General theory of mixture procedures for gatekeeping

The paper introduces a general approach to constructing mixture-based gatekeeping procedures in multiplicity problems with two or more families of hypotheses. Mixture procedures serve as extensions of and overcome limitations of some previous gatekeeping approaches such as parallel gatekeeping and tree-structured gatekeeping. This paper offers a general theory of mixture procedures constructed from nonparametric (p-value based) to parametric (normal theory based) procedures and studies their properties. It is also shown that the mixture procedure for parallel gatekeeping is equivalent to the multistage gatekeeping procedure. A clinical trial example is used to illustrate the mixture approach and the implementation of mixture procedures.