Extension of adaptive alpha allocation methods for strong control of the family-wise error rate.

With recent advancements in clinical trial design and the availability of rigorous statistical methods that provide strong control of the family-wise type I error rate for multiple testing of hypotheses, it is now common for sponsors to design clinical trials with prospectively specified multiple testing of hypotheses of both primary and secondary endpoints and with the intent to obtain labeling claims for secondary endpoints. One of these recent advancements in multiple testing techniques is the adaptive alpha allocation approach (4A) proposed by Li and Mehrotra (Statistics in Medicine 2008; 27:5377-5391), which groups the hypotheses into two families on the basis of perceived trial power and allows the significance level for the second family to be set adaptively on the basis of the largest observed p-value in the first family. We introduce a class of flexible functions that generalize the 4A procedure and can lead to relatively more powerful test statistics. In the case when the test statistics are correlated, we introduce well-defined functions to calculate the significance level for the second family. The numerical computation for our methods is straightforward, making application in practice easy.