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Data Fusion for Partial Identification of Causal Effects
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Proposes a partial identification framework with sensitivity parameters for simultaneous violations of no unmeasured confounding and study exchangeability when fusing RCT and observational data, with doubly robust estimators and breakdown frontier analysis applied to Project STAR.
Problem
Causal effects are not point-identified when both no unobserved confounding in observational data and study exchangeability fail in data fusion of RCT and observational studies; existing methods assume only one fails.
Approach
Introduces two relative sensitivity parameters (rho for unmeasured confounding, gamma for study exchangeability violation), derives identifiable ATE/CATE bounds via min/max, smooths them with a Boltzmann operator, and builds doubly robust EIF-based estimators combined with breakdown frontier plots.
Key results
- On Project STAR, the positive ATE of small classes remains conclusive while study exchangeability violations stay below 5%, even under substantial unmeasured confounding.
- Breakdown frontiers show the positive effect is more robust for students entering kindergarten at age six or older than for those entering before age six.
- Simulations show the conclusive region expands with larger treatment effects and the incompatible region grows with greater unobserved confounding.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase the magnitude of the treatment effect | Synthetic data breakdown frontier · Synthetic data | conclusive-region size | Helped |
| Decrease the magnitude of the treatment effect | Synthetic data breakdown frontier · Synthetic data | conclusive-region size | Hurt |
| Decrease the amount of unobserved confounding | Synthetic data breakdown frontier · Synthetic data | incompatible-region size | Helped |
| Increase the amount of unobserved confounding | Synthetic data breakdown frontier · Synthetic data | incompatible-region size | Hurt |
| Allow simultaneous violations of study exchangeability and no unobserved confounding | Proposed partial identification framework · Project STAR third-grade test scores (population ATE) | robustness of positive ATE: below 5% | Helped |
| Increase study selection bias | Project STAR population ATE analysis · Project STAR third-grade test scores (population ATE) | robustness of positive ATE: over 30 points | Hurt |
| Compare students enrolled at six or older with those enrolled before age six | Project STAR subgroup analysis · Project STAR third-grade test scores (subgroup CATEs) | robustness of positive treatment effect | Helped |
| Use a larger smoothing parameter α | Proposed partial identification estimator · Small-sample estimation | estimator stability | Hurt |
Surprising findings
- The older-entrant subgroup has a larger incompatible region despite a more robust positive effect, which the authors attribute to possible additional unmeasured confounding.
Limitations
- Supports only a single binary treatment and a single experimental and observational dataset
- Incompatibility test uses a simplified resampling that ignores nuisance estimation uncertainty
- Choice of sensitivity parameter values requires domain expertise; large alpha causes instability in small samples
Experimental setup
Datasets: Project STAR
Benchmarks: Project STAR third-grade test scores
Metrics: ATE bounds CATE bounds breakdown frontier conclusive/tentative/inconclusive/incompa 95% confidence intervals
Baselines: Rosenman et al. two-parameter sensitivity analysis for fusion
Builds on: breakdown frontier analysis efficient influence function estimators double machine learning Boltzmann operator
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