Minimax-Regret Estimation of Heterogeneous Treatment Effect with Multi-Site Data

Music City Center 

Estimation of heterogeneous treatment effects plays an essential role in various scientific fields, industries, and policy-making settings. Although many existing methods estimate conditional average treatment effects (CATEs) based on the data from a single population, in practice, researchers often have access to the data collected from multiple sites, whose characteristics differ in unknown ways. While a naive pooled model risks bias, the estimates from site-specific models lack external validity. In this paper, we introduce a robust CATE estimation methodology with multi-site data from heterogeneous populations. We propose a minimax-regret framework that learns a generalizable CATE model by minimizing the worst-case regret over a class of distributions, represented as convex combinations of observed distributions across sites. Using robust optimization, the proposed methodology accounts for distribution shifts in both individual covariates and CATEs across sites. We show that the resulting CATE model has an interpretable closed-form solution, expressed as a weighted average of site-specific CATE models. This result allows researchers to leverage flexible CATE estimation methods across each site, which can then be aggregated to produce the final model. Through simulations and a real-world application, we show that the proposed methodology improves the robustness and generalizability of the existing approaches.

distributional robustness

generalizability

transportability

robust optimization