Weighted multiple testing correction for correlated tests.

Virtually all clinical trials collect multiple endpoints that are usually correlated. Many methods have been proposed to control the family-wise type I error rate (FWER), but these methods often disregard the correlation among the endpoints, such as the commonly used Bonferroni correction, Holm procedure, Wiens' Bonferroni fixed-sequence (BFS) procedure and its extension, and the alpha-exhaustive fallback (AEF). Huque and Alosh proposed a flexible fixed-sequence (FFS) testing method, which extended the BFS method by taking into account correlations among endpoints. However, the FFS method faces a computational difficulty when there are four or more endpoints. Similar to the BFS procedure, the FFS method requires the prespecified testing sequence and the type I error rate used for first endpoint in the sequence (usually the most important endpoint) cannot be adjusted for the correlation among the endpoints or from the rejection of other null hypotheses for other endpoints. Thus, the power for this test is not maximized. In this paper, I present a weighted multiple testing correction for correlated tests. By using the package 'mvtnorm' in R, the proposed method can handle up to a thousand endpoints. Simulations show that the proposed method shares the advantage of the FFS and the AEF methods (having high power for the second or later hypotheses in the testing sequence) and has higher power for testing the first hypothesis than the FFS and the AEF methods. The proposed method has higher power for each individual hypothesis than the weighted Holm procedure, especially when the correlation between endpoints is high.