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Generalizing Causal Effects from Randomized Controlled Trials to Target Populations across Diverse Environments
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Proposes Two-Stage Doubly Robust (2SDR), which uses shadow variables to impute covariates of the separating set that are observed in only one of the RCT and target observational datasets, then runs a doubly robust TATE estimator.
Problem
Generalizing RCT treatment effects to target populations under environmental shift when separating-set covariates are missing from one of the two datasets, violating the standard full-observability assumption.
Approach
Relaxes the fully-observed separating-set assumption to partial observability across the two datasets, identifies the TATE using shadow variables to recover missing covariates, and estimates it with a two-stage doubly robust procedure (shadow variable selection and imputation, then doubly robust TATE estimation).
Key results
- On synthetic data with nR=2000, nO=10000 (Setting 1), 2SDR achieves MAE 0.268 vs 0.539 for the best baseline (G-formula Imp / ACW Imp).
- On ACTG, 2SDR achieves MAE 0.011 (x10^-3 scaled) vs 0.032 for the RCT estimate and 0.035 for G-formula.
- On JTPA, 2SDR achieves MAE 0.992 (x10^-3 scaled) vs 1.064 for IPSW and 1.366 for RCT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use 2SDR instead of G-FORMULAImp | Low-dimensional synthetic, nR = 2000, nO = 10000, Setting 1 · Low-dimensional synthetic, nR = 2000, nO = 10000, Setting 1 | MAE: 0.539±0.305 -> 0.268±0.212 | Helped |
| Use 2SDR instead of G-FORMULA | Low-dimensional synthetic, nR = 2000, nO = 10000, Setting 2 · Low-dimensional synthetic, nR = 2000, nO = 10000, Setting 2 | MAE: 0.659±0.266 -> 0.284±0.224 | Helped |
| Use 2SDR instead of G-FORMULAImp | Low-dimensional synthetic, nR = 1000, nO = 10000, Setting 1 · Low-dimensional synthetic, nR = 1000, nO = 10000, Setting 1 | MAE: 0.614±0.355 -> 0.423±0.264 | Helped |
| Use 2SDR instead of G-FORMULAImp | Low-dimensional synthetic, nR = 1000, nO = 10000, Setting 2 · Low-dimensional synthetic, nR = 1000, nO = 10000, Setting 2 | MAE: 0.998±0.450 -> 0.431±0.296 | Helped |
| Use 2SDR instead of AIPSWImp | Low-dimensional synthetic, nR = 500, nO = 10000, Setting 1 · Low-dimensional synthetic, nR = 500, nO = 10000, Setting 1 | MAE: 0.960±0.625 -> 0.533±0.387 | Helped |
| Use 2SDR instead of ACWImp | Low-dimensional synthetic, nR = 500, nO = 10000, Setting 2 · Low-dimensional synthetic, nR = 500, nO = 10000, Setting 2 | MAE: 1.789±0.946 -> 0.489±0.327 | Helped |
| Use 2SDR instead of RCT | ACTG · ACTG | MAE: 0.032±0.016 -> 0.011±0.010 | Helped |
| Use 2SDR instead of IPSW | JTPA · JTPA | MAE: 1.064±0.519 -> 0.992±0.490 | Helped |
Surprising findings
- Imputation improves regression-based baselines in Setting 1 but not in Setting 2, because imputation errors accumulate in the RCT-side regression.
- Most baselines perform worse than simply using the RCT average treatment effect on the real-world datasets when separating-set covariates are missing.
Limitations
- Shadow variable selection becomes time-consuming in extremely high-dimensional covariate settings.
- Assumption 3.2 is hard to ensure when the number of partially observable covariates exceeds the number of common covariates.
Experimental setup
Datasets: ACTG 175 JTPA Synthetic low-dimensional dataset Synthetic high-dimensional dataset
Benchmarks: ACTG 175 JTPA Synthetic low-dimensional dataset
Metrics: MAE mean standard deviation
Baselines: RCT IPSW Calibration Weighting G-formula AIPSW ACW IPSWImp CWImp G-formulaImp AIPSWImp ACWImp
Builds on: Doubly robust TATE estimation (Dahabreh et al., 2019) Shadow variable framework (d'Haultfoeuille, 2010; Miao et al., 2024) Adaptive Lasso (Zou, 2006) Randomized Conditional Independence Test (Strobl et al., 2019)
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