  The primary endpoint in oncology is usually overall survival, where
differences between therapies may only be observable after many years. To avoid
withholding of a promising therapy, preliminary approval based on a surrogate
endpoint is possible. The approval can be confirmed later by assessing overall
survival within the same study. In these trials, the correlation between
surrogate endpoint and overall survival has to be taken into account for sample
size calculation and analysis. For a binary surrogate endpoint, this relation
can be modeled by means of the responder stratified exponential survival (RSES)
model proposed by Xia, Cui, and Yang (2014). We derive properties of the model
and confidence intervals based on Maximum Likelihood estimators. Furthermore,
we present an approximate and an exact test for survival difference. Type I
error rate, power, and required sample size for both newly developed tests are
determined exactly. These characteristics are compared to those of the logrank
test. We show that the exact test performs best. The power of the logrank test
is considerably lower in some situations. We conclude that the logrank test
should not be used within the RSES model. The proposed method for sample size
calculation works well. The interpretability of our proposed methods is
discussed.
