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Abstract

The aim of this thesis is to develop a rigorous and consistent framework for all statistical aspects of planning and evaluating a single-arm phase II trial with binary endpoint ‘tumour response to treatment’. This includes guidance on the definition of a situation-specific objective criterion under planning uncertainty, methods to react flexibly to new trial-external evidence that might arise during the course of the trial, and inference after concluding the trial. To this end, a novel numerical approach is presented which makes the global optimisation of such design feasible in practice and improves existing approaches in terms of both flexibility and speed. The problem of incorporating a priori uncertainty about the true effect size in the planning process is discussed in detail taking a Bayesian perspective on quantifying uncertainty about the unknown response probability p is taken. Subsequently, the close interplay between point estimation, p values, confidence intervals, and the final test decision is illustrated and a framework is developed which allows consistent and efficient inference in binary single-arm two-stage designs. Finally, issues are addressed that may arise during the implementation of the proposed methods in practice. In particular, the problem of unplanned design modifications is revisited and the distinction between pre-specified adaptations within optimal two-stage designs and unplanned adaptations of ongoing designs discussed in more depth.