Entropy Balancing for Causal Generalization with Target Sample Summary Information

TL;DR

This paper introduces a novel weighting method that leverages summary-level data from a target population to adjust for covariate shift in estimating the average treatment effect, enabling causal inference when individual data from the target is unavailable.

Contribution

We develop a weighting approach that uses summary statistics from the target population to correct for covariate shift in causal effect estimation, extending existing methods to scenarios with limited target data.

Findings

The proposed method effectively adjusts for covariate shift in simulations.

The estimator demonstrates desirable asymptotic properties.

Application to real data confirms practical utility.

Abstract

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 a representative target sample. We develop a weighting approach based on 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.