An efficient and flexible multiplicity adjustment for chi-square endpoints

This manuscript proposes a fast and efficient multiplicity adjustment that strictly controls the type I error for a family of high-dimensional chi-square distributed endpoints. The method is flexible and may be efficiently applied to chi-square distributed endpoints with any positive definite correlation structure. Controlling the family-wise error rate ensures that the results have a high standard of credulity due to the strict limitation of type I errors. Numerical results confirm that this procedure is effective at controlling familywise error, is far more powerful than utilizing a Bonferroni adjustment, is more computationally feasible in high-dimensional settings than existing methods, and, except for highly correlated data, performs similarly to less accessible simulation-based methods. Additionally, since this method controls the family-wise error rate, it provides protection against reproducibility issues. An application illustrates the use of the proposed multiplicity adjustment to a large scale testing example.