# Predicting the impact of treatments over time with uncertainty aware neural differential equations

arXiv: https://arxiv.org/abs/2202.11987 · HTML: https://mlsanity.com/paper/2202.11987/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 21 of 21)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Generative ODE Modeling with Known Unknowns](https://mlsanity.com/paper/2003.10775/) (2020)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)
- [Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes](https://mlsanity.com/paper/2006.09914/) (2020)
- [Characterization of Overlap in Observational Studies](https://mlsanity.com/paper/1907.04138/) (2019)
- [Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series](https://mlsanity.com/paper/2111.13037/) (2021)
- [Adaptive Path-Integral Autoencoder: Representation Learning and Planning for Dynamical Systems](https://mlsanity.com/paper/1807.02128/) (2018)
- [Deep Ensemble Tensor Factorization for Longitudinal Patient Trajectories Classification](https://mlsanity.com/paper/1811.10501/) (2018)

## Built on by (most cited first, 23 of 23)

- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Trajectory Flow Matching with Applications to Clinical Time Series Modeling](https://mlsanity.com/paper/2410.21154/) (2024)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [medDreamer: Model-Based Reinforcement Learning with Latent Imagination on Complex EHRs for Clinical Decision Support](https://mlsanity.com/paper/2505.19785/) (2025)
- [Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems](https://mlsanity.com/paper/2403.00178/) (2024)
- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [Deep Counterfactual Estimation with Categorical Background Variables](https://mlsanity.com/paper/2210.05811/) (2022)
- [Uncertainty-Aware Optimal Treatment Selection for Clinical Time Series](https://mlsanity.com/paper/2410.08816/) (2024)
- [Anamnesic Neural Differential Equations with Orthogonal Polynomial Projections](https://mlsanity.com/paper/2303.01841/) (2023)
- [CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Prediction](https://mlsanity.com/paper/2308.09735/) (2023)
- [Learning predictive checklists from continuous medical data](https://mlsanity.com/paper/2211.07076/) (2022)
- [multivariateGPT: a decoder-only transformer for multivariate categorical and numeric data](https://mlsanity.com/paper/2505.21680/) (2025)
- [Conservative Continuous-Time Treatment Optimization](https://mlsanity.com/paper/2603.16789/) (2026)
- [GDBN: a Graph Neural Network Approach to Dynamic Bayesian Network](https://mlsanity.com/paper/2302.10804/) (2023)
- [Continuous Time Evidential Distributions for Irregular Time Series](https://mlsanity.com/paper/2307.13503/) (2023)
- [Learning Predictive Checklists with Probabilistic Logic Programming](https://mlsanity.com/paper/2411.16790/) (2024)
- [Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2511.16427/) (2025)
- [Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time](https://mlsanity.com/paper/2604.26070/) (2026)
- [From Static Risk to Dynamic Trajectories: Toward World-Model-Inspired Clinical Prediction](https://mlsanity.com/paper/2605.16927/) (2026)

## Abstract (arXiv)

Predicting the impact of treatments from observational data only still represents a majorchallenge despite recent significant advances in time series modeling. Treatment assignments are usually correlated with the predictors of the response, resulting in a lack of data support for counterfactual predictions and therefore in poor quality estimates. Developments in causal inference have lead to methods addressing this confounding by requiring a minimum level of overlap. However,overlap is difficult to assess and usually notsatisfied in practice. In this work, we propose Counterfactual ODE (CF-ODE), a novel method to predict the impact of treatments continuously over time using Neural Ordinary Differential Equations equipped with uncertainty estimates. This allows to specifically assess which treatment outcomes can be reliably predicted. We demonstrate over several longitudinal data sets that CF-ODE provides more accurate predictions and more reliable uncertainty estimates than previously available methods.