Title: Adaptive Marginal Sensitivity with Limited RCT Data for CATE Estimation
Primary area: causal reasoning
Keywords: Marginal Sensitivity Model; Bayesian Inference; Unmeasured Confounding; Treatment Effect Estimation

Abstract: The conditional average treatment effect (CATE) is pivotal for personalized decision-making across numerous domains. While observational studies (OBS) are a primary data source for estimating CATE, they are susceptible to bias from unmeasured confounding. The marginal sensitivity model (MSM) addresses this by quantifying the robustness of causal conclusions to such confounding via a sensitivity parameter, Γ. However, a significant limitation of MSM is the need for researchers to subjectively specify Γ, which lacks a data-driven basis and undermines the reliability of inferences. Recent methods that use randomized controlled trial (RCT) data to calibrate Γ are promising but critically depend on having a large RCT sample, which is often unavailable in practice. To overcome this limitation, we propose the Bayesian Marginal Sensitivity Calibration (BMSC) framework. BMSC learns the sensitivity parameter Γ directly from fused RCT and OBS data, shifting the paradigm from subjective specification to data-driven estimation. Our approach constructs a CATE envelope from OBS, calibrates Γ by assessing the alignment with RCT estimates, and produces robust CATE intervals with valid coverage guarantees. Theoretical analysis and extensive experiments show that BMSC provides sharper, more accurate intervals than methods using subjective Γ values, and remains effective even when the RCT sample size is very small. This work provides a practical and robust solution for sensitivity analysis in real-world settings with limited experimental data.

TL;DR: This paper proposes a Bayesian framework to calibrate confounding sensitivity.