Estimating Treatment Effect across Heterogeneous Data Sources: An Instrumental Variable Approach

To estimate treatment effect in the presence of unmeasured confounders, instrumental variable (IV) approachs have achieved promising advances, but have strict requirements on data collection. To alleviate this issue, the two-sample IV approach is proposed by fusing estimations across two complementary and homogeneous data sources. However, the homogeneous assumption, i.e., data sources share the same joint distribution, is restrictive for realistic cases. Motivated by this, this paper proposes a novel IV problem named Shifted Two-Sample IV (S2IV), which aims to estimate the treatment effect across heterogeneous data sources, i.e., the joint distributions of different data sources are skewed differently. Theoretically, we first show that solving the S2IV problem is equivalent to learning the unbiased treatment-IV relationship from the joint of data sources. To this end, we propose a Recovery-Aided Transferable Instrumental Variable (RATIV) framework by transferring the instruments from one data source and recovering the treatments on the other data source at the same time. Extensive experimental results on both synthetic and real-world datasets verify the effectiveness of our method.