Personalized treatment design in the context of functional confounding

One of the primary goals of individualized treatment rule (ITR) methodology is to identify optimal decision rules using clinical predictors. While functional data has become increasingly available in biomedical research, there has been limited work on incorporating functional data into ITR estimation, particularly in observational studies. In this paper, we propose a novel approach that integrates outcome-weighted learning (OWL) with reproducing kernel Hilbert space to determine optimal treatment regimes involving functional data. Furthermore, to address the issue of data piling, we employ the distance-weighted discrimination classifier instead of traditional support vector machines. We establish the theoretical consistency of the decision functional estimator with its risk bound. Extensive simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative dataset demonstrate the superior performance of our method compared to existing OWL approaches. The results highlight critical factors in Alzheimer's Disease progression and reveal limitations of the original OWL method in this context.