Entropy balancing for causal generalization with target sample summary 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 the 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 a representative target sample. We develop a weighting approach based on the summary-level information from the target sample to adjust for possible covariate shift in effect modifiers. In particular, weights of the treated and control groups within a source sample are calibrated by the summary-level information of the target sample. Our approach also seeks additional covariate balance between the treated and control groups in the source sample. 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.

Automated summary

This paper discusses how to estimate the average treatment effect (ATE) of a target population with both individual-level data from a source population and summary-level data from the target population. When there is heterogeneity in treatment effects, the ATE of the target population can differ from that of the source population due to covariate shift. Existing methods to adjust for covariate shift typically require individual covariates from a representative target sample. We propose a weighting approach using summary-level information from the target sample to adjust for possible covariate shift and achieve covariate balance in the source sample. Theoretical implications are supported by simulation studies and real-data application.