# Errors-in-variables Modeling of Personalized Treatment-Response Trajectories

arXiv: https://arxiv.org/abs/1906.03989 · HTML: https://mlsanity.com/paper/1906.03989/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

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

- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions](https://mlsanity.com/paper/2306.09656/) (2023)
- [Nonparametric modeling of the composite effect of multiple nutrients on blood glucose dynamics](https://mlsanity.com/paper/2311.03129/) (2023)
- [Personalized Treatment Outcome Prediction from Scarce Data via Dual-Channel Knowledge Distillation and Adaptive Fusion](https://mlsanity.com/paper/2510.26444/) (2025)

## Abstract (arXiv)

Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model considers measurement error not only in treatment covariates, but also in treatment times, a problem which arises in practice for example when treatment information is based on self-reporting. In a challenging and timely problem of estimating the impact of diet on continuous blood glucose measurements, our model leads to significant improvements in estimation accuracy and prediction.