In Oncology research, using biomarkers to identify patients who can benefit from an investigational anti-cancer treatment is becoming increasingly important. For instance, the PD-L1 expression has been utilized broadly in cancer immunotherapy setting. For continuous biomarkers, to determine patient subgroups, it is often necessary to determine cut-off point(s) based on their relationship to clinical responses of interest (e.g., overall survival). To find cut-off values of a continuous biomarker, we consider the following approaches when the response of interest is a survival endpoint: time-dependent receiver operating characteristic (ROC) curve, hazard ratio comparing dichotomized groups, and maximum partial likelihood approach. We apply those methods to a historical Phase III study to locate optimal cut-off points for serum IL-8, with covariates information adjusted. In addition, we discuss some practical considerations in finding cut-off points.