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Adaptive Data-Borrowing for Improving Treatment Effect Estimation using External Controls
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Proposes an influence-function-based ranking of external control samples and a MSE-minimizing selection of top-K borrowed controls, combined with a semiparametric efficient AIPW-style estimator for RCT treatment effects.
Problem
Estimating average treatment effects in small RCTs by borrowing external control data, where exchangeability between external controls and RCT controls may be violated, causing bias and efficiency loss.
Approach
Quantify per-sample comparability of external controls via influence functions on an RCT-control outcome model, build nested top-K borrowing sets, derive a semiparametric efficient fused estimator for a borrowed set, and choose K by minimizing estimated MSE (bias-variance trade-off) under possible exchangeability violation.
Key results
- On the linear simulation at Top-K=250, the proposed estimator has |bias| 0.0252 and std 0.0807, versus 0.0665 bias and 0.1023 std for the adaptive lasso approach; it has lower std than AIPW (0.1075).
- On the NSW & PSID real data, the proposed method achieves |bias| 0.0026 at Top-K=30 and 0.0013 at Top-K=35, versus lasso's 0.0152 and 0.0174 at those K.
- The full borrowing estimator has large bias (0.4492 in nonlinear simulation) because it integrates biased external controls, motivating selective borrowing.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · Linear, Top-K=200 | std: 0.1039 -> 0.0808 | Helped |
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · Linear, Top-K=200 | |bias|: 0.0851 -> 0.0307 | Helped |
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · Nonlinear, Top-K=300 | std: 0.2280 -> 0.2128 | Helped |
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · Nonlinear, Top-K=300 | |bias|: 0.1709 -> 0.1028 | Helped |
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · NSW & PSID, Top-K=35 | std: 0.0140 -> 0.0130 | Helped |
| Use influence-score-ranked borrowing instead of adaptive-lasso borrowing | Treatment effect estimation with external controls · NSW & PSID, Top-K=35 | |bias|: 0.0174 -> 0.0013 | Helped |
| Borrow all external controls instead of selecting a subset | AIPW treatment effect estimation · Linear | |bias|: 0.0951 | Hurt |
| Increase the number of influence-ranked external controls borrowed | Influence-based borrowing · Synthetic datasets | MSE | Mixed |
Surprising findings
- In the nonlinear simulation at Top-K=10, the lasso approach has lower absolute bias (0.0130) than the proposed method (0.0179), and at Top-K=300 the proposed method's bias rises to 0.1028.
Limitations
- Computing the Hessian for influence functions may be computationally burdensome for large models such as deep neural networks.
- Efficiency theory requires nuisance parameters to be estimated at rates faster than n^{-1/4}.
- Experiments are limited to small simulated data and one small real-data application (NSW/PSID).
Experimental setup
Datasets: NSW (National Supported Work) program data PSID (Population Survey of Income Dynamics) synthetic linear and nonlinear simulation data
Benchmarks: NSW & PSID real-data application synthetic linear simulation synthetic nonlinear simulation
Metrics: standard deviation absolute bias MSE
Baselines: AIPW without borrowing full borrowing AIPW adaptive lasso-based borrowing (Gao et al. 2025)
Builds on: AIPW estimator adaptive lasso borrowing (Gao et al. 2025) influence functions (Cook and Weisberg 1980)
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