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

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 tre...

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Bibliographic Details
Published in:arXiv.org 2019-06
Main Authors: Zhang, Guangyi, Ashrafi, Reza, Juuti, Anne, Pietiläinen, Kirsi, Marttinen, Pekka
Format: Article
Language:English
Subjects:
Conditioning
Error analysis
Estimation
Gaussian process
Response functions
Trajectory analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422