Abstract
Hierarchically ordered objectives often occur in clinical trials. Many multiple testing adjustment methods have been proposed to control family-wise error rates while taking into account the logical relations among the null hypotheses. However, most of them disregard the correlation among the endpoints within the same family and assume the hypotheses within each family are equally weighted. This paper proposes a gatekeeping procedure based on Xie's weighted multiple testing correction for correlated tests (Xie, StatMed 31(4): 341-352, 2012). Simulations have shown that it has power advantages compared to those non-parametric methods (which do not depend on the joint distribution of the endpoints). An example is given to illustrate the proposed method and show how it can be used in complex clinical trials.