Treatment Effect Estimation with Unmeasured Confounders in Data Fusion

In the presence of unmeasured confounders, we address the problem of treatment effect estimation from data fusion, that is, multiple datasets collected under different treatment assignment mechanisms. For example, marketers may assign different advertising strategies to the same products at different times/places. To handle the bias induced by unmeasured confounders and data fusion, we propose to separate the observational data into multiple groups (each group with an independent treatment assignment mechanism), and then explicitly model the group indicator as a Latent Group Instrumental Variable (LatGIV) to implement IV-based Regression. In this paper, we conceptualize this line of thought and develop a unified framework to (1) estimate the distribution differences of observed variables across groups; (2) model the LatGIVs from the different treatment assignment mechanisms; and (3) plug LatGIVs to estimate the treatment-response function. Empirical results demonstrate the advantages of the LatGIV compared with state-of-the-art methods.