covariates) from the target population are available. In the presence of heterogeneous treatment effect, the ATE of the target population can be different from that of the source population when distributions of treatment effect modifiers are dissimilar in these two populations, a phenomenon also known as covariate shift. Many methods have been developed to adjust for covariate shift, but most require individual covariates from the target population. We develop a weighting approach based on summary-level information from the target population to adjust for possible covariate shift in effect modifiers. In particular, weights of the treated and control groups within the source population are calibrated by the summary-level information of the target population. In addition, our approach also seeks additional covariate balance between the treated and control groups in the source population. We study the asymptotic behavior of the corresponding weighted estimator for the target population ATE under a wide range of conditions. The theoretical implications are confirmed in simulation studies and a real data application.