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

## TL;DR

This paper introduces a novel data-driven method for estimating personalized treatment-response trajectories in the presence of measurement errors in covariates and treatment timing, improving accuracy in complex real-world scenarios.

## Contribution

The paper presents a new modeling approach that accounts for measurement errors in both covariates and treatment times, combining parametric response functions and sparse Gaussian processes.

## Key findings

- Significant improvements in estimation accuracy for blood glucose response.
- Effective handling of measurement errors in treatment timing and covariates.
- Enhanced prediction of treatment effects in personalized medicine.

## Abstract

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.

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Source: https://tomesphere.com/paper/1906.03989