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Cancer biomarker discoveries typically involve using patient specimens. In practice, there is often strong desire to preserve high quality biospecimens for studies that are most likely to yield useful information. Previously, we proposed a two-stage adaptive design for binary endpoints which terminates the biomarker study in a futility interim if the model performance is unsatisfactory. In this work, we extend the two-stage design framework to accommodate time-to-event endpoints. The first stage of the procedure involves testing whether the measure of discrimination for survival models (C-index) exceeds a prespecified threshold. We describe the computation of cross-validated C-index and evaluation of the statistical significance using resampling techniques. The second stage involves an independent model validation. Our simulation studies show that under the null hypothesis, the proposed design maintains Type I error at the nominal level and has high probabilities of terminating the study early. Under the alternative hypothesis, power of the design is a function of the true event proportion, the sample size, and the targeted improvement in the discriminant measure. We apply the method to design of a prognostic biomarker study in patients with triple-negative breast cancer. Some practical aspects of the proposed method are discussed. [ABSTRACT FROM AUTHOR]