Research map / Probabilistic and scientific modeling / Treatment effects
Longitudinal Targeted Minimum Loss-based Estimation with Temporal-Difference Heterogeneous Transformer
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Deep LTMLE, a decoder-only transformer with heterogeneous type embeddings trained by temporal-difference learning, followed by a TMLE targeting step to estimate counterfactual survival under dynamic treatment policies with valid confidence intervals.
Problem
Estimating counterfactual mean outcomes under dynamic longitudinal treatment policies in high-dimensional, non-Markovian time-series data, where existing LTMLE regressions are hard to scale and errors propagate backward through time.
Approach
A temporal-difference heterogeneous-token transformer (TDHT) jointly estimates all Q_t and propensity scores in one non-sequential model, then a one-dimensional logit fluctuation with a single shared epsilon across time points performs TMLE targeting to solve the efficient influence function and yield confidence intervals.
Key results
- On complex synthetic survival data with tau=30, Deep LTMLE RMSE 0.0533 vs LTMLE (SL) 0.0545 and LTMLE (GLM) 0.1381, with coverage 0.75 vs 1.00 for LTMLE variants.
- On semi-synthetic CIRCS data with unmeasured confounding at tau=30, LTMLE (SL) coverage dropped to 0.25 while Deep LTMLE kept nominal coverage (1.00).
- Deep LTMLE ran in 116 s at tau=30 on complex synthetic data versus 2122 s for LTMLE (SL) on CPU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Deep LTMLE instead of LTMLE (SL) | Complex synthetic survival estimation · Complex synthetic survival, τ = 20 and τ = 30 | RMSE: 0.0344 vs 0.0332; 0.0545 vs 0.0533 | Helped |
| Use Deep LTMLE instead of LTMLE (SL) | Complex synthetic survival estimation · Complex synthetic survival, τ = 10 | RMSE: 0.0185 vs 0.0263 | Hurt |
| Use Deep LTMLE instead of LTMLE (SL) | Semi-synthetic survival with unmeasured confounding · Semi-synthetic survival, unmeasured confounding, τ = 10, 20, 30 | Bias: 0.0075 vs -0.0002; 0.0341 vs 0.0108; 0.0574 vs 0.0041 | Helped |
| Use Deep LTMLE instead of LTMLE (SL) | Semi-synthetic survival with unmeasured confounding · Semi-synthetic survival, unmeasured confounding, τ = 10, 20, 30 | Coverage: 0.70 -> 1.00; 0.45 -> 0.95; 0.25 -> 1.00 | Helped |
| Use Deep LTMLE instead of LTMLE (SL) | Simple synthetic survival estimation · Simple synthetic survival, τ = 10, 20, 30 | RMSE: 0.0203 -> 0.0280; 0.0263 -> 0.0328; 0.0311 -> 0.0710 | Mixed |
| Use Deep LTMLE instead of LTMLE (SL) | Complex synthetic survival computation · Complex synthetic survival, τ = 10, 20, 30 | running time (sec): 271 -> 38; 958 -> 39; 2122 -> 116 | Helped |
| Add sequential targeting (ablation) | Deep LTMLE · Complex synthetic survival, τ = 10, 20, 30 | RMSE: 0.0263 -> 0.0571; 0.0332 -> 0.0379; 0.0533 -> 0.0571 | Hurt |
| Add temporal-difference targeting (ablation) | Deep LTMLE · Complex synthetic survival, τ = 10, 20, 30 | RMSE: 0.0263 -> 0.0218; 0.0332 -> 0.0344; 0.0533 -> 0.0541 | Helped |
| Add sequential targeting (ablation) | Deep LTMLE · Simple synthetic survival, τ = 10, 20, 30 | RMSE: 0.0280 -> 0.0225; 0.0328 -> 0.0295; 0.0710 -> 0.0347 | Helped |
| Add sequential targeting (ablation) | Deep LTMLE · Simple synthetic survival, τ = 10, 20, 30 | Coverage: 0.82 -> 0.91; 0.87 -> 0.91; 0.73 -> 0.92 | Helped |
Surprising findings
- Deep LTMLE remained robust and provided nominal-looking inference even with unmeasured confounding violating sequential randomization in semi-synthetic data.
- DeepACE with added targeting loss failed to solve the efficient influence function and showed notable bias at longer horizons.
Limitations
- Does not yet address visiting processes, competing risks, or continuous time horizons.
- Coverage of Deep LTMLE diminished to 0.75 at tau=30 in complex synthetic data.
- Targeting via additional loss in DeepACE-style approaches is hard to tune; the proposed separated targeting relies on a finite-sample approximation to solving the EIF.
Experimental setup
Datasets: Simple synthetic data (continuous and survival) Complex synthetic survival data Semi-synthetic data from CIRCS covariates CIRCS cohort (13,485 participants)
Benchmarks: Simple synthetic data Complex synthetic survival data Semi-synthetic CIRCS data
Metrics: bias RMSE coverage mean estimated standard error running time
Baselines: LTMLE (GLM) LTMLE (SL) DeepACE
Builds on: LTMLE DeepACE TMLE decoder-only transformer
Closest papers by meaning
- Causal Transformer for Estimating Counterfactual Outcomes (ICML 2022 · similarity 0.85)
- Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data (NeurIPS 2025 · similarity 0.84)
- Model-agnostic meta-learners for estimating heterogeneous treatment effects over time (ICLR 2025 · similarity 0.84)
- Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing (AAAI 2024 · similarity 0.84)
- Conditional Counterfactual Mean Embeddings: Doubly Robust Estimation and Learning Rates (NeurIPS 2026 · similarity 0.83)
- Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring (NeurIPS 2026 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.