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