FAST: a Fused and Accurate Shrinkage Tree for Heterogeneous Treatment Effects Estimation

This paper proposes a novel strategy for estimating the heterogeneous treatment effect called the Fused and Accurate Shrinkage Tree ($\mathrm{FAST}$). Our approach utilizes both trial and observational data to improve the accuracy and robustness of the estimator. Inspired by the concept of shrinkage estimation in statistics, we develop an optimal weighting scheme and a corresponding estimator that balances the unbiased estimator based on the trial data with the potentially biased estimator based on the observational data. Specifically, combined with tree-based techniques, we introduce a new split criterion that utilizes both trial data and observational data to more accurately estimate the treatment effect. Furthermore, we confirm the consistency of our proposed tree-based estimator and demonstrate the effectiveness of our criterion in reducing prediction error through theoretical analysis. The advantageous finite sample performance of the $\mathrm{FAST}$ and its ensemble version over existing methods is demonstrated via simulations and real data analysis.