Combining adaptive designs with control of the false discovery rate--a generalized definition for a global p-value

When combining adaptive designs with control of the False Discovery Rate one has to keep in mind that the most frequently used procedure for controlling the False Discovery Rate--the explorative Simes procedure--is a stepwise multiple testing procedure. At the interim analysis of an adaptive design it is however not yet known what the boundaries for rejection of hypotheses in the final analysis will be as these boundaries depend on the size of the final p-values. Therefore classical adaptive designs with a predefined stopping criterion for early rejection of hypotheses are not well suited. We propose a generalized definition of a global p-value for a two-stage adaptive design permitting a flexible decision for stopping at the interim analysis. By means of a simulation study in the field of genetic epidemiology we illustrate how applying such a two-stage design can reduce costs.