Research map / Probabilistic and scientific modeling / Treatment effects
ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference
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Proposes a framework that converts ODE discovery methods into longitudinal heterogeneous treatment effect estimators, instantiated as INSITE (SINDy-based closed-form ODEs with per-patient parameter fine-tuning).
Problem
Estimating individualized longitudinal treatment effects under time-dependent confounding with interpretable models, while existing methods rely on black-box neural networks.
Approach
Treat treatment effects as a closed-form ODE discovered from trajectories: learn a population ODE (one per categorical treatment) with SINDy, then fine-tune per-patient constants with a regularization toward population constants, yielding interpretable counterfactual predictions and a new set of identification assumptions.
Key results
- INSITE achieves 6-step counterfactual normalized RMSE of 0.02 on the A-class dataset, versus 0.11 for A-SINDy and about 0.90 for the best neural LTE baseline (CT).
- On the Cancer PKPD dataset, INSITE reaches 0.79 normalized RMSE versus 0.92 for CRN and 1.07 for CT at 6-step prediction.
- INSITE keeps low error across increasing time-dependent confounding (gamma), indicating it can still discover good approximating equations under low overlap.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use INSITE instead of the strongest reported baseline | Longitudinal treatment effect prediction · Synthetic PKPD datasets A-D and Cancer PKPD | 6-step counterfactual normalized RMSE: INSITE achieves the lowest test counterfactual normalized RMSE across all methods | Helped |
| Add individualized fine-tuning of patient-specific ODE constants (ablation) | INSITE · Synthetic longitudinal treatment-effect datasets | counterfactual prediction performance | Helped |
| Add separate ODEs per categorical treatment (ablation) | INSITE and adapted ODE discovery methods · Synthetic longitudinal treatment-effect datasets | counterfactual prediction performance | Helped |
Surprising findings
- Neural longitudinal treatment effect models can be outperformed by a closed-form ODE model with per-patient fine-tuning, even though the ODE library is misspecified for the Cancer PKPD and classes A-D datasets.
Limitations
- Requires a correct candidate function library; misspecified libraries degrade performance.
- ODE discovery works best for sparse equations; non-sparse equations are less interpretable and harder to recover.
- Recovered ODEs are noise-free, so noise is not modelled explicitly in the equation.
Experimental setup
Datasets: synthetic PKPD datasets (classes A-D) Cancer PKPD synthetic dataset
Benchmarks: synthetic PKPD datasets A-D Cancer PKPD
Metrics: counterfactual normalized RMSE tau-step ahead prediction RMSE
Baselines: MSM RMSN CRN G-Net CT A-SINDy A-WSINDy
Builds on: SINDy WSINDy Marginal Structural Models Counterfactual Recurrent Networks
Closest papers by meaning
- Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time (NeurIPS 2026 · similarity 0.87)
- Model-agnostic meta-learners for estimating heterogeneous treatment effects over time (ICLR 2025 · similarity 0.87)
- Hybrid$^2$ Neural ODE Causal Modeling and an Application to Glycemic Response (ICML 2024 · similarity 0.87)
- Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation (ICLR 2024 · similarity 0.87)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.86)
- Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments (ICML 2024 · similarity 0.86)
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