Selection of the Optimal Treatment with CATE Curve

In this paper, we proposed a statistical framework for optimal treatment selection for a subgroup of patients, using their biomarker values based on casual inference. This new method was based on a concept, called conditional average treatment effect (CATE) curve, and CATE curve's simultaneous confidence bands (SCBs), which could be used to represent the average treatment effect for a given value of the covariate (biomarker) and to select an optimal treatment for one particular patient. We then proposed B-splines methods for estimating the CATE curves and constructing simultaneous confidence bands for the CATE curves. We derived the asymptotic properties of the proposed methods. We also conducted extensive simulation studies to evaluate finite-sample properties of the proposed simultaneous confidence bands. Finally, we illustrated the application of the CATE curve and its simultaneous confidence bands in optimal treatment selection in a real-world data set.