Gatekeeping strategies for clinical trials that do not require all primary effects to be significant

In this paper we describe methods for addressing multiplicity issues arising in the analysis of clinical trials with multiple endpoints and/or multiple dose levels. Efficient 'gatekeeping strategies' for multiplicity problems of this kind are developed. One family of hypotheses (comprising the primary objectives) is treated as a 'gatekeeper', and the other family or families (comprising secondary and tertiary objectives) are tested only if one or more gatekeeper hypotheses have been rejected. We discuss methods for constructing gatekeeping testing procedures using weighted Bonferroni tests, weighted Simes tests, and weighted resampling-based tests, all within the closed testing framework. The new strategies are illustrated using an example from a clinical trial with co-primary endpoints, and using an example from a dose-finding study with multiple endpoints. Power comparisons with competing methods show the gatekeeping methods are more powerful when the primary objective of the trial must be met.