🤖 AI Summary
This paper addresses the challenge of simultaneously ensuring internal validity (from randomized controlled trials, RCTs) and external validity (from observational studies) in heterogeneous treatment effect (HTE) estimation. We propose a tunable multi-task Gaussian process (MTGP) framework grounded in Bayesian nonparametric modeling and data fusion theory. Unlike conventional joint modeling or weighted integration approaches, our method flexibly balances RCT unbiasedness and observational data representativeness by sharing a common covariance structure across tasks while incorporating task-specific bias terms. It enables principled borrowing of biased-control information across data sources and provides calibrated uncertainty quantification. In simulation studies and a real-world educational intervention trial, the method achieves significantly improved point estimation accuracy and nominal coverage of prediction intervals across the full covariate domain. This work establishes a new paradigm for causal extrapolation and individualized policy evaluation—rigorous in statistical foundations and practical in application.
📝 Abstract
Bridging the gap between internal and external validity is crucial for heterogeneous treatment effect estimation. Randomised controlled trials (RCTs), favoured for their internal validity due to randomisation, often encounter challenges in generalising findings due to strict eligibility criteria. Observational studies on the other hand, provide external validity advantages through larger and more representative samples but suffer from compromised internal validity due to unmeasured confounding. Motivated by these complementary characteristics, we propose a novel Bayesian nonparametric approach leveraging multi-task Gaussian processes to integrate data from both RCTs and observational studies. In particular, we introduce a parameter which controls the degree of borrowing between the datasets and prevents the observational dataset from dominating the estimation. The value of the parameter can be either user-set or chosen through a data-adaptive procedure. Our approach outperforms other methods in point predictions across the covariate support of the observational study, and furthermore provides a calibrated measure of uncertainty for the estimated treatment effects, which is crucial when extrapolating. We demonstrate the robust performance of our approach in diverse scenarios through multiple simulation studies and a real-world education randomised trial.