# Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time

arXiv: https://arxiv.org/abs/2306.04255 · HTML: https://mlsanity.com/paper/2306.04255/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 69 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Predicting the impact of treatments over time with uncertainty aware neural differential equations](https://mlsanity.com/paper/2202.11987/) (2022)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)
- [Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosis](https://mlsanity.com/paper/1705.05267/) (2017)
- [Policy Analysis using Synthetic Controls in Continuous-Time](https://mlsanity.com/paper/2102.01577/) (2021)
- [G-Net: A Deep Learning Approach to G-computation for Counterfactual Outcome Prediction Under Dynamic Treatment Regimes](https://mlsanity.com/paper/2003.10551/) (2020)
- [Effective Sample Size, Dimensionality, and Generalization in Covariate Shift Adaptation](https://mlsanity.com/paper/2010.01184/) (2020)
- [Doubly robust treatment effect estimation with missing attributes](https://mlsanity.com/paper/1910.10624/) (2019)
- [Efficient nonparametric causal inference with missing exposure information](https://mlsanity.com/paper/1802.08952/) (2018)
- [Disentangled Counterfactual Recurrent Networks for Treatment Effect Inference over Time](https://mlsanity.com/paper/2112.03811/) (2021)
- [To Impute or not to Impute? Missing Data in Treatment Effect Estimation](https://mlsanity.com/paper/2202.02096/) (2022)
- [DeepJoint: Robust Survival Modelling Under Clinical Presence Shift](https://mlsanity.com/paper/2205.13481/) (2022)
- [Understanding the Impact of Competing Events on Heterogeneous Treatment Effect Estimation from Time-to-Event Data](https://mlsanity.com/paper/2302.12718/) (2023)
- [Treatment-Response Models for Counterfactual Reasoning with Continuous-time, Continuous-valued Interventions](https://mlsanity.com/paper/1704.02038/) (2017)
- [Mixed effects models for healthcare longitudinal data with an informative visiting process: a Monte Carlo simulation study](https://mlsanity.com/paper/1808.00419/) (2018)
- [Balancing Suspense and Surprise: Timely Decision Making with Endogenous Information Acquisition](https://mlsanity.com/paper/1610.07505/) (2016)

## Built on by (most cited first, 15 of 15)

- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Model-agnostic meta-learners for estimating heterogeneous treatment effects over time](https://mlsanity.com/paper/2407.05287/) (2024)
- [IGC-Net for conditional average potential outcome estimation over time](https://mlsanity.com/paper/2405.21012/) (2024)
- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Stabilized Neural Prediction of Potential Outcomes in Continuous Time](https://mlsanity.com/paper/2410.03514/) (2024)
- [Adaptive Instrument Design for Indirect Experiments](https://mlsanity.com/paper/2312.02438/) (2023)
- [Partially Stochastic Infinitely Deep Bayesian Neural Networks](https://mlsanity.com/paper/2402.03495/) (2024)
- [MILM: Large Language Models for Multimodal Irregular Time Series with Informative Sampling](https://mlsanity.com/paper/2605.13711/) (2026)
- [Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time](https://mlsanity.com/paper/2507.07271/) (2025)
- [Conservative Continuous-Time Treatment Optimization](https://mlsanity.com/paper/2603.16789/) (2026)
- [Time After Time: Deep-Q Effect Estimation for Interventions on When and What to do](https://mlsanity.com/paper/2503.15890/) (2025)
- [Counterfactual Forecasting for Panel Data](https://mlsanity.com/paper/2511.06189/) (2025)
- [From Static Risk to Dynamic Trajectories: Toward World-Model-Inspired Clinical Prediction](https://mlsanity.com/paper/2605.16927/) (2026)
- [Efficient Learning of Survival Analysis Models Under Outcome-Dependent Truncation and Censoring](https://mlsanity.com/paper/2610.12538/) (2026)

## Abstract (arXiv)

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.