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Prediction-powered Generalization of Causal Inferences
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Proposes prediction-powered estimators that combine a small RCT with an assumption-free observational study's outcome predictor (via additive bias correction or augmented outcome modeling) to generalize causal effects to a target population.
Problem
Generalizing average potential outcomes from a small randomized trial to a target population with different effect-modifier distributions is statistically infeasible with trial data alone because estimating complex outcome functions from small trials yields high variance and bias.
Approach
Fit a flexible predictor from a large observational study with no assumptions on it, then either correct its predictions with a bias function learned from trial residuals (ABC) or use its predictions as an extra covariate in the trial outcome model (AOM); the bias function is simpler to learn when the OS predictor is good, and the methods remain robust when it is not.
Key results
- Prediction-powered estimators (ABC and AOM) yield significant RMSE improvements over the trial-only OM estimator when the trial is small, the outcome function is complex, and hidden confounding is small.
- AOM retains baseline performance when the observational predictor is pure noise, whereas ABC suffers high RMSE in that case.
- In polynomial-model simulations with n1=200 and 5th-order fits, ABC and OM tie in some settings, while with 1st-order fits ABC achieves much lower MSE (e.g., 0.0001 vs 0.0092 with no confounding and small noise).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,0.1²), β ~ N(0,1), λ=1; 1st order poly. fit | MSE: .0092 -> .0001 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,0.1²), β ~ N(0,1), λ=1; 5th order poly. fit | MSE: .0002 -> .0002 | No clear effect |
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 1, ε ~ N(0,0.1²), β ~ N(0,1), λ=1; 1st order poly. fit | MSE: .0183 -> .0087 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 1, ε ~ N(0,0.1²), β ~ N(0,1), λ=1; 5th order poly. fit | MSE: .0148 -> .0148 | No clear effect |
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,1), λ=1; 1st order poly. fit | MSE: .0054 -> .0044 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,1), λ=1; 5th order poly. fit | MSE: .0066 -> .0066 | No clear effect |
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,2²), λ=1; 1st order poly. fit | MSE: .0082 -> .0044 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,2²), λ=1; 5th order poly. fit | MSE: .0066 -> .0066 | No clear effect |
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,2²), λ=2; 1st order poly. fit | MSE: .0127 -> .0048 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 0, ε ~ N(0,2²), β ~ N(0,2²), λ=2; 5th order poly. fit | MSE: .0151 -> .0151 | No clear effect |
| Replace the 1st order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 1, ε ~ N(0,2²), β ~ N(0,2²), λ=2; 1st order poly. fit | MSE: .0141 -> .0060 | Helped |
| Replace the 5th order polynomial outcome model with additive bias correction | Target-population mean estimation · γ = 1, ε ~ N(0,2²), β ~ N(0,2²), λ=2; 5th order poly. fit | MSE: .0139 -> .0139 | No clear effect |
Surprising findings
- With high hidden confounding and complex bias functions, the prediction-powered estimators provide no significant gain over the trial-only baseline.
- The IPW estimator performs worst due to high variance of propensity weights.
Limitations
- Results rely on finite-sample approximations valid for large target sample size n0.
- Gains vanish when the bias function is complex, e.g., under large hidden confounding or complex outcome functions.
- Doubly-robust estimators and representation-based methods are only sketched as future work.
Experimental setup
Datasets: synthetic data from Gaussian process and polynomial data-generating processes
Benchmarks: synthetic data-generating processes (1200 GP scenarios)
Metrics: RMSE squared bias variance MSE
Baselines: OM (trial-only outcome model) OS-OM (observational predictor alone) IPW doubly-robust estimators
Builds on: prediction-powered inference outcome model generalization estimator (Degtiar & Rose style)
Closest papers by meaning
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- An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation (NeurIPS 2025 · similarity 0.87)
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