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Abstract

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. When planning and analysing trials in this context, the correlation between surrogate endpoint and overall survival has to be taken into account. For the binary surrogate endpoint response, this relation can be modeled by means of the responder stratified exponential survival (RSES) model that was proposed elsewhere. The RSES model has three parameters: response probability, the logarithmic hazard of responders, and the logarithmic hazard of non-responders. The aim of this dissertation is to investigate the RSES model and to develop and evaluate methods for parameter estimation, hypothesis testing, and sample size calculation within the RSES model.

Estimators for the parameters are derived by the Maximum Likelihood method. Approximate confidence intervals for the model parameters are constructed and are found to have very satisfying coverage probability. A hypothesis test for the difference of model parameters between two treatment groups, called approximate RSES test, is constructed. When it is compared with the logrank test and the stratified logrank test regarding power, results vary based on the scenario. When survival benefit in one group is mainly due to response benefit, the approximate RSES test is considerably more powerful than the other tests. Approximate confidence intervals for the parameter differences are derived and show very satisfying coverage probability. Where possible, exact formulas for the calculation of coverage probabilities and rejection probabilities are given. An approximate and an exact sample size calculation method for the approximate RSES test are developed. The sample size calculation method is applied to a clinical example and the power of the approximate RSES test, the logrank test, and the stratified logrank test is compared within this example. The approximate RSES test turns out to be considerably more powerful.

It is discussed that the assumptions of the RSES model are relatively strict. Also, the results of the approximate RSES test have to be interpreted carefully, since a rejection of the null hypothesis does not necessarily translate to a uniform survival benefit. In practice, more flexible methods may be desired for estimating and testing survival distributions conditional on a binary response variable. Testing could be based on an effect measure that indicates survival benefit, like the Restricted Mean Survival Time (RMST). Combining a non-parametric survival estimation method that considers the response status with a meaningful effect measure like RMST could be a flexible way to analyse studies in the described context. When planning such a study with concrete assumptions, the RSES model can be applied. Also, it is pointed out that the approach presented in this thesis is applicable to other parametric survival models. Further research is needed to develop distribution estimators and a test of survival difference with more flexible distribution assumptions, as well as extending the methods to the situation of an early interim decision based on response rates.

It is concluded that this thesis contains a comprehensive investigation of the RSES model. It provides point estimators and confidence interval estimators for the RSES model which are necessary for applying the RSES model in practice. Furthermore, the general approaches used in this dissertation regarding the derivation of estimators, confidence intervals, hypothesis tests, sample size calculation, and exact calculations can be applied to further models describing the relationship between a surrogate endpoint and a survival endpoint.