# Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputation

arXiv: https://arxiv.org/abs/2605.05125 · HTML: https://mlsanity.com/paper/2605.05125/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 12 of 12)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [LLM-Forest: Ensemble Learning of LLMs with Graph-Augmented Prompts for Data Imputation](https://mlsanity.com/paper/2410.21520/) (2024)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Large Language Models for Missing Data Imputation: Understanding Behavior, Hallucination Effects, and Control Mechanisms](https://mlsanity.com/paper/2603.22332/) (2026)

## Built on by (most cited first, 1 of 1)

- [Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihood](https://mlsanity.com/paper/2609.37664/) (2026)

## Abstract (arXiv)

Target trial emulation (TTE) enables causal questions to be studied with observational data when randomized controlled trials (RCTs) are infeasible. Yet treatment-effect methods often address causal estimation, missingness, and temporal structure separately, limiting their robustness in electronic health records (EHRs), where time-varying confounding and missing-not-at-random (MNAR) biomarkers can reach 50%--80%. We propose a two-stage pipeline for treatment effect estimation from incomplete longitudinal EHRs. First, CausalFlow-T, a directed acyclic graph (DAG)-constrained normalizing flow with long short-term memory (LSTM)-encoded patient history, performs exact invertible counterfactual inference, avoiding approximation errors from variational inference and separating confounding through explicit causal structure. Ablations on four synthetic and one semi-synthetic benchmark with known counterfactuals show that DAG constraints and exact inference address distinct failure modes: neither compensates for the other. Second, because CausalFlow-T requires completed inputs, we introduce an LLM-driven evolutionary imputer that proposes executable imputation operators rather than individual entries, and evaluate it with three large language model (LLM) backends, including two open-source models. Across 30%--80% MNAR missingness, this imputer achieves the best pooled rank over biomarker and causal metrics, leading in point-wise accuracy and temporal extrapolation while preserving average treatment effect (ATE) recovery as statistical baselines degrade. On Swiss primary-care EHRs from adults with type 2 diabetes initiating a GLP-1 receptor agonist or SGLT-2 inhibitor, the pipeline estimates a per-protocol weight-loss difference of -0.98 kg [95% CI -1.01, -0.96] favoring GLP-1 receptor agonists, consistent with randomized evidence and obtained from realistically incomplete real-world EHRs.