A multiple comparison procedure for hypotheses with gatekeeping structure

We develop gatekeeping procedures that focus on comparing multiple treatments with a control when there are multiple endpoints. Our procedures utilize estimated correlations among individual test statistics without parametric assumptions. We make comparisons with other gatekeeping procedures with respect to properties of the trade-off in statistical power between families of hypotheses. We introduce a reward function to facilitate these comparisons. We illustrate our methods by simulation and an analysis of data from a randomized, multi-armed clinical trial.