For time-to-event data in a randomized clinical trial, we discuss two new methods for selecting an optimal treatment for a patient based on the Covariate-Specific Treatment Effect (CTE) Curve, which is used to represent the clinical utility of a predictive biomarker. To select an optimal treatment for a patient with a specific biomarker value, we propose pointwise confidence intervals for each CTE curve and the difference between CTE curves of two treatments. Furthermore, to select an optimal treatment for a future biomarker-defined sub- population of patients, we propose confidence bands for each CTE curv and the difference between each pair of CTE curve over a fixed interval of biomarker values. We constructed the confidence bands, based on a resampling technique. We also conducted simulation studies to evaluate finite-sample properties of the proposed estimation methods. Finally, we illustrated the application of the proposed method in a real-world data set. This is a joint work with Dr. Yunbei Ma.