In this paper, for time-to-event data, we propose a new statistical framework for casual inference in evaluating clinical utility of predictive biomarkers and in selecting an optimal treatment for a particular patient. This new casual framework is based on a new concept, called Biomarker Adjusted Treatment Effect (BATE) curve. The BATE curve can be used for assessing clinical utility of a predictive biomarker, for designing a subsequent confirmation trial, and for guiding clinical practice. We then propose semi-parametric methods for estimating the BATE curves of biomarkers and establish asymptotic results of the proposed estimators for the BATE curves. We also conduct extensive simulation studies to evaluate finite-sample properties of the proposed estimation methods. Finally, we illustrate the application of the proposed method in a real-world data set.