Beyond Ignorable Selection: Causal Fusion with Shadow Calibration

Randomized controlled trials (RCTs) provide credible causal evidence but are often limited in size and representativeness, whereas observational studies (OBS) offer broader coverage but may suffer from hidden treatment confounding. Many data-fusion approaches that combine randomized and observational data rely on sample-selection ignorability or require treatment effects to be transportable across sources. We study data fusion when source selection is nonignorable, so source membership may remain associated with potential outcomes after conditioning on observed covariates. We introduce Causal Fusion with Shadow Calibration (CFSC), which uses shadow-variable restrictions to recover target-population outcome laws and calibrate randomized supervision for estimating treatment effects in the OBS target population. CFSC combines the observational treatment–outcome structure with a structured correction supervised by the recovered target-specific RCT signal. Under the stated conditions, we establish identification for target conditional and average treatment effects. In controlled simulations, CFSC remains stable as source selection strengthens and outperforms conventional fusion methods when both biases coexist. Constructed real-data benchmarks also show remarkable mean ATE-reference agreement and treatment-benefit ranking.