One fundamental problem in many applications is to estimate treatment-response trajectories given multidimensional treatment variables.
However, in reality, the estimation suffers severely from measurement error both in treatment timing and covariates, for example when the treatment data are self-reported by users.
We introduce a novel data-driven method to tackle this challenging problem, which models personalized treatment-response trajectories as a sum of a parametric response function, based on restored true treatment timing and covariates and sharing information across individuals under a hierarchical structure, and a counterfactual trend fitted by a sparse Gaussian Process.
In a real-life dataset where the impact of diet on continuous blood glucose is estimated, our model achieves a superior performance in estimation accuracy and prediction
