Adaptive group sequential designs with control of the population-wise error rate

The aim of individualized medicine is to provide each patient with a therapy tailored to his or her genetic profile. This is particularly important in diseases where the efficacy of a treatment depends on various individual-specific factors. Especially in rarer diseases or in highly stratified patient populations, proof of superiority of a new therapy may now prove difficult to achieve, as the necessary test power cannot be reached due to too small sample sizes. A good example is the field of pediatric oncology, where individualization of therapies plays an increasingly important role, but the underlying study populations are so limited that proof of superiority of therapy and stratification strategies is hardly possible under classical statistical principles. The aim of this work is to combine the flexibility of adaptive designs for clinical trials with the new requirements and dynamic development in individualized medicine. For this purpose, situations are considered in which the superiority of potentially different treatments is to be investigated in different, not necessarily disjoint subgroups of an overall population. In particular, these subgroups may thus be overlapping or nested. Since a multiplicity problem arises from testing several hypotheses on partly the same data material, but the family-wise error rate (FWER) often used here is too conservative, a new, less conservative multiple type I error criterion tailored to the particular subgroup structures is used in this work. This error criterion, termed the population-wise error rate (PWER), will be used as the basis for developing new multiple, sequential, and adaptive trial designs for testing individualized therapies. Specifically, single-stage test designs with PWER control were first developed and compared with corresponding FWER-controlling designs using various special cases. Next, group sequential designs controlling for PWER were constructed, here adapting various methods from the classical theory of group sequential designs. Last, adaptive designs with PWER-control were conceived and tested in numerical examples and simulations.