Multistage and mixture parallel gatekeeping procedures in clinical trials

Gatekeeping procedures have been developed to solve multiplicity problems arising in clinical trials with hierarchical objectives where the null hypotheses that address these objectives are grouped into ordered families. A general method for constructing multistage parallel gatekeeping procedures was proposed by Dmitrienko et al. (2008). The objective of this paper is to study two related classes of parallel gatekeeping procedures. Restricting to two-family hypothesis testing problems, we first use the mixture method developed in Dmitrienko and Tamhane (2011) to define a class of parallel gatekeeping procedures derived using the closure principle that can be more powerful than multistage gatekeeping procedures. Second, we show that power of multistage gatekeeping procedures can also be improved by using -exhaustive tests for the component procedures. Extensions of these results for multiple families are stated. Illustrative examples from clinical trials are given.