The union closure method for testing a fixed sequence of families of hypotheses

Statistical analyses often involve testing multiple hypotheses that are naturally grouped into a fixed sequence of families. An effective approach to control the familywise error rate is to prioritize the importance of prespecification in the testing order. A gatekeeping testing procedure examines the first family with no multiple adjustment and then examines the subsequent family depending on the decision made with respect to the previous one. In this paper, we describe the union closure method that can be used to design gatekeeping procedures. A bipolar disorder trial with three primary and two secondary outcomes is presented as an example. Power comparisons based on the bipolar disorder trial show that the proposed gatekeeping procedures under the union closure framework are more powerful than competing methods. Copyright 2011, Oxford University Press.