Causal-ICM: A Data Fusion Framework For Heterogeneous Treatment Effect Estimation With Multi-Task Gaussian Processes

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, may provide stronger external validity through larger and more representative samples but can suffer from compromised internal validity due to unmeasured confounding. Motivated by these complementary characteristics, we propose a novel Bayesian nonparametric approach, Causal-ICM, leveraging multi-task Gaussian processes to integrate data from both RCTs and observational studies. In particular, we introduce a parameter that controls the degree of borrowing between the datasets and prevents the observational dataset from dominating the estimation. We propose a data-adaptive procedure for choosing the optimal value of the parameter. Causal-ICM outperforms other data fusion methods in point estimation across the covariate support of the observational study and provides principled uncertainty quantification for the estimated treatment effects. We demonstrate the robust performance of Causal-ICM in diverse scenarios through multiple simulation studies and a real-world study.

💡 Research Summary

The paper introduces Causal‑ICM, a Bayesian non‑parametric framework that fuses randomized controlled trial (RCT) data with observational study data to estimate heterogeneous treatment effects (HTE) across a target population. The authors recognize that RCTs provide high internal validity but limited external validity due to strict eligibility criteria, while observational studies offer broader representativeness but suffer from unmeasured confounding. To combine the strengths of both sources, Causal‑ICM models the outcome surfaces for each study as separate tasks within a multi‑task Gaussian process (GP) framework.

Each task corresponds to the expected outcome under treatment (A=1) for the RCT and the observational study, respectively. A 2×2 matrix‑valued kernel captures the correlation between the two tasks, enabling information sharing while preserving the unbiased nature of the RCT. A borrowing parameter ρ controls the degree of information transfer: ρ=0 yields independent GPs, ρ≈1 forces near‑complete borrowing. The authors propose a data‑adaptive procedure—based on marginal likelihood or cross‑validation—to select ρ automatically for a given dataset, thereby preventing the observational data from overwhelming the RCT when it is heavily biased.

The methodological foundation rests on standard causal assumptions (consistency, conditional exchangeability for treatment and selection, positivity, and covariate‑distribution alignment). Under these assumptions, the conditional average treatment effect τ(x) equals the RCT contrast ω_e(x) within the RCT covariate support. Outside this support, the observational data can inform the GP posterior, but the borrowing parameter and the GP’s posterior variance naturally inflate uncertainty in regions with little RCT evidence. The authors also provide theoretical guarantees that the borrowing mechanism limits the influence of biased observational information, ensuring calibrated uncertainty.

Implementation follows a T‑learner strategy: separate GP models estimate E