Weighted multiple testing correction for correlated binary endpoints

Multiple binary endpoints often occur in clinical trials and are usually correlated. Many multiple testing adjustment methods have been proposed to control familywise type I error rates. However, most of them disregard the correlation among the endpoints, for example, the commonly used Bonferroni correction, Bonferroni fixed-sequence (BFS) procedure, and its extension, the alpha-exhaustive fallback (AEF). Extending BFS by taking into account correlations among endpoints, Huque and Alosh proposed a flexible fixed-sequence (FFS) testing method, but this FFS method faces computational difficulty when there are four or more endpoints and the power of the first hypothesis does not depend on the correlations among endpoints. In dealing with these issues, Xie proposed a weighted multiple testing correction (WMTC) for correlated continuous endpoints and showed that the proposed method can easily handle hundreds of endpoints by using the R package and has higher power for testing the first hypothesis compared with the FFS and AEF methods. Since WMTC depends on the joint distribution of the endpoints, it is not clear whether WMTC still keeps those advantages when correlated binary endpoints are used. In this article, we evaluated the statistical power of WMTC method for correlated binary endpoints in comparison with the FFS, the AEF, the prospective alpha allocation scheme (PAAS), and the weighted Holm-Bonferroni methods. Furthermore the WMTC method and others are illustrated on a real dataset examining the circumstance of homicide in New York City.