Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment

Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose CALM (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source's features into a common representation space. OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate CALM in two forms: a closed-form linear version, CALM-Lin, and a neural representation-learning version, CALM-NN. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while CALM-NN wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies CALM-NN delivers the largest gains over the trial-only baseline.