# Treatment-Response Models for Counterfactual Reasoning with Continuous-time, Continuous-valued Interventions

arXiv: https://arxiv.org/abs/1704.02038 · HTML: https://mlsanity.com/paper/1704.02038/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2017.

## Built on by (most cited first, 4 of 4)

- [Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Time](https://mlsanity.com/paper/2306.04255/) (2023)
- [Neural Pharmacodynamic State Space Modeling](https://mlsanity.com/paper/2102.11218/) (2021)
- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Multi-Task Dynamical Systems](https://mlsanity.com/paper/2210.04023/) (2022)

## Abstract (arXiv)

Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time. Further, the outcome variable may not be measured at a regular frequency. Our proposed solution represents the treatment response curves using linear time-invariant dynamical systems---this provides a flexible means for modeling response over time to highly variable dose curves. Moreover, for multivariate data, the proposed method: uncovers shared structure in treatment response and the baseline across multiple markers; and, flexibly models challenging correlation structure both across and within signals over time. For this, we build upon the framework of multiple-output Gaussian Processes. On simulated and a challenging clinical dataset, we show significant gains in accuracy over state-of-the-art models.