Estimation, testing and sample size calculation within the responder-stratified exponential survival model

The primary endpoint in phase III oncology trials 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 a binary surrogate endpoint, this relation can be modeled with the responder stratified exponential survival (RSES) model. We develop novel estimators, an approximate test, and a sample size calculation method in the context of the RSES model. We evaluate the performance of the derived methods and compare the approximate test to the logrank test and the stratified logrank test. In most cases, all derived methods perform very well if the model assumptions hold. However, for sample sizes under 100, the approximate test's Type I error rate exceeds the 5% level by up to 1.5%. Conversely, the approximate test is considerably more powerful than the logrank test or stratified logrank test, respectively, in situations where the survival benefit in the experimental group is mainly due to more responders. We apply the methods to a clinical trial example, with the approximate test again proving to be more powerful. Finally, we discuss the assumptions and limitations of the RSES model. Particularly, the approximate test does not control the Type I error rate if the assumption of exponentially distributed survival times is violated.