Flexible regression methods for estimating optimal individualized treatment regimes with scalar and functional covariates

In personalized medicine study, how to estimate the optimal individualized treatment regime based on available individual information is a fundamental problem. In recent years, functional data analysis has appeared extensively in medical research, while the optimal individualized treatment regime based on the combination of scalar covariates and functional covariates have rarely been studied and the only few studies are mostly conducted in the context of randomized trials. In this article, we propose a flexible regression-based approach in which the outcome variable is real-valued and the covariates contain multiple scalar covariates and a functional covariate. Our approach is applicable to both randomized trials and observational studies, and the convergence rates of the proposed optimal individualized treatment regime estimators are presented for both situations. Sufficient simulation studies and a real data analysis are conducted to justified the validity of our proposed method.