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Model-agnostic meta-learners for estimating heterogeneous treatment effects over time
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Proposes model-agnostic meta-learners (PI-HA, PI-RA, RA, IPW, DR) for heterogeneous treatment effects over time, plus an inverse-variance-weighted DR-learner (IVW-DR) that stabilizes the doubly robust loss under low overlap.
Problem
Estimating heterogeneous treatment effects (CAPO/CATE) over time from observational longitudinal data, where time-varying confounding, growing histories, and low overlap make estimation hard, and existing methods are mostly model-based.
Approach
Model-agnostic meta-learners for time-varying HTEs built on history, regression, propensity, and doubly robust adjustments, with a novel time-varying inverse-variance weighting of the DR loss that downweights extreme products of inverse propensities.
Key results
- On simulated D1, IVW-DR-learner achieves RMSE 1.29 at tau=1 versus 1.39 for DR-learner, and 1.28 vs 5.70 at tau=4 (x10 scale).
- On D1 at tau=2, DR-learner RMSE 14.60 and IPW 14.77 while IVW-DR achieves 2.40, showing stabilization under low overlap.
- On real MIMIC-III data, IVW-DR-learner achieves the best factual RMSE for tau=1,2,3 (0.62, 0.67, 0.71).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IVW-DR instead of DR | CATE estimation · D1, τ=2–4 | RMSE (× 10): 14.60 ± 6.50 -> 2.40 ± 0.43; 6.82 ± 2.45 -> 2.36 ± 1.12; 5.70 ± 3.84 -> 1.28 ± 0.36 | Mixed |
| Use IVW-DR instead of DR | CATE estimation · D2, τ=0–4 | RMSE (× 10): 0.14 ± 0.07 -> 0.11 ± 0.07; 0.42 ± 0.32 -> 0.32 ± 0.31; 0.52 ± 0.09 -> 0.57 ± 0.24; 1.84 ± 0.89 -> 0.80 ± 0.46; 2.69 ± 0 | Mixed |
| Use IVW-DR instead of DR | CAPO estimation · MIMIC III, τ=0–3 | Factual RMSE: 0.52 ± 0.09 -> 0.39 ± 0.03; 0.72 ± 0.03 -> 0.62 ± 0.01; 0.97 ± 0.43 -> 0.67 ± 0.01; 1.00 ± 0.43 -> 0.71 ± 0.02 | Mixed |
| Use IVW-DR instead of DR | CATE estimation · D3, τ=1, low overlap | RMSE | Helped |
| Use the two-stage RA, IPW, DR, or IVW-DR learner rather than plug-in learners | CATE estimation · D1 and D2, τ=0–4 | RMSE (× 10) | Helped |
| Use PI-HA rather than the other meta-learners | CATE estimation · D1 and D2, τ>0 | RMSE (× 10) | Hurt |
| Use RA rather than IPW | CATE estimation · D1, τ>0 | RMSE (× 10) | Helped |
| Use IPW rather than RA | CATE estimation · D2 | RMSE (× 10) | Mixed |
| Increase prediction horizon while using IPW or DR | IPW-learner and DR-learner · D1 and MIMIC III | RMSE | Hurt |
Surprising findings
- PI-HA-learner, despite being theoretically biased under time-varying confounding, performs similarly to PI-RA on real-world data, attributed to lower finite-sample variance.
- IPW and DR learners become highly unstable at intermediate horizons on D1 due to products of small propensities.
Limitations
- Specific model architectures were not studied; transformer instantiation is proof-of-concept.
- Limited to discrete time; continuous-time extension left open.
- Real-world evaluation uses factual RMSE as a proxy, which is an imperfect measure of causal performance.
Experimental setup
Datasets: simulated datasets D1, D2, D3 MIMIC-III
Benchmarks: simulated datasets D1-D3 MIMIC-III
Metrics: RMSE of CATE factual RMSE
Baselines: PI-HA-learner PI-RA-learner RA-learner IPW-learner DR-learner R-learner
Builds on: R-learner DR-learner IVW-DR-learner (static setting) G-computation marginal structural models
Closest papers by meaning
- Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments (ICML 2024 · similarity 0.90)
- Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data (NeurIPS 2025 · similarity 0.89)
- A Meta-learner for Heterogeneous Effects in Difference-in-Differences (ICML 2025 · similarity 0.89)
- ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference (ICLR 2024 · similarity 0.87)
- Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects (ICML 2024 · similarity 0.86)
- AutoCATE: End-to-End, Automated Treatment Effect Estimation (ICML 2025 · similarity 0.86)
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