Keywords: Mixture gatekeeping procedures
An important class of multiple testing procedures, known as gatekeeping procedures, was derived using the mixture method that enables clinical trial sponsors to set up efficient multiplicity adjustments that account for clinically relevant logical relationships among the hypotheses of interest. The mixture method, can be applied to develop efficient gatekeeping procedures, including procedures derived from semiparametric tests such as the Hochberg or Hommel tests or parametric tests such as the Dunnett-based tests. The original mixture method supports a very broad set of logical relationships and it could be improved if a specific family of logical restrictions was considered. This family, known as the family of serial logical restrictions, includes multiplicity problems where hypotheses of interest are organized into several sequences. For serial logical restrictions, Dmitrienko et al. proposed a modified version of the mixture method and proved that gatekeeping procedures derived using this method are more powerful than procedures based on the standard mixture method. In this presentation, we discuss further enhancement of the mixture method that results in a uniform power advantage over the modified method if serial logical restrictions satisfy transitivity condition.