Bonferroni-based gatekeeping procedure with retesting option
  In complex clinical trials, multiple research objectives are often grouped into sets of objectives based on their inherent hierarchical relationships. Consequently, the hypotheses formulated to address these objectives are grouped into ordered families of hypotheses and thus to be tested in a pre-defined sequence. In this paper, we introduce a novel Bonferroni based multiple testing procedure for testing hierarchically ordered families of hypotheses. The proposed procedure allows the families to be sequentially tested more than once with updated local critical values. It is proved to control the global familywise error rate strongly under arbitrary dependence. Implementation of the procedure is illustrated using two examples. Finally, the procedure is extended to testing multiple families of hypotheses with a complex two-layer hierarchical structure. 
Zhiying Qiu, Wenge Guo, Sanat Sarkar
stat.ME stat.AP