# Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time

arXiv: https://arxiv.org/abs/2507.07271 · HTML: https://mlsanity.com/paper/2507.07271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Questioning the AI: Informing Design Practices for Explainable AI User Experiences](https://mlsanity.com/paper/2001.02478/) (2020)
- [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)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference](https://mlsanity.com/paper/2403.10766/) (2024)
- [Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing](https://mlsanity.com/paper/2401.15447/) (2024)
- [No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs](https://mlsanity.com/paper/2501.18563/) (2025)

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

- [Attention-Based Estimation of the Individual Treatment Benefit Probability under Dose Variation](https://mlsanity.com/paper/2606.13821/) (2026)

## Abstract (arXiv)

The Average Treatment Effect (ATE) is a foundational metric in causal inference, widely used to assess intervention efficacy in randomized controlled trials (RCTs). However, in many applications -- particularly in healthcare -- this static summary fails to capture the nuanced dynamics of treatment effects that vary with both dose and time. We propose a framework for modelling treatment effect trajectories as smooth surfaces over dose and time, enabling the extraction of clinically actionable insights such as onset time, peak effect, and duration of benefit. To ensure interpretability, robustness, and verifiability -- key requirements in high-stakes domains -- we adapt SemanticODE, a recent framework for interpretable trajectory modelling, to the causal setting where treatment effects are never directly observed. Our approach decouples the estimation of trajectory shape from the specification of clinically relevant properties (e.g., maxima, inflection points), supporting domain-informed priors, post-hoc editing, and transparent analysis. We show that our method yields accurate, interpretable, and editable models of treatment dynamics, facilitating both rigorous causal analysis and practical decision-making.