  In applications of clinical trials, tested hypotheses are often grouped as
multiple hierarchically ordered families. To test such structured hypotheses,
various gatekeeping strategies have been developed in the literature, such as
series gatekeeping, parallel gatekeeping, tree-structured gatekeeping
strategies, etc. However, these gatekeeping strategies are often either
non-intuitive or less flexible when addressing increasingly complex logical
relationships among families of hypotheses. In order to overcome the issue, in
this paper, we develop a new family-based graphical approach, which can easily
derive and visualize different gatekeeping strategies. In the proposed
approach, a directed and weighted graph is used to represent the generated
gatekeeping strategy where each node corresponds to a family of hypotheses and
two simple updating rules are used for updating the critical value of each
family and the transition coefficient between any two families. Theoretically,
we show that the proposed graphical approach strongly controls the overall
familywise error rate at a pre-specified level. Through some case studies and a
real clinical example, we demonstrate simplicity and flexibility of the
proposed approach.
